Splitting and Merging in Microfluidics

{"cards":[{"_id":"38c8d10a72f07c8c8b000020","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":null,"content":"#Introduction [http://en.wikipedia.org/wiki/Microfluidics - @wikipedia]\nMicrofluidics is a multidisciplinary field intersecting engineering, physics, chemistry, nanotechnology and biotechnology, with practical applications to the design of systems in which small volumes of fluids will be handled. Microfluidics emerged in the beginning of the 1980s and is used in the development of inkjet printheads, DNA chips, lab-on-a-chip technology, micro-propulsion, and micro-thermal technologies. It deals with the behavior, precise control and manipulation of fluids that are geometrically constrained to a small, typically sub-millimeter, scale.\n"},{"_id":"38c8e4cd72f07c8c8b000021","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"38c8d10a72f07c8c8b000020","content":"##Microfluidic Basics [http://en.wikipedia.org/wiki/Microfluidics - @wikipedia]\nTypically fluids are moved, mixed, separated or otherwise processed. Numerous applications employ passive fluid control techniques like capillary forces. In some applications external actuation means are additionally used for a directed transport of the media. Examples are rotary drives applying centrifugal forces for the fluid transport on the passive chips. Active microfluidics refers to the defined manipulation of the working fluid by active (micro) components as micropumps or micro valves. Micro pumps supply fluids in a continuous manner or are used for dosing. Micro valves determine the flow direction or the mode of movement of pumped liquids. Often processes which are normally carried out in a lab are miniaturized on a single chip in order to enhance efficiency and mobility as well as reducing sample and reagent volumes.\nTypically, micro means one of the following features: small volumes (µL, nL, pL, fL), small size, low energy consumption and effects of the micro domain."},{"_id":"3a73c349616cbc410c000013","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":0.5,"parentId":"38c8e4cd72f07c8c8b000021","content":"###Microfluidic Droplet Manipulations [http://www.springer.com/cda/content/document/cda_downloaddocument/9781461432647-c1.pdf - @springer]\n\"Droplet microfluidics\" enables the manipulation of discrete fluid packets in the form of microdroplets that provide numerous benefits for conducting biological and chemical assays. Among these benefits are a large reduction in the volume of reagent required for assays, the size of sample required, and the size of the equipment itself. Such technology also enhances the speed of biological and chemical assays by reducing the volumes over which processes such as heating, diffusion, and convective mixing occur. Once the droplets are generated, carefully designed droplet operations allow for the multiplexing of a large number of droplets to enable large-scale complex biological and chemical assays. The four major unit operations in droplets are: droplet fusion, droplet fission, mixing in droplets, and droplet sorting. Combined, these operations allow for much complexity in executing chemical reactions and biological assays at the microscale."},{"_id":"3a6d9b7285d22cf72600000f","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":2,"parentId":null,"content":"#Categorization (Aggregation)\nA large number of methods available for handling droplets in microfluidic channel. In order to generate, move, merge, split, mix and sort droplets several design parameters need to be considered.\nThe most trivial categorization based on developing droplets in the meaning of the manipulation of the available number of droplets in a system what leads to merge and split categories. If possible, these categories are followed basically.\nA most manifest categorization divides the techniques into passive and active category. Passive techniques means no additional circuitry used for manipulation just the necessary input and output channels for a microfluidic device in order to set the flow of droplets. Therefore passive methods follow an easy and simple realization. In addition to passive methods active elements gives a wide variety of further control of flow. Active methods allow effective and more sophisticated control of parameters.\nMethods and techniques can overlap each other. Merging and splitting channels can be formed using the same geometry from different sides. Also there are active techniques that may applicable for both merging and splitting.\nThere is an opportunity to create other categories, e.g. the type of manipulation that is allowed to use electric or magnetic filed, laser beam or acoustic waves. "},{"_id":"3a6da83585d22cf726000010","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":3,"parentId":null,"content":"#Dependent and Independent parameters of the flow formation\nIn microfluidics there are a bunch of physical parameters that depend on different conditions. Microfuidics also employs some dimensionless numbers that makes properties independent of factual geometries."},{"_id":"3a77a188616cbc410c00004a","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a6da83585d22cf726000010","content":"##Theoretical approach [http://www.ncbi.nlm.nih.gov/pubmed/15269790 - 169]\nBreakup and coalescence transitions are the result of the complex interplay of viscous, inertial, capillary, Marangoni, electrostatic and van der Waals forces over a wide variety of spatial and timescales. Asymptotic (e.g. lubrication) theories describe the limiting behaviors (e.g. pinching or film-drainage rates) of the geometrical and field variables at the onset of these transitions based on simplified assumptions on geometry (e.g. one-dimensionality), fluid and flow conditions. Numerical methods are capable of describing transitions accurately and efficiently in simulations of a variety of flow geometries (2-D and 3-D) and conditions where interfaces deform significantly in principle without relying on simplifying assumptions. A weakness of numerical simulations is computational expense because the transition regions characterized by small length- (and time-) scales need to be resolved by the numerical discretization requiring a very large number of computational elements. Thus it is often practice to incorporate asymptotic theories in numerical simulations, limiting direct numerical solution to the larger scales. "},{"_id":"3a8f685654737fc265000044","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a77a188616cbc410c00004a","content":"###Theoretical and numerical investigations of droplet breakup and coalescence [http://www.ncbi.nlm.nih.gov/pubmed/15269790 - 169]\n\n####Drop breakup \nDroplet generation in flow-focusing design, and breakup in flow, are the result of the competition of viscous stresses associated with the imposed flow field, and capillary stresses due to surface tension between the two phases. In the flow-focusing design of water-in-oil emulsions (e.g. see refs. 9 and 16), the shearing comes from the relative magnitude of the co-flowing streams of oil and water. At a channel T-junction,18 droplets are sheared and extended as they travel through the junction and can be split. It is necessary to know under which conditions for the microphysical parameters and flow type breakup occurs and at what rates, or droplets are stable (non breaking), and the extent of droplet deformation. \nConsider a drop of size (e.g. undeformed diameter) D, in a matrix fluid of viscosity m undergoing flow with characteristic magnitude G of the local velocity gradient, and with surface tension s. Viscous stresses scale as mG, and extend a drop on a timescale22 (1 + l)/G, where l is the ratio of drop-to-matrix viscosities, taking equally into account the contributions to friction coming from the fluid viscosities. Surface tension s tends to relax a deformed drop back to spherical. From a dimensional analysis, the capillary relaxation velocity scales as s/m, thus the drop relaxation timescale is (1 + l) mD/s, and capillary stresses scale as s/D. The relevant dimensionless number is the capillary number Ca = mGD/s (assuming that inertia is negligible), the ratio of viscous-to-capillary stresses, or equivalently, the inverse ratio of the two corresponding timescales. When Ca = O(1), viscous stresses deform the droplet significantly and breakup may occur. The velocity gradient in a micro channel of hydraulic diameter ~ Di and flow rate Qo can be estimated as G ~ Qo/Di3 and, under conditions of Ca = O(1), this gives a simple relationship between generated droplet size and imposed flow rate: \nD ~ sDi3/mQo\nThus, the larger the flow rate, the smaller the droplet size. Using9 \n ~ 1023 N m21, Di = 40 mm, m ~ 30 3 1023 kg ms21 and Qo = 12 ml min21, formula (1) gives a droplet size of D ~ 10mm (and Re ~ 0.01) and is in agreement with the data in Fig. 4. These and similar scalings have been employed to generate monodispersed emulsions of controlled droplet sizes by Thorsen et al.,14 Anna et al.16 and by Tan et al.9 as illustrated in Figs. 4 and 5. Fig. 4 reveals that droplet sizes fall in the theoretical scaling (1) when D < Di, that is, droplets are small enough that the hydrodynamic forces exerted by the channel walls are not important and breakup fully relies on the straining of the imposed flow. When drops are large, wall effects are dominant over the stresses directly imposed by the flow, and the dependence of droplet sizes on flow rate is weaker. These considerations are corroborated by the trend observed in Fig. 5. Similar scalings for breakup criteria have also been successfully applied (Fig. 6) to the design of channel T-junction geometry and inlet and outlet flow rates.18 Interestingly, they found that the capillary number above which droplets passively break at a T-junction scales as\nCa ~ e0 (1/e02/3 2 1)\nwhere e0 ~ l0/w0, the ratio of length-to-width of the droplets in the mother channel are upstream of the junction. Downstream of the junction, split droplet volumes scale inversely with the lengths of the side arms.\nExperimental, theoretical and numerical studies of drop breakup in imposed flows have been reviewed by Rallison23, Stone24 and Guido and Greco25 (see also the review by Basaran26 for jets). Criteria for breakup were investigated experimentally (e.g. by Bentley and Leal27) and analytically (e.g. by Navot28 and Blawzdziewicz et al.29,30). The distribution of drop fragments resulting from breakup in shear flow was studied (e.g. see refs. 22 and 31). Numerical simulations have been developed (e.g. see refs. 22,32-34). Emulsification is typically promoted using surfactants that decrease surface tension on the droplet interfaces thus favouring drop and jet breakup (see refs. 35-42 and the review by Maldarelli and Huang43). Methods for producing controlled micro sized droplets were developed for shear flow,22,31,44-47 using co-flowing streams (see ref. 48 and the recent microfluidics literature listed above) and extrusion flow.49 Monodispersed emulsions of large numbers of droplets with controlled sizes were generated in flow using the tip-streaming phenomenon due to redistribution of surfactants to localized end caps on the drop interface.50,51 Cristini et al.22 reported a study on the deformation and breakup of drops in shear flow demonstrating that nearly bi-disperse emulsions of large numbers of microscopic droplets of controlled sizes and generation times can be achieved even without surfactants (Fig. 7). Interestingly, the two sizes alternate (as also found by Tan et al.9). The reason for this lies perhaps in the asymmetrical evolution of the drop interface near the pinch-off region into cones with different angles during the latest stages of pinch-off (Fig. 8, top), as described by the theories of Blawzdziewicz et al.52 and Lister and Stone.53 It was also found22 that the breakup times have a non-monotonic dependence on the capillary number, and have a (broad) minimum corresponding to moderately supercritical shear rates. This information can be used to optimize emulsification times. \nIt has been shown,52,53 that during pinch-off of a thin liquid thread under zero-Reynolds-number conditions (Fig. 8), the thinning rate becomes asymptotically constant in time. Thus pinch-off occurs in a finite time. As the thread thickness hmin decreases, viscous stresses mu/hmin (u = 2dhmin/dt is the thinning rate) balance the capillary pressure : s/hmin : mu/hmin ~ s/hmin. Thus the neck pinching velocity u ~ s/m and is (asymptotically) constant. This is illustrated in Fig. 8 (bottom).53 The axial curvature H'' of the thread (rescaled with hmin(t)) at the minimum hmin(t) is also found to be asymptotically constant as hmin ? 0, thus revealing self-similarity of the shape in the transition region. These scalings for the capillary-driven pinch-off can be used when estimating drop formation times in a micro channel. In a flow-focusing design9,16 for water-in-oil emulsions, the time for accumulation of enough water for one droplet is given by D3/Qw (the volume of the droplet divided by the water flow rate). Capillary driven pinch-off time can be estimated as (1 + l) mD/s. Droplet generation time will be determined by the larger of these two times. For droplets that are \nsmaller than the channel width (D < Di), the droplet size D is given \nby the scaling (1), and thus the ratio of the two times is O(D/Di)3 \nindicating that droplet generation time is dominated by the capillary \ntime for small droplets. \n\n####Drop coalescence \nCoalescence rates and efficiencies between droplets depend on the \nlocal dynamics of the fluid drainage in the near contact region between the two approaching fluid interfaces. Asymptotic theories and numerical simulations of film drainage between coalescing fluid-fluid interfaces,54-63 including surfactant effects,64-70 provide useful information such as the rates of drop-drop approach. \nTwo drops approaching each other trap a thin film of the continuous phase between their interfaces. At small enough gaps the hydrodynamic forces overcome capillarity and the drop interfaces deform and often acquire a dimpled shape that traps more fluid thus opposing coalescence.55,62,69 In flow-driven drop interactions, coalescence occurs for capillary numbers smaller than a critical value such that the drop interaction time is larger than the drainage time for the fluid trapped in the gap.57 For sub-critical capillary numbers, at sub-micron separations, van der Waals forces become dominant leading to rapid coalescence (film rupture). Surfactants (through Marangoni stresses, surface viscosity, Gibbs elasticity, surface and/or bulk diffusivity and intermolecular forces) can have a significant effect and stabilize emulsions by increasing deformation and causing surface tension gradients (Marangoni stresses, see the book by Edwards et al.71) that resist radial flow in the gap and interface-interface approach thus preventing coalescence.68-70,72,73 Chesters and Bazhlekov69 studied numerically the axi-symmetric film drainage and rupture between two drops approaching each other under a constant force in the presence of an insoluble surfactant. For drops in the millimeter size range the influence of surfactant diffusion is typically negligible. Drainage is virtually unaffected by the presence of surfactants down to a film thickness at which high Marangoni stresses and a transition to immobile interfaces set in, leading to drainage orders of a slower magnitude. These phenomena are illustrated in Fig. 969 for the minimum film thickness hmin. Analytical approximations for the drainage time were derived.69 For smaller drops the influence of diffusion alleviates gradients in surfactant concentration reducing the effect of surfactants. Yeo et al.70 (see also ref. 73) using theory and numerical simulations focused on constant approach velocity collisions and highlighted the differences in dynamics that arise. They showed that adding even a slight amount of insoluble surfactant results in the immobilization of the interface. Three regimes of drainage and possible rupture exist depending on the relative magnitudes of the drop approach velocity and the van der Waals interaction force: nose rupture, rim rupture, and film immobilization and flattening. The possibility of forming secondary droplets by encapsulating the continuous phase film into the coalesced drop at rupture was also quantified. \nRecent experimental74,75 and numerical investigations76 of flow driven drop-drop coalescence with surfactants revealed that there is a non-monotonic dependence of the critical capillary number for coalescence on the surfactant coverage (Fig. 10). The critical capillary number has a minimum for intermediate coverage due to Marangoni stresses, and increases at high coverage (close to the maximum packing of molecules on the interface) perhaps as a consequence of interface immobilization and reduced deformation. These findings demonstrate that while much progress has been made in the theoretical understanding of film drainage, there are still open questions. "},{"_id":"3a8f938554737fc265000046","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":2,"parentId":"3a6da83585d22cf726000010","content":"##Dimensionless Numbers in Microfluidics [http://link.aps.org/doi/10.1103/RevModPhys.77.977 - @x21]\nA wide variety of physical phenomena occur in microfluidic devices, the importance of which must be judged against competing phenomena. Dimensionless numbers expressing the ratio of these phenomena give a sense for where a system sits in fluidic parameter space. These are the Reynolds number Re, relating inertial forces to viscous forces; the Péclet number Pe, relating convection to diffusion; the capillary number Ca, relating viscous forces to surface tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, expressing elastic effects; the Grashof and Rayleigh numbers Gr and Ra, relating transport mechanisms in buoyancy-driven flows; and the Knudsen number Kn, relating microscopic to macroscopic length scales. "},{"_id":"3a99c2e214ad04a285000049","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":0.5,"parentId":"3a8f938554737fc265000046","content":"###Dimensionless Numbers [http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3127135&tool=pmcentrez&rendertype=abstract - @x13]\nIn engineering, the behavior of liquids is often described in terms of dimensionless numbers which compare the importance of different physical properties. The Bond number Bo = ΔρgL2/σ, with Δρ the difference in mass density between the two fluids, g the gravity acceleration, L a characteristic length scale, and σ the interfacial tension, compares gravitational and surface forces [15]. In microfluidic applications, generally Bo << 1, this means that gravity effects can be ignored. The Reynolds number Re = ρνL/μ, where ρ is the mass density, μ the dynamic viscosity and ν the mean velocity of the fluid, compares inertial and viscous forces. Generally, in microfluidics Re < 1 [16]. A third quantity is the Weber number, which compares inertial forces to surface forces: We = ρν2L/σ. Also We < 1 in most applications at the microscale. From the definitions and typical magnitudes of Re and We, it follows that inertia generally becomes unimportant when the flow geometry is downscaled to dimensions in the micron range [10]. Exceptions include flows at very high speeds as they sometimes occur in flow focusing and co-flow devices [17], and the moment of the breakup of droplets. Otherwise the dominant forces at the microscale are interfacial forces and viscous forces. \nThe relative strength of these two is represented by the (dimensionless) Capillary number Ca, expressed by Ca = μν/σ. Here μ is generally the viscosity of the most viscous fluid in the two-phase system, ν is the velocity of that phase, and σ is the interfacial tension as before. Inherently, the interfacial tension tends to reduce the interfacial area, which is crucial in the formation of droplets and also for their subsequent stability. In many flow situations, viscous forces act to extend and stretch the interface [18]. At low Ca (<1) the interfacial tension dominates, and spherical droplets are found. In contrast, at high Ca (>>1) the viscous forces play an important role, leading to deformation of the droplets and sometimes to asymmetric shapes. In co-flowing liquid streams, high Ca numbers can induce a transition between different drop generation scenarios [19,20]. In some cases of high Ca, a completely different flow architecture, named stratified flow, can occur [21,22]."},{"_id":"3a981c9a14ad04a285000046","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a8f938554737fc265000046","content":"###The Reynolds number: Inertial irrelevance\nOf all dimensionless numbers, the Reynolds number Re is the one most often mentioned in connection with microfluidics. Ironically, it may also be the least interesting number for microfluidics: after all, almost without exception, microfluidic devices employ fluids with Reynolds numbers that are small enough for inertial effects to be irrelevant. Nevertheless, because low Reynolds number flows contradict day-to-day human experience with fluids, one must unlearn a lifetime’s worth of high-Re intuition in order to effectively think about microfluidics. Purcell’s description of this counterintuitive world, Life at low Reynolds number Purcell, 1977 provides an excellent overview, and Brody et al. 1996 explore its biotechnological analog. More detailed accounts are given in conference proceedings Batchelor, 1977; Hinch, 1988 and textbooks Happel and Brenner, 1983; Kim and Karilla, 1991; Leal, 1992; Pozrikidis, 1992; Deen, 1998.\nFor the physicist more familiar with Newton’s laws than with the convective derivative u• u of the Navier-Stokes equations, Fig. 3 depicts two simple illustrations. The first involves a fluid that flows with velocity U0 through a microchannel of width w that makes a sudden right turn. During the turn time 0w/U0, a fluid element rounding the corner loses momentum density\nU0 by exerting an inertial centrifugal force density fi U0/0=U20/w. The other involves a fluid flowing in a channel that contracts over a length l. By mass conservation, the velocity increases as uU01+z/l, causing a fluid element to gain momentum at a rate\nfi du = U0du U20 \nThe force exerted on the rest of the fluid is equal and opposite to the force required to accelerate each fluid element. Thus the force on the fluid due to a curved streamline points outwards centrifugally, and the inertial force in an expansion or contraction points towards the wide end of the channel, regardless of the flow direction. An oscillatory flow through an asymmetric channel can drive a rectified, steady fluid motion which forms the basis for valveless diffuser pumps Stemme and Stemme, 1993; Olsson et al., 1999.\nIn both cases, the magnitude of inertial and viscous force densities must be compared. Viscous force densities result from gradients in viscous stress, and thus scale as fvU0/L20, where L0 is a typical length scale. The ratio of these two force densities,\nfi U0L0\nis known as the Reynolds number.\nReynolds numbers for common microfluidic devices can be estimated as follows. With water as the typical working fluid, typical velocities of 1 m/s–1 cm/s, and typical channel radii of 1–100 m, the Reynolds numbers range between and . These low values of Re affirm that viscous forces typically overwhelm inertial forces, and the resulting flows are linear. The loss of nonlinearity at low Re led to the demise of the research effort devoted to miniaturized fluidic computation, whose fundamental elements relied upon inertial effects and thus could not scale down like their solidstate electronic competition Humphrey and Tarumoto, 1965; Foster and Parker, 1970; Joyce, 1983.\nWhen Re is very small, the nonlinear terms in Eq. 1 disappear, resulting in linear and predictable Stokes flow Eq. 2. As Re increases, the first features of inertia become apparent. For example, in flow through a circular channel that is slightly curved with radius of curvature R much larger than the channel radius w, centrifugal forces on fluid elements drive a secondary flow. The no-slip boundary condition and inhomogeneous flow profile, uU01−r/w2, cause inhomogeneous centrifugal forcing, fiU201−r/w22/R, and give the secondary “Dean flow” UDRew/RU0 shown in Fig. 4 Dean, 1927, 1928; McConalogue and Srivastava, 1968; Leal, 1992. Secondary flow in twisted pipes have served as a model system for mixing studies Jones et al., 1989; Sharp et al., 1991; Jones and Young, 1994, and have recently been applied to create a passive, threedimensional “serpentine” micromixer Liu et al., 2000; Rush et al., 2002, albeit with rectangular channels and appreciable Re. As Re gets still higher, the nonlinear inertial term destabilizes the flow, resulting in unpredictable, irregular turbulent flow. The standard example for the transition to turbulence involves flow through a straight circular pipe, where the transition occurs for Re between 2000 and 3000. Such Reynolds numbers are significantly higher than those encountered in microfluidic devices, and microfluidic flows generally fall safely within the laminar flow regime.\nThus far we have focused on steady inertial forcing due to the convective derivative u• u, which is almost always unimportant for microfluidic flows because its time dependence arises from U0. The linear unsteady term u/t, on the other hand, sets the inertial time scale i required to establish steady flows. This time scale can be estimated by balancing the unsteady inertial force density U0/i with the viscous force density U0/L20, giving\ni L20 \nThe inertial time scale can be interpreted as the time required for vorticity to diffuse a distance L0, with diffusivity =/. This time scale is typically small, and pressure-driven flow requires i10 ms to reach steady state in rigid 100-m channels. However, inertial effects from rapidly oscillating flows can give rise to the steady streaming flow discussed in Sec. III.B.\nInertia rarely plays a significant role in microfluidic systems, and as systems are made ever smaller, it becomes even less relevant. Without the inertial nonlinearity, straightforward microfluidic systems have regular, deterministic flow. There do exist, however, many physical processes exploited in microfluidics—capillary effects at free surfaces, viscoelasticity in polymer solutions, and electrokinetic effects, to name a few—whose nonlinearities may even increase as device dimensions diminish, and which give rise to a rich variety of microfluidic phenomena. The remainder of this review explores this world."},{"_id":"3a9824a014ad04a285000047","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":2,"parentId":"3a8f938554737fc265000046","content":"###The Péclet number and the problem of mixing\nIn the everyday high-Re world, random eddies continuously churn the fluids in which we live—and in the process, stretch and fold fluid elements chaotically. As a result of this so-called turbulent mixing, gradients are significantly enhanced and time scales for mixing are dramatically reduced. In fact, without turbulent mixing or thermal convection, it would take about a year to smell your feet after taking off your shoes! The laminar fluid flows that naturally arise in the low-Re world of microfluidics, however, force mixing to occur by diffusion alone, which can result in unacceptably long mixing times of order minutes or more.\nPurely diffusive mixing can be desirable or not, depending on the application. Microfluidic chemical reactors require different solutions to be brought together and mixed rapidly, allowing the dynamics of the reactions to be probed, rather than the diffusive dynamics of the molecules themselves. The opposite problem is faced, however, in sorting and analyzing the products of those same reactions: the faster the mixing, the harder the separation. Controlling dispersion in microfluidic devices, then, is often of paramount importance.\nFor example, consider a T junction in which two fluids are injected to flow alongside each other, as in Fig. 5a. How far down the channel must the fluids flow before the channel is homogenized? A simple estimate requires the particles or molecules to diffuse across the entire channel, giving a time Dw2/D, where w is the width of the channel. During this time, the stripe will have moved a distance ZU0w2/D down the channel, so that the number of channel widths required for complete mixing would be of order\n\tZ\tU0w\nThe dimensionless number on the right is known as the Péclet number Pe, which expresses the relative importance of convection to diffusion. In this example, the number of channel widths required for full mixing varies linearly with Pe. Using the diffusivities in Table III, we see that even a small protein flowing with the fluid through a 100-m channel at 100 m/s requires Pe ~250 channel widths approximately 2.5 cm and 4 min to completely mix."},{"_id":"3a982b8214ad04a285000048","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":3,"parentId":"3a8f938554737fc265000046","content":"###The capillary number: Free-surface deformations\nThus far, we have assumed that fluids are miscible: parallel streams were assumed to flow alongside each other, and tracers diffused freely from one stream to the other. Between immiscible fluids, however, a surface tension affects the dynamics of the free surface. For example, Fig. 14 Anna et al., 2003 shows a thin central stream of water breaking into drops due to the Rayleigh-Plateau instability Rayleigh, 1879; Chandrasekhar, 1981; de Gennes, Brouchard-Wyart, and Quere, 2004. Clearly, surface tension can play an important role in microfluidic flows when immiscible free surfaces are present."},{"_id":"3a6db57085d22cf726000011","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":4,"parentId":null,"content":"#Review of Manipulation Techniques\nThere are several passive and active techniques to manipulate droplets.\nSplit and merge design can both handle the combination of active techniques enhanced with active methods."},{"_id":"3a7611da616cbc410c000046","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a6db57085d22cf726000011","content":"##Combining and Splitting Reactions [http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1766322&tool=pmcentrez&rendertype=abstract @initial]\nTo perform a multiple-step reaction, reaction mixtures must be combined and split in a controlled manner. By using droplet-based microfluidics, a range of interactions between reactions can be controlled in time.[1] Reactions can be combined by merging two droplets, and reactions can be split by splitting one droplet into two smaller droplets (Figure 14).[1,162]\nVarious methods have been developed for merging and splitting droplets. To combine two parallel reactions, two sets of droplets can be formed in two parallel microchannels that converge into one main channel. The two sets of droplets will merge within the main channel if the frequency is matched between the two droplets and the droplets are of different sizes (Figure 14a).[1] The merging of several smaller droplets with a single larger droplet[163] and of two droplets of the same size has also been shown.[164] The splitting of droplets in a constricted T junction (Figure 14b)[1,125] and at isolated obstacles has also been studied.[165]\nNumerous studies have investigated how droplets can be manipulated and controlled within microchannels;[166] examples include the sorting of droplets with dielectrophoretic forces,[167] the control of droplet volume, chemical concentrations, and sorting of droplets,[168] as well as numerical studies on the deformation, breakup, and coalescence of droplets.[110,130,169] A method was developed recently that uses electric forces to combine and split droplets in microchannels. In this method, two streams of droplets are produced, and opposite charges are applied to the interfaces of aqueous and carrier fluid (Figure 15); the two streams are synchronized and combine completely in a 1:1 ratio upon confluence.[170a] Neutral droplets could be recharged by splitting each droplet into two droplets of opposite charge.[170a] Charged droplets were also sorted by means of electric interactions.[170a] Another method used alternating current field to control the coalescence of plugs.[170b] These techniques should be useful for developing automated, droplet-based microfluidic platforms."},{"_id":"3a76aae5616cbc410c000047","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":2,"parentId":"3a6db57085d22cf726000011","content":"##Electrohydrodynamic manipulation [http://linkinghub.elsevier.com/retrieve/pii/S0165993609002647 - @y21]\nThe electrohydrodynamic (EHD) force generated by an electric field is also widely used to accomplish the basic operations in a droplet-based microfluidics. At the lm scale, interfacial tension forces dominate the hydrodynamic behavior of the droplets, so EHD forces used in the manipulation of droplets must first overcome or change the interfacial tension. According to energy-transduction mechanisms [43], two typical EHD methods are available {i.e. electrowetting (EW) [4,44] and dielectrophoresis (DEP) [45]}. Generally, for conductive liquids, the EW force might dominate the formation of droplets. However, for dielectric liquids, both DEP and EW might contribute, and the DEP force may dominate the process [46]. \n\n3.1. Electrowetting \nElectrowetting for the formation of droplets was first reported by Washizu [4]. When a water droplet is in contact with a solid electrode coated with a hydrophobic film, a wetting force may arise upon application of an electric field. This wetting force can reduce the contact angle, and difference in wetting force arising from an electric field can make a droplet move [43,44]. Fig. 11 showed that electrolysis might occur when a high voltage is applied. By naming the voltage of electrolysis as the critical voltage, an insulating layer can be inserted between the droplet and the electrode so that the critical voltage is raised and electrolysis is avoided, acquiring a stronger wetting force. This so-called electrowetting on dielectric (EWOD) [47] has become one of the most promising ways to manipulate droplets in microfluidic systems. \nGenerally, EWOD devices are fabricated on two-plane devices. The droplet is sandwiched between the two electrode planes and surrounded by gas, silicone oil or another immiscible liquid. The channel is wetted by the fluid when activating the electrodes and the fluid begins to form a short liquid finger between the electrodes.\nWhen the electrodes are switched off, the surface reverts back to hydrophobic, causing the finger to break off from the reservoir or mother droplet, and to form a new droplet or daughter droplet [43] (Fig. 12). \nBy sequentially applying voltages underneath control electrodes, the droplet can be moved in the direction of the activated electrode. This is the typical process for transporting droplets. When adjusting the procedure to activate the electrodes, the daughter droplets may be moved towards each other and finally merge. \nThe size of the droplet depends on the strength and the frequency of the electric field, as well as the width of the channel opening. For example, higher frequencies produce smaller droplets. The concentration of daughter droplets can be controlled by combining fission and other techniques (e.g., electrophoresis [48]). Three modes of mixing based on EWOD are available: based on diffusion inside an immovable droplet; by oscillation while the droplet is moving; and, \nduring the process of a droplet splitting into two droplets and then remerging [49-51]. \nThe key to accurate accomplishment of each process of manipulation is to design the size and the configuration of the array of independently-addressable control electrodes [52,53]. This needs complex, refined micro-fabrication techniques. In addition, EWOD may cause surface contamination in real world biological analysis, because translational electrowetting forces depend closely on the difference of wetting between leading and trailing edges of droplets while the surface is less likely to be even and clean. \n\n3.2. Dielectrophoresis \nDEP is another method of manipulating droplets based on electrically neutral but polarizable fluid [46], a nonuniform electric field and the movement of droplets to the regions of maximum electric field intensity [3,53-55]. \nGenerally, a DEP system contains coplanar electrodes (i.e. smooth and insulating substrate), covered by a thin dielectric layer, and the fluid involved has higher dielectric permittivity than its surrounding fluid. When the fluid remains on the hydrophobic substrate, it can be transported and divided into hemispherical nanodroplets by short application of voltage and appropriate change in electrode connections [54,55] (Fig. 13). \nThe droplets can be sorted into the collection stream by applying an electric field on the electrodes to generate a DEP force [56].\nIn practice, the dielectric permittivity of the droplet is higher than that of the surrounding fluid, so joule heating is inevitable. The increase in temperature can be controlled effectively with a proper electrode design and an operational mode where voltage is applied for very short time [55]. When using a DEP technique to manipulate droplets in a direct current or low-frequency alternating current field, fast formation (0.1 s) [45] and sorting (1.6 kHz) of droplets can be achieved [56]. \n\n3.3. Combination of electric control and other methods Sometimes, the manipulation of droplets by a single method is monotonous and insufficient for flexible applications. The combination of an electric field with other methods (e.g., hydrodynamic stress) can also perform droplet manipulations comfortably. By combining hydrodynamic stress and electric field, fusion can be realized in a simple geometric device [57-60]. As illustrated in Fig. 14a, the adjacent droplets in two arrays were merged by applying an electric field on vapor-deposited-gold electrodes on the cover plate of a micro-channel [57]. A double-T-junction can form two series of droplets with same or different compositions [58], and a non-uniform electric field can be generated by applying a DC voltage across the electrodes embedded under the junction. Consequently, the adjacent droplets will merge (Fig. 14b). Fig. 14c shows that, by applying an increasing electric field, droplets are attracted closer, thus initiating their fusion [60]. \nA system incorporating an electric field and flow-focusing geometry can realize the functions of creating, recombining, splitting and sorting droplets [61]. By applying high voltage to the aqueous stream and charging the oil-water interface, an electrically-addressable emulsification system was created [61]. To generate droplets, the electric field assisted to reduce the dependence of the droplet size on the flow rate and the channel dimensions (Figs. 15 and 16). A pre-requisite for such a system is that the discontinuous phase should be conductive and charged. \nFrom the above discussion, we can see that, to manipulate droplets, self-contained EHD requires no moving parts or fixed channels, consumes little power, and imposes minimal constraints upon the fluid involved. In addition, EHD is flexible and suitable for manipulating single droplets or a small number of droplets. However, it needs fabrication of electrodes or electrode arrays on the micro scale. \nConsidering that hydrodynamic stress can form droplets, while EHD is able to reconfigure the droplets, both approaches deserve further investigation and more protocols are required to combine them. "},{"_id":"3a76b684616cbc410c000048","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":3,"parentId":"3a6db57085d22cf726000011","content":"##Droplet manipulation by thermocapillary, magnetic actuation and acoustic radiation [http://linkinghub.elsevier.com/retrieve/pii/S0165993609002647 - @y21]\nExcept for the approaches mentioned above, some other protocols for manipulating droplets have also been exploited. Because the micro-scale droplet is mainly controlled by surface tension, successful manipulation of droplets will be closely related to overcoming the surface tension. At present, the methods based on thermocapillary [62,63], magnetism [64-66] and acoustics [67] are successfully used to manipulate droplets in microfluidic systems, as discussed briefly in the following sections. \n\n4.1. Thermocapillary \nThermocapillary is a phenomenon that occurs with the change of the surface tension at a two-phase interface due to temperature variation. It can be cited as a mechanism for driving droplets immersed in a second immiscible phase. Interfacial tension usually decreases with increase in temperature [68,69]. When the droplet lies in a temperature gradient, the tension exerts a tangential surface force that pulls liquid toward the cold spot [70-73]. In this respect, droplets can be driven by the thermocapillary effect, depending on the means of heating. By using integrated microheater arrays for the formation of temperature gradients in combination with partial wetting surfaces, droplet transport can be facilitated without volume loss and cross-contamination between individual droplets is virtually eliminated [72]. With a focused laser for providing local heating of a liquid interface, the thermocapillary force can prevent the advance of a droplet in a micro-channel [73,74]. By combining with a T-junction as a contactless optical microfluidic valve, the laser can also be used to control droplet formation, sorting, fusion and division (Fig. 17). \nDroplets of fL volume generated in a microfluidic system can be manipulated and transported by using optical vortex traps [75]. Shah integrated electrowetting-on-dielectric (EWOD) and optoelectronic tweezers (OETs) to isolate and to analyze cells [76]. OETs manipulated individual particles (e.g., cell) to accumulate in one part of a droplet, and then EWOD split the droplet into a concentrated daughter droplet and a diluted one. Based on these two techniques, a series of droplet manipulations can be accomplished. \nIn addition, droplets can be formed simply by light scattering-induced flow. Casner's group [77,78] used a laser to shine onto a soft, near-critical liquid-liquid interface. When the beam with modest powers traveled from the phase with a higher refractive index to the phase with a lower refractive index, a jet of the upper-layer liquid formed along the beam axis and the droplets regularly formed at the end of the jet. We predict that this method would also be effective in forming droplets as long as suitable droplet manipulations with other functions are available in the system. \n\n4.2. Magnetic actuation \nMagnetic actuation is unique because it is independent of surface charge, pH and ionic strength, so it is compatible with a wide range of substrate materials and biochemical processes. It needs only a simple device to include a reservoir and a magnet. The process involves the formation of droplets containing magnetic beads and the droplets are moved by the draw force of the magnetic beads actuated by an external magnet. The external permanent magnet or electromagnet remotely controls the superparamagnetic particles inside the droplet. The actuation is affected by particle type, droplet size, surrounding oil layer, surface tension and viscosity [79]. The quantity of superparamagnetic beads in each droplet also decides whether the motion of droplet is successful or not. It is worth mentioning that, for aqueous droplets, the surface of magnetic beads should be hydrophilic, so that the force due to their interaction with water can force the droplets to move. In this respect, silica is usually coated on magnetic beads to form hydrophilic surfaces. In addition, magnetic beads play important roles in polymerase chain reaction (PCR) [64,80-82], sample isolation and preconcentration [65,83,84] and immunoassay [66,85]. \nAn aqueous suspension of anti-CD15-coated super-paramagnetic particles in an immiscible mineral oil was driven by an external permanent magnet [71]. The droplets were transported, merged, mixed and split to prepare the sample of CD15-bound GFP-transfected THP-1 cells from a blood droplet and real-time PCR. \nElectrostatic forces and magnetic forces have been used to anchor and to drive droplets on hydrophobic substrate [65]. This method could be applied to bio-chemical processes, (e.g., dilution, washing, extraction and purification). Hence, magnetic actuation has capability in droplet-based microfluidics, and the combination of magnetic force with other forces might result in more effective approaches to driving droplets. \n\n4.3. Acoustic radiation \nAcoustic radiation from a surface wave leads to internal streaming in the fluid and eventually to form small droplets along predetermined trajectories. Chemical modification of the planar surface of the piezoelectric chip is employed to modulate wetting properties of the surface and define a fluidic network. It does not need a micro-channel or a micro-valve, but operates in an open system [67]. \nSurface acoustic waves (SAWs) on a piezoelectric substrate can produce acoustic radiation in the fluid. This stress is basically the origin of SAW-mediated internal streaming in the fluid and small droplet formation. When a droplet passed through the modified surface, it was dispensed to remain small on the surface or merged with the original droplet at the location. The combination of acoustic radiation with a sensor or a heater might bring more attractive application of the droplets [67]."},{"_id":"3a6db9ce85d22cf726000012","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":5,"parentId":null,"content":"#Merging and Related Literature\nMerging means the coalescence of droplets..."},{"_id":"3a749cf2616cbc410c000030","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a6db9ce85d22cf726000012","content":"#Theory of Merging [http://www.springer.com/cda/content/document/cda_downloaddocument/9781461432647-c1.pdf - @springer]\nDroplet fusion is a critical operation for droplet manipulation, since it allows for the combination of different reagents and for the initiation of chemical and biological reactions in microfluidic devices. Contrary to intuition, simply initiating droplet collisions does not frequently result in fusion between the droplets. In fact, a systematic study of a passive droplet fusion technique revealed that it is the separation process of closely spaced microdroplets, rather than their collision, which results in coalescence of the droplets [1]. Bibette et al. provide a set of equations for predicting coalescence. For coalescence of droplets to occur, the continuous phase separating the two droplets must first be drained, bringing the droplets into close contact. Then, the droplets must be kept in close contact for a critical minimum amount of time, in order for fusion to occur. Fusion occurs due to fluctuations in the surface tension on the surface of droplets, which cause destabilization of the interface between the oil and water phases [2]. \nAlthough the fusion of droplets may seem straightforward, there are several key challenges involved in this process. In order for droplets to fuse, they must achieve temporal and spatial synchronization. Several creative strategies have been employed to synchronize droplets prior to fusion, both for passive and active droplet fusion systems. Still, with the development of more complex microfluidic systems with a large number of inputs, new strategies for the synchronization of droplets are being sought. The addition of surfactant to either the continuous or dispersed phases of a droplet microfluidic device is a common practice to stabilize the droplets; however, the presence of surfactant makes droplet fusion much more difficult. Other important considerations for any droplet fusion mechanism are its throughput and efficiency. While some methods presented below demonstrate a very high efficiency of fusion, with the vast majority of droplet pairs undergoing fusion, the throughput of such systems may be much lower than a system where the efficiency of fusion is not quite as high. While both high fusion efficiency and high throughput are desirable, it may be necessary to compromise one or the other of these qualities in order to satisfy the demands of the intended application. Due to the fact that fusion involves the coming together of contents from different droplets, inter-droplet contamination is also a concern. Additionally, preservation of the viability of biological material may be a concern in active fusion methods where electricity is used to fuse droplets. While passive fusion methods often carry a lower risk of contamination and are more biocompatible, they generally have a much lower throughput than active fusion methods. As a result, a variety of both passive and active methods for inducing the fusion of droplets have been developed. While each design has its strengths and shortcomings, a suitable method for inducing droplet fusion may certainly be found for a variety of applications."},{"_id":"3a748eb2616cbc410c000025","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":5.5,"parentId":null,"content":"#Splitting and Related Literature"},{"_id":"3a74a399616cbc410c000031","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a748eb2616cbc410c000025","content":"#Theory of Splitting [http://www.springer.com/cda/content/document/cda_downloaddocument/9781461432647-c1.pdf - @springer]\nThe fusion or combining of the contents of different droplets has obvious importance for the execution of chemical reactions in droplet microfluidic systems; however, the ability to divide droplets is also a necessary operation for the execution of assays and the production of sample replicates. A simple way to introduce multiple sample types into a microfluidic device involves the consecutive aspiration of a large plug of fluid from a number of microtiter plate wells. In these devices, droplet fission is used to divide the plug into many smaller volume droplets, which allow individual droplets to be paired and mixed with different reagents [31], and also provide a smaller volume container, which allows for rapid mixing and reduces the reaction time in the droplet [32]. Droplet fission designs also provide the potential to increase the throughput of droplet production, and to digitize biological assays, increasing their sensitivity. Like droplet fusion, both passive, geometry-mediated droplet fission schemes have been developed, along with active droplet fission schemes, which employ the use of electricity or localized heating to split droplets."},{"_id":"3a6ff5378bda8f38d0000026","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":5.75,"parentId":null,"content":"#Microfluidics Methods Review\nInvestigation includes optical or infrared cameras and also incorporates laser detections..."},{"_id":"3a7591aa616cbc410c00003d","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a6ff5378bda8f38d0000026","content":"##Magnetic [http://www.springer.com/cda/content/document/cda_downloaddocument/9781461432647-c1.pdf - @springer]\nJust as magnetic particles have been used to tag and separate cell populations of interest, this technique can also be used to separate droplets containing magnetic particles from those which do not contain the particles. In 2004, a research group showed that such technology could be used to move aqueous droplets in air over a surface using a magnetic field. The aqueous droplets contained iron oxide nanoparticles, encased in silicon particles, which enabled control over the direction of the droplets [56]. Although efficient, the throughput of this approach was limited. Several years later, another group incorporated this concept into a microfluidic device to enable continuous sorting of droplets in this manner. Superparamagnetic magnetite nanoparticles were produced and incorporated into droplets, which could then be deflected into different channels by the targeted application of a perpendicular magnetic field (Fig. 2.10). To change the destination of the droplets and switch them to different outlets, the magnets were moved to different locations parallel to the main channel flow. This technique allowed separation of droplets at a rate of 10 per second. The use of such small magnetic particles ensures that they retain no magnetic \"memory\", reducing the possibility of aggregation of the particles, and increasing their biocompatibility. Indeed, similar particles have been used safely in several types of biological assays [57]. "},{"_id":"3a759449616cbc410c00003e","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":2,"parentId":"3a6ff5378bda8f38d0000026","content":"##Dielectrophoresis [http://www.springer.com/cda/content/document/cda_downloaddocument/9781461432647-c1.pdf - @springer]\nJust as dielectrophoresis has been used to facilitate the fission of droplets, it has also been used to sort droplets for further processing. The application of a nonuniform electric field exerts a force on droplets that can be used to direct droplets into one of several outlets of a device. In a device by Ahn et al., droplets flowed into the lower resistance outlet in the absence of DEP force. With the application of this force, however, the droplets were directed to a higher resistance outlet of the device (Fig. 2.11a-d). Sorting could occur at rates of up to 4,000 droplets per second using this approach [58]. For more precise manipulation of droplets, an array of 128 × 256 individually addressable electrodes was designed and used to move droplets. Droplets could be moved over the surface of this array at speeds of up to 30 mm per second by selectively activating electrodes. A lubrication layer of oil separate from the continuous phase surrounding the droplets facilitates movement of the droplets. This layer also prevents contamination between droplets during sorting. In addition, the application of DEP is made biocompatible by the application of an AC field, which is not as harmful to cells as DC fields [59, 60]. Several other devices employing dielectrophoresis with different electrode designs have been used for the separation of cells or beads [61-63]. \nIn much the same manner as fluorescent cells can be sorted by a technique known as fluorescence-activated cell sorting (FACS), droplets containing fluorescent contents have been separated using dielectrophoresis. Such a device, termed a fluorescence-activated droplet sorter (FADS) detects passing fluorescent droplets and applies an AC field to direct fluorescent droplets to an alternate outlet channel. In the absence of the AC field, droplets are carried to the lower resistance outlet by default. A device by Baret et al. was able to achieve a sorting speed of up to 2,000 droplets per second, with a false sorting rate of 1 in 10,000 droplets, under optimal conditions for speed and accuracy, respectively. The FADS device was used to sort cells encapsulated in the droplets, and successfully distinguished between droplets with an active enzyme (which fluoresced) and those without the active enzyme (which did not fluoresce) [64]."},{"_id":"3a759932616cbc410c00003f","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":3,"parentId":"3a6ff5378bda8f38d0000026","content":"##Optical [http://www.springer.com/cda/content/document/cda_downloaddocument/9781461432647-c1.pdf - @springer]\nFor precise manipulation of droplets, focused laser light can also be used. In a device fabricated with a post structure in the middle of a microfluidic channel, a laser can be focused to one side of the post to prevent the droplet from passing the post on that side. After a droplet passes the post on the other side, hydrodynamic flow will direct the droplet into the corresponding branch of a bifurcation that follows the post structure in the channel. In this way, by positioning the laser on either side of the post, droplets can be sorted into one of two daughter channels. Although not addressed directly in the paper, the comparatively low throughput of the system as well as the biocompatibility of a laser could be issues [40]. To sort droplets into more than two daughter channels, a pattern of laser light spots has been used to direct droplets into one of three outlets (Fig. 2.11e-g). The sorting speed using a laser light pattern was between 30 and 60 droplets per second [65]. In a more complex approach, Kovac et al. enabled phenotype sorting of cells using an infrared laser—however, the technique could presumably be applied to sorting of cells encapsulated in droplets. Cells were first allowed to settle onto an array inside a microfluidic device, and cells of interest were identified manually by observation. Selected cells were lifted from the array using an infrared laser, into the flow through the device, and collected at the outlet. This approach avoids the manufacture and control issues associated with making an array of individually addressable electrodes. In addition, a low divergence laser beam was used in this method, which provided a large enough working distance to move the cells to the desired area, while operating at a lower intensity than optical tweezers to avoid damaging the cells. One disadvantage to this approach is its low throughput— between 18 and 45 s were needed to sort a single cell [66]. Despite a lower throughput, these approaches offer a greater degree of precision in the sorting of droplets and may prove valuable for an application where the purity of the sorted population must be very high. Several other optical sorting approaches, including the use of optical tweezers and handles have been used for sorting particles or cells, and the technology could potentially be applied to droplet sorting as well [67]."},{"_id":"3a759ac9616cbc410c000040","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":4,"parentId":"3a6ff5378bda8f38d0000026","content":"##Other [http://www.springer.com/cda/content/document/cda_downloaddocument/9781461432647-c1.pdf - @springer]\nA handful of other techniques have been used to sort droplets, using electrical phenomena, fluid pressure induced by mechanical actuation, heat, surface acoustic waves (SAW), and others. An electric field imposed at a bifurcating junction has been shown in a device to induce sorting of droplets into one daughter channel or the other, depending on the direction in which the field is applied [24]. In another technique employing use of an electric field, selected droplets could be pushed into a separate stream by applying an electric field. Once selected, droplets were pushed into an aqueous stream flowing adjacent to the continuous phase flow, and the sorted aqueous droplets were absorbed into the continuous aqueous flow stream. Such a technique could be useful for downstream processing and enable droplets to be characterized using techniques that rely on analog, rather than digital flow, such as chromatography [27]. \nA unique approach to droplet sorting induced by mechanical actuation is the use of piezoelectric materials to produce a cross flow across the main channel of a microfluidic device containing droplets. To sort a droplet or train of droplets, a piezoelectric material is actuated, which depresses a PDMS membrane above a reservoir of continuous phase fluid. Depression of this membrane induces a flow of the continuous phase fluid in a channel perpendicular to the main channel flow. When streamlines from this side channel occupy at least 50% of the crosssectional area of the main fluidic channel, droplets are diverted into a secondary outlet. Depending on the type of detector used to identify droplets for sorting, droplets could be sorted based on their volume or fluorescence [68]. Using similar device geometry, another group enabled droplet sorting by inducing electrokinetic crossflow in a device. In contrast to the device enabling crossflow using a piezoelectric actuator, fluid movement can be induced instantaneously upon activation of the electrodes which induce the electrokinetic flow. The disadvantage to this approach is that electrokinetic flow can only occur in a continuous phase where ions are present—thus the technique would not work well in a system where the droplets comprise the aqueous phase and the continuous phase is hydrophobic oil. Nevertheless, this sorting approach may be useful for some applications and was demonstrated successfully for the sorting of fluorescent beads from a stream of water [69], as well as cell sorting [70]. Franke et al. also demonstrated success in droplet sorting using a piezoelectric actuator. In the absence of actuation, droplets in the main channel sort into the device outlet with lower resistance. For sorting, the piezoelectric material is actuated, which creates SAW that induces acoustic streaming to move droplets in the main channel. In this manner, droplets may be sorted into the higher resistance outlet, simply by actuating the piezoelectric material [71]. \nAs mentioned earlier, passive sorting designs employ asymmetric bifurcation junction geometries to induce sorting based on flow rates and hydrodynamic resistance. Using a similar approach, Yap et al. induced droplet sorting by designing a device in which the fluidic resistance of the bifurcation junction daughter channels could be changed. A microheater, integrated into the microfluidic device, allowed switching of droplets into the higher resistance daughter channel following a bifurcation by heating the fluid in that channel. This heat reduced the hydrodynamic resistance in that daughter channel, which caused droplets to sort into the heated channel [42]."},{"_id":"3a6dbe5d85d22cf726000014","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":6,"parentId":null,"content":"#Methods for Droplets Merging\nIn order to form a single droplet from two droplets..."},{"_id":"3a74bcea616cbc410c000033","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a6dbe5d85d22cf726000014","content":"#Droplet Fusion Basics [http://www.sciencedirect.com/science/article/pii/S0165993609002647 - @y21]\nChemical and biological analysis commonly needs coalescence of different liquids (e.g., samples and reagents) to complete the reactions. In droplet microfluidics, this approach is replaced by fusion of droplets. Introducing some substances into a droplet and merging two droplets with different contents are both indispensable. In practice, merging droplets should at least fulfill the following pre-requisites: touching each other; and, overcoming the stabilizing forces caused by surface tension and lubrication. \nSo far, extensive investigations have been directed to ensure contact of two adjacent droplets. A number of novel configurations have been constructed in the micro-channel to make the droplets meet each other (e.g., small and big droplets moving at two different velocities will coalesce until they enter a wide main channel, due to the difference of flow pressures in the two inlet channels with different dimensions [35]). A recent flow-rectifying design facilitates simultaneous fusion of three or more droplets [27,33]. In addition, a tapered expansion in a micro-channel generates a velocity gradient [22], which allows approach to the droplets, oil-film drainage between the droplets, and finally leading to the fusion of the droplets (Fig. 7). \nTo overcome the stabilizing forces related to surface tension and lubrication, fusion depends on the viscosity ratio of the internal and external fluids as well as the presence of surfactant at the interface. When the internal phase (i.e. the droplet) has a lower viscosity, the film between the immiscible fluids will be easy to drain and rupture, facilitating coalescence of the droplets [26]. However, by contrast, if the droplet has a higher viscosity, the interface is less mobile, and it is therefore more difficult for the two droplets to coalesce. In addition, presence of surfactant at the interface of two droplets also arrests coalescence [37,38]."},{"_id":"3a99c90f14ad04a28500004b","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a74bcea616cbc410c000033","content":"###Droplet Merging [http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3127135&tool=pmcentrez&rendertype=abstract - @x13]\nDroplets can be used as independent microreactors for a number of chemical and biological applications, e.g., chemical synthesis, kinetics studies, the screening of biological contents and bio-medical diagnostics. The merging of two droplets is a key step in this approach since (in the large majority of cases) this forms the trigger to start the chemical reaction(s). Practical prerequisites for merging are that the droplets (i) touch each other and (ii) overcome the stabilizing forces caused by surface tension and lubrication. Several designs have been used to bring droplets together [90–98]. To subsequently overcome the stabilizing forces, both the viscosity ratio of two-phase fluids [39], and the presence of surfactant at the interface [99–101] have to be considered. \nSurfactants are generally used to stabilize emulsion droplets against coalescence. These molecules generally consist of a compact polar head and a long-chain hydrophobic tail. Surfactants reduce the interfacial tension between two liquids by adsorbing at the liquid-liquid interface where they often align perpendicular to the surface. Stabilization of droplets can be realized in different ways: (i) via repulsion between the interfaces due to electrostatic and/or steric effects; (ii) by slowing down the hydrodynamic flow along the interface via Marangoni effects or via enhanced surface viscosity [102,103]. Basically, there are two main approaches, namely passive merging and active merging, to coalesce droplets. In the case of passive merging, droplets are normally not stabilized by surfactant. Then coalescence occurs spontaneously when the droplets meet; the occurrence of which can be organized with a suitably shaped channel geometry [91]. For droplets that are stabilized by surfactants, active merging is required. For this, thermocapillary effect [76,104] or electrocoalescence [105–110] can be used. "},{"_id":"3a751f9b616cbc410c000034","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":2,"parentId":"3a6dbe5d85d22cf726000014","content":"##Passive Fusion Methods [http://www.springer.com/cda/content/document/cda_downloaddocument/9781461432647-c1.pdf - @springer]\nPassive droplet fusion mechanisms are those which do not require active control or electricity. These designs are often simpler than active fusion mechanisms, which may require complicated circuitry and control systems. One advantage of most passive droplet fusion techniques is that the possibility of inter-droplet contamination is lower than for active droplet fusion techniques. However, passive droplet fusion techniques are limited by the rate at which natural phenomena, such as surface tension fluctuations occur, and are therefore often slower than most active droplet fusion techniques."},{"_id":"3a99cb6a14ad04a28500004c","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":0.5,"parentId":"3a751f9b616cbc410c000034","content":"###Passive Merging [http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3127135&tool=pmcentrez&rendertype=abstract - @x13]\nIn passive droplet merging, the design of the channel geometry is a key to achieve proper merging, since droplet synchronization is required and active means to compensate for any synchronization errors are missing. In principle merging can occur simply at a channel junction, if the generation and transport of each pair of droplets is such that both drops arrive there at the same time. However in practice this can be difficult to achieve, and therefore special designs of geometries are often used. \nOne widely used geometry for droplet merging consists of a widening channel follow by a narrower channel (Figure 11) [90–93]. In this geometry the droplet velocity decreases in the widening channel because of drainage of the continuous phase, after which it increases again upon entry in the narrow channel. Due to this changing flow field, two subsequent droplets are allowed to come close together and let the liquid that separates them drain away. Bremond et al. observed that the merging does not occur during the first interdroplet encounter in the extended channel, but rather during the separation stage of two droplets when the first droplet begins to enter the narrow channel (Figure 11c) [93]. The separation induces the formation of two facing protrusions (Figure 11d) which then bring the two interfaces close enough until they merge. Later Lai et al. reported a theoretical study based on this observation [111]. The created protrusions lead to a rapid increase of the surface area locally, and thus to destabilize the interface at certain locations. The conditions under which droplet merging occurs, can be predicted on the basis of their model. Alternatively in other channel geometries, droplets are merged by slowing down or stopping the leading droplet at a constriction [97,98], or in a channel with an array of pillar elements [94,95]. \nIt should be noted that typically no surfactant is used in these passive merging experiments. However, the absence of surfactant has its drawbacks: unintended merging events can occur, and also the possibilities for further manipulation of the droplets after the merging can be limited. By exception, a case of passive merging of surfactant-covered droplets has also been reported. Mazutis et. al. demonstrated a channel design for merging droplets with significant asymmetry in size, both formed in the presence of surfactant [100]. However, undesired coalescence still occurred often. It is therefore often preferred to use surfactant stabilized drops and achieve merging with the help of external forces. "},{"_id":"3a752708616cbc410c000035","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a751f9b616cbc410c000034","content":"###Geometry-Mediated Passive Fusion [http://www.springer.com/cda/content/document/cda_downloaddocument/9781461432647-c1.pdf - @springer]\nAmong the earliest and simplest designs for passive fusion of microdroplets employs a section of widened channel, termed an \"expansion volume.\" By controlling the continuous phase velocity and the dimensions of the expansion volume, consecutive droplets can be induced to fuse in this region. The expansion volume enables fusion by draining the continuous phase that separates one or more consecutive droplets in a channel. Upon entering the expansion volume, the continuous phase fluid spreads around the droplets to fill the increased volume, while droplets remain in the center of the channel. This removal of spacing between droplets allows interaction between the surfaces of adjacent droplets and induces fusion of the droplets as a result of minute disturbances in surface tension. Either a gradually tapering channel [3] or a wider section of the channel [4, 5] may be employed as an expansion volume (Fig. 2.1). Careful control of the frequencies of droplet generation from each droplet source is necessary for reliable fusion when using an expansion volume [6]. Another early method for passively inducing the fusion of consecutive droplets involved active drainage of the continuous phase between droplets, known as a flow-rectifying design. In this design, the droplet stream would flow past a junction with channels perpendicular to the direction of droplet transport. Through these perpendicular channels, continuous phase could be actively removed using an off-chip syringe pump, which induced droplet fusion by bringing consecutive droplets close together [4, 7, 8]. Alternatively, a 3D expansion volume can be used to fuse droplets. In this design, droplets carried along a microchannel \"track\" are carried through a chamber of larger width and height than the track. A control line adds continuous phase at a prescribed rate to control the number of fusion events that occur in the chamber. By controlling the flow rate of continuous phase from this line, researchers were able to perform arithmetic operations with the droplets, similar to the operation of an abacus [9]. \nUsing an expansion volume, droplets from two different inlets have been fused in a tapering region of a microfluidic device. In this device, alternating droplets from two different inlets were produced. The droplet pairs fuse downstream in a tapering region of the channel to yield CdS nanoparticles within the fused droplets [3]. This development enabled the execution of simple chemical reactions, comprising a single mixing step, on a chip. The microfluidic platform enables synthesis of very small volumes of product, useful in situations where the reactants are expensive, hazardous, or simply limited. \nWhile an expansion volume provides a way to fuse droplets passively, there are several limitations to this design. With the expansion volume approach, only consecutive droplets in a channel can fuse. This restriction requires that the order of droplets in a microchannel be carefully controlled, in order to achieve the desired fusion. In addition, an expansion volume is only able to fuse droplets that have a relatively small and uniform inter-droplet spacing. In order to enable more complex applications involving droplet fusion, several devices have been developed which overcome the problem of inter-droplet spacing, to ensure reliable droplet fusion. Building from the expansion volume concept for droplet fusion, Niu et al. designed an expansion volume containing two sets of tapering pillars in its center (Fig. 2.1). As a droplet enters the expansion volume, it is squeezed between the sets of pillars. Once the droplet has completely entered the expansion volume, continuous phase behind the droplet is allowed to drain around the droplet into the widened channel. The droplet is stopped in the pillar array due to the increase in surface tension it experiences. As the pillars narrow, the radius at the front of the droplet becomes smaller than the radius at the back of the droplet, which produces a net surface tension pressure that counters the hydrostatic pressure induced by the continuous phase. In this device, a droplet can be held indefinitely until the next droplet in the line approaches—this feature allows for droplet fusion to occur even if inter-droplet spacing does not remain constant. In addition, by changing the size of the expansion chamber and the size of the droplets, multiple droplets can be induced to fuse in the pillar array [10]. In another design, droplets from one inlet become trapped in a narrowing channel, due to the increase in surface tension they experience as the radius of the front of the droplet decreases. Once a droplet is trapped, it is held in place indefinitely by surface tension forces. A bypass channel allows continuous phase and other droplets to continue to flow around the trapped droplet. Another droplet inlet, perpendicular to the first inlet, joins a fusion chamber at the location where a droplet is trapped. As a droplet from this second inlet approaches the fusion chamber, the second droplet fuses with the trapped droplet as it passes by. Due to the ability of this device to trap the first droplet and hold it indefinitely, droplets from separate inlets, and generated at different respective frequencies, can be fused. In addition, the inter-droplet spacing need not be uniform or short, for fusion to occur [11]. \nInstead of using surface tension forces to trap droplets before fusing, a membrane valve has also been used (Fig. 2.2). For fusion to occur, a membrane that occludes most of the width of an expansion volume is depressed. Droplets are constrained to the center of the expansion volume by a set of pillars as the membrane is depressed, while continuous phase is allowed to flow around the pillars and the depressed membrane. Once the desired number of droplets has been trapped in the expansion volume, the membrane valve is opened [12]. Droplets fuse as they are pulled away from one another out of the expansion volume. This is in accordance with recent theory and characterization describing how droplets are observed to merge as they are moving away from one another, instead of when they are pushed together [1]. "},{"_id":"3a752b60616cbc410c000036","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":2,"parentId":"3a751f9b616cbc410c000034","content":"###Passive Fusion Induced by Physical and Chemical Phenomena [http://www.springer.com/cda/content/document/cda_downloaddocument/9781461432647-c1.pdf - @springer]\nIn addition to the above methods for passive droplet fusion, several designs which exploit physical or chemical phenomena have been developed. For instance, droplets of different sizes or of different viscosity travel at different speeds within microfluidic channels. If a small droplet is introduced to the channel after a larger droplet, the small droplet will travel faster in the channel than the larger droplet, which decreases the inter-droplet spacing and allows fusion to occur at an expansion volume. As the viscosity of the dispersed phase is increased, the droplets travel with slower velocity. Hence, a droplet of lower viscosity will travel faster through a microchannel than a droplet of higher viscosity, allowing the lower viscosity droplet to \"catch up\" to a higher viscosity droplet. Droplets paired in this way can then become merged when they enter an expansion volume. One advantage to this technique is that droplets can self-synchronize if conditions are right, eliminating the need for an active mechanism of pairing droplets [13]. \nSurfactants are often added to a microdroplet emulsion to stabilize the droplets and prevent unwanted fusion events. One group has exploited the readiness with which surfactant-free droplets fuse to reliably fuse two populations of droplets one-to-one. A population of droplets with a surfactant concentration of 2.8% was generated and injected into a chip, where each surfactant-stabilized droplet was paired with a surfactant-free droplet. Upon entering a microchannel with 1171 bends, the droplet pairs readily fused. Fusion occurs as a result of the geometric constraints imposed by the zigzag channel as well as the partial instability of the surfactant-free droplets. Since the droplets were paired one-to-one, secondary fusion of droplets was avoided, as fused droplets all contained surfactant and were thus stabilized against further fusion. Although useful for one-to-one fusion of two different droplet populations, this technique requires careful consideration of the chemistry of the system. Furthermore, the relatively high surfactant concentration required for the surfactant-stabilized population of droplets may be incompatible with some chemical or biological assays [14]. \nAnother method which does not require synchronization of droplets for fusion relies on a hydrophilic patch inside a microchannel to trap droplets before fusion. A photomask is used to allow selective polymerization of acrylic acid on a PDMS device, using UV light. Areas exposed to the UV light are patterned with polyacrylic acid, rendering these areas hydrophilic. The rest of the PDMS device retains its native hydrophobicity. When a hydrophilic droplet approaches the hydrophilic patch in the channel, the droplet is slowed and stopped over the patch. Additional droplets gather behind the first droplet near the patch, until the viscous drag force generated by their presence is enough to overcome the interfacial forces holding the first droplet to the patch. At this point, the first droplet begins to move downstream, and the trapped droplets all fuse. Since this device functions by balancing the interfacial interaction force between the droplets and the patch, and the viscous drag force imposed by the continuous phase, the number of droplets to be trapped and fuse can be tuned by changing the continuous phase flow rate, which changes the viscous drag force on the droplets [15]. Although this fusion mechanism requires no special geometry and could potentially be incorporated into any straight microchannel, the possibility for contamination between droplets exists, due to the requisite interaction of droplets with the polyacrylic acid patch in the channel.\nA unique approach to droplet fusion using a laser has been attempted in recent years. By carefully directing an Argon ion laser in a microchannel, localized heating is induced in the channel which can induce fusion between two droplets. Droplet fusion is induced when the laser is directed to the interface between the two droplets. Heat applied at this location leads to disturbances in the surface tension which result in destabilization of the droplet interfaces and eventually fusion. The laser is also capable of stopping droplets in a channel, potentially allowing for trapping a given number of droplets and fusing them together, using only a laser. Although this design minimizes the chance of inter-droplet contamination, due to the fact that droplets are not physically constrained on a surface, the throughput of this approach may be lower due to the need to precisely control the timing and location of laser heating [16]. "},{"_id":"3a752f1b616cbc410c000037","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":3,"parentId":"3a751f9b616cbc410c000034","content":"###Adding Reagents into Passing Droplets [http://www.springer.com/cda/content/document/cda_downloaddocument/9781461432647-c1.pdf - @springer]\nAn alternative to passive droplet fusion schemes that generate two droplets and then fuse them together is a technique where reagent is metered into a passing droplet from a microchannel intersecting the main channel. This strategy accomplishes the same goal of droplet fusion and precludes the need to generate many different populations of droplets. This technique has been used to produce nanoparticles in microdevices that are more monodispersed than nanoparticles produced in a benchtop process [17]. One drawback to this technique is that the possibility for contamination is more significant, since passing droplets come into direct contact with the second reagent stream. To overcome this issue, a device has been introduced more recently that uses several narrow hydrophilic channels to introduce the second reagent (Fig. 2.3). This reduction in the dimension of the injection channel raises the dimensionless Peclet number in this design, meaning that addition of reagent to passing droplets is due more to convection than diffusion. The authors postulate that the smaller injection channel dimension minimizes the effect of diffusion, which causes contamination between droplets due to the chaotic mixing it introduces. Although temporal synchronization of the release of the second reagent was a problem in the earlier designs, the technique employing several narrow channels can avoid the problem of extra droplet formation by carefully selecting the volumetric flow rate of the continuous and dispersed phases [18]. One disadvantage to this approach is less control over the specific amount of reagent that is added to a passing droplet. In systems where two separate droplets are generated and then brought together, the calculation of the specific volume of added reagent is more straightforward."},{"_id":"3a99ce1f14ad04a28500004d","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":4,"parentId":"3a6dbe5d85d22cf726000014","content":"##Active Merging [http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3127135&tool=pmcentrez&rendertype=abstract - @x13] \nTo achieve active and selective droplet merging, the most widely utilized method is to ensure the presence of an electric field at the location where two droplets meet. Link et al. showed that droplets can be merged by applying voltages with opposite sign across the two droplets during their formation. This is supposed to result in oppositely charged surfaces, which will attract each other strongly as soon as the droplets reach close proximity [72]. Alternatively, Chabert et al. achieved merging of individual droplet pairs via electrocoalescence (EC) [112]. This appears to be a promising method, although the mechanistic aspects of EC still remain to be understood [105,109,113,114]. \nThe general picture of EC is sketched in Figure 12. Due to the electric field, the two droplets experience an electrical (Maxwell) stress σE that tends to deform their shape from spherical to prolate spheroid. This stress is then balanced by the interface tension and the viscous stresses due to the deformation rate [115]. For Newtonian fluids at low Reynolds and Bond numbers, this is described by: \n\t2UPT \t(2) \nwith µ the viscosity, U the velocity, P the pressure and T the stress field in each phase of the two-phase fluid. Since the velocity is continuous across the interface, the total stress difference (electric plus viscous) between inside and outside the droplet is balanced by the interfacial tension: \n\tnTnTN nTE nSn \t(3) \nwhere n is the unit normal vector at the interface, σ is the interfacial tension,Sn is the mean curvature of the interface, TE is the Maxwell stress tensor (proportional to the square of the applied electric field) and TN is the tensor of viscous forces [115]. Hence the field, the viscosities and the interfacial tension all play a role. \nPriest et al. argued that EC involves an electric-field-induced dynamic instability of the oil/water interface, which subsequently leads to the formation of a liquid bridge and coalescence (Figure 13a) [105]. Thiam et al. analyzed the merging of droplets as a function of their separation distance (Figure 13b) [109], and also explained their observations in terms of a competition between electrical stress and restoring capillary pressure. Qualitatively speaking, it is clear that the electric field near the droplet surfaces can be amplified by dipole-dipole interactions between the droplets, and hence become stronger as the droplets get closer. It is conceivable that this will lead to destabilization of the surfaces [116]. Furthermore, also the surfactant molecules can be involved. In the case of surfactants with dipolar head-groups, a redistribution or re-alignment along the electric field lines can take place. Also this can destabilize the interface and lead to coalescence [117]. \nOne of the first applications of EC in two-phase flow microfluidics was presented by Tan et al. [118]. Two droplets containing biological molecules were brought into an expanded channel and merged there, due to an electric field generated by an embedded electrode. Later, several variations based on this geometry were adopted to implement EC in microfluidic chips [72,109,112]. For each of these EC-based systems, droplet synchronization and precise electrode alignment are required. \nTo overcome these limitations, Gu et al. used EW-induced on demand formation to obtain synchronization of two streams of produced droplets [119]. These two streams then meet at a T-junction where interdigitated electrodes are embedded (Figure 14a and b). Merging on demand can be achieved there based on EC. As illustrated in Figure 14c, Niu et al. depicted an alternative method, by combining a passive merging approach (a pillar array in the channel) with an active merging approach (built-in electrodes) [110]. In this scheme, the pillar array slows down and traps the droplet during the drainage of the oil phase. EC then occurs when droplets have reached close proximity. Also a double T-junction geometry with embedded electrodes has been reported in the context of active merging. In the system of Wang et. al., two series of droplets can be produced and merged at the same time [108]. \nYet another method for the active merging of droplets is dielectrophoresis (DEP). A drawback of this method is that it requires rather high voltages, up to several kV [120–122]. Finally, thermo-capillary effects can also be cited as a mechanism to perform active merging of droplets [76,104,123,124]. Heating two adjacent droplets with a focused laser beam was reported to cause convective motions in the droplets, as well as depletion of surfactant molecules from the interface. Also this turned out to be effective for droplet merging. "},{"_id":"3a99d54d14ad04a28500004f","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a99ce1f14ad04a28500004d","content":"###Active Fusion Methods [http://www.springer.com/cda/content/document/cda_downloaddocument/9781461432647-c1.pdf - @springer]\nIn addition to the passive fusion techniques discussed above, other fusion methods employing active controls, such as electrocoalescence, dielectrophoresis, and optical tweezers have also been developed. Such methods are inherently more complex than many passive droplet fusion schemes, since many require fabrication of electrodes and precise timing of electrical signals in order to fuse droplets. With the use of electricity come concerns of contamination between droplets, if some of the droplet contents become deposited on an electrode, as well as biocompatibility of electrical signals on biological molecules, such as DNA or proteins. The advantage to such systems is that the use of electricity can hasten the development of instabilities in the surface tension between droplets [19], initiating fusion more quickly and increasing the throughput capabilities of the device. \nWhile several research groups have developed devices to fuse microdroplets using electrodes, the size and positioning of the electrodes in these devices is diverse, with each design presenting its own strengths for particular applications. In one design with applications for studying chemical kinetics, the electrodes comprise a platinum wire that is positioned inside the main microfluidic channel where continuous phase flows, and an indium tin oxide ground electrode on the base of the microfluidic device. Perpendicular to this main channel, two dispersed phase streams enter near the wire and form droplets through a simple T-junction configuration. When voltage is applied across the electrodes, fusion of one droplet entering from each of the dispersed phase channels occurs at the tip of the wire. The application of voltage in this nonuniform electric field induces a positive dielectrophoretic (DEP) force on the droplets, which pulls them toward the wire. Once both droplets have been pulled close to the wire, the layer of continuous phase separating them becomes thin, and instabilities in the surface tension between the droplets result in fusion. Using this device, the progress of a chemical reaction can be tracked optically in the droplets, which each act as individual microreactors. Since the rate of droplet formation in the device is constant, the droplets produced display the progress of the chemical reaction at discrete time points, providing a simple means of studying the kinetics of a reaction [20]. While well suited for this purpose, this device is limiting in that the contents of all the fused droplets are exactly the same. For many applications, the production of many droplets with diverse contents is necessary. \nFor more complicated reactions or assays, the fusion of multiple droplets may be desired or needed. In 2009, Tan et al. developed a round microfluidic chamber in which a variable number of droplets could be fused. The chamber is designed to slow entering droplets, to give them more time for fusion, and helps to position the droplets parallel to the electric field. This orientation minimizes the electric field strength needed for droplet fusion, which occurs when the electric field disrupts surfactant molecules on the surface of the droplets. The fusion chamber is also designed large enough that droplets do not contact the electrodes during the fusion process, which decreases the risk of droplet-to-droplet contamination that may occur in devices where droplets come into contact with the electrodes. For fusion of two droplets, only the electric field is necessary both to align the droplets correctly and to fuse them. To fuse several droplets, however, laser tweezers were employed to position all of the droplets in a line parallel to the electrical \nfield. The disadvantage to this technique is its low throughput. Five 10 ms pulses of DC voltage, space 0.2 s apart, were required for a single fusion event [21]. Due to the spaces between pulses, the maximum rate of fusion would be less than one event per second, which is much slower than most other droplet fusion mechanisms. \nAnother device traps passing droplets on the electrode surface to induce the fusion of multiple droplets. As the droplet slows and becomes trapped, it deforms and spreads on the electrode surface, which provides space allowing continuous phase to flow around the droplet. The next droplets carried through the channel also become trapped on top of the electrodes and fuse with previously trapped droplets (Fig. 2.4). The ability of the electrodes to trap and hold the droplets on their surface is a balance achieved between the DEP force imposed by the electrodes and the hydrodynamic force imposed by the flow of the continuous phase in the channel. Eventually, as multiple droplets become trapped on the electrodes, the hydrodynamic force on the droplets overcomes the DEP force from the electrodes, and the fused droplet is released from the electrode surface. The number of droplets to be fused on the electrodes can thus be controlled by careful selection of the DEP force and hydrodynamic pressure applied to the system. Fusion rates of 50 per second were routinely demonstrated with this device. Higher rates of up to 100 fusions per second were achieved, but at high voltage levels, which could provide problems for biological assays and can also induce hydrolysis of water in the droplets. In addition, the reliance of this technique on droplet contact with the electrodes could mean that contamination from droplet-to-droplet is likely. One advantage to this technique is that no synchronization system is required. The first trapped droplet can wait indefinitely on the electrode surface until subsequent droplets arrive [19]. \nA common shortcoming in active fusion designs is their incompatibility to accommodate biological solutions, owing to the high voltages applied to induce droplet fusion. To address this problem, Priest et al. demonstrated a device that requires only a 1 V DC pulse to fuse droplets—a considerably lower voltage than many other systems. Lower voltages are required in this system due to the proximity of the droplets to the electrodes. While other designs used an expansion chamber to fuse their droplets, necessitating high voltage values to span a larger area [21], these design droplets are tightly packed as they flow past the electrodes. Even with tightly packed droplets, isolated fusion events between adjacent droplets can occur, as long as the droplet interface where fusion takes place is parallel to the electrodes. For different types of droplet packing, different electrode orientations could be used to achieve this purpose. Fusion rates of around 10 per second can be obtained using this technique. In addition to the increased biocompatibility of this approach, an insulating layer of Poly(methyl methacrylate) coats the electrodes in the device, which reduces the chance of contamination, another significant concern for active fusion devices [22]. \nOne unique approach to active droplet fusion allows for the trapping and storage of an array of fused droplets, in order to observe a reaction or the behavior of a cell over time. The first droplet is trapped in a side compartment adjoining the main fluidic channel when a DC voltage is applied (Fig. 2.5a). Voltage, applied across the channel, induces a DEP force on the droplet that causes it to move in one direction or another, depending on the type of DEP force applied. Using the DC voltage again, this trapped droplet can be induced to move toward the main channel, where it can contact and fuse with a passing droplet. Once fused, the droplet returns to the side compartment as the DC voltage is switched off, and the droplet may be observed indefinitely in the side compartment. These structures are designed to keep the fused droplet trapped at lower continuous phase flow rates, but allow the compartments to be cleared when the continuous phase flow rate is increased [23].\nInstead of using electrodes to induce coalescence at the point of droplet contact, \nan alternative design imposes an opposite electrical charge on different populations of droplets, which then become fused together in the presence of an electrical field. As droplets are generated, either a positive or negative charge is imposed on them, such that droplets from one inlet become positively charged, while droplets from a second inlet become negatively charged. A potential disadvantage to this approach is that fused droplets become electrically neutral. In order to perform more than one fusion step, droplets would need to undergo charging after each fusion event [24]. \nExpanding upon a concept used to fuse droplets passively, one active fusion scheme induces pairing of droplets prior to fusion by generating droplets of different sizes. Smaller droplets move more rapidly through microfluidic channels, which cause them to catch up to and pair with larger droplets. Once paired, the droplets are fused controllably by a pair of electrodes across the microfluidic channel [25]. \nElectrowetting is another approach that has been used to manipulate droplets, inducing droplet formation as well as fusion. In this approach, droplets are positioned atop an array of individually addressable electrodes, and deform over the electrode when a voltage is applied, due to a minimum in the electric field that is induced over the electrode. Using computer software, the electrodes can be activated in a certain order to induce movement of the droplet. To fuse droplets using this technique, two droplets need only to be brought into close proximity using the electrode array. Although this technique offers very precise control over the movement of droplets, inter-droplet contamination is a concern, since the droplets wet the surface of the electrodes when they are trapped [26]. \nFor most applications, droplet fusion is desired to initiate a chemical reaction; however, it may be necessary for some applications to convert information contained in individual droplets into a continuous stream for the purpose of analysis of droplet contents. For this purpose, Fidalgo et al. designed a device whereby selected droplets in a stream of oil could be induced to merge with an adjacent aqueous stream. If a droplet is selected to merge with the aqueous stream, an electric field is applied, inducing a DEP force on the droplet which causes it to move into the aqueous stream [27]. \nOne particularly exciting application for droplet fusion technology is the ability to fuse liposomes or cells. Using a device with embedded electrodes, liposomes and prokaryotic cells were fused using a device which applied alternately AC and DC voltages. First, AC voltage is applied to align the liposomes or cells for fusion. This alignment is followed by the application of a DC voltage which fuses the liposomes or cells. Although this technique could find wide application in a wide variety of studies on cellular gene regulation, the fusion rate is relatively low at 75%, and the throughput of the technique is also very low, requiring 5 s alone to position liposomes close together, and another full second for the fusion event to occur [28]. \nRecently, electrofusion has also been used to combine reagents for the study of the kinetics of a biological reaction, such as the activity of the translated protein of the cotA laccase gene. Using electrodes on either side of the microfluidic channel, AC voltage was applied at a frequency of 30 kHz. Fusion events occurred at a rate of 3,000 per second, and a high fusion efficiency of 90% was achieved (Fig. 2.5b). This high fusion rate provided by this active droplet fusion scheme allows a more precise study of the kinetics of the reaction, since more samples are produced with a shorter time step between them than could be achieved using a passive droplet fusion device [29]. \nElectrical fields may also be used to introduce reagent into passing droplets, as demonstrated by Abate et al. A series of fluid-dispensing channels were oriented perpendicular to a main microfluidic channel, and each dispensing channel contained a set of electrodes. By momentarily applying an electrical field across a set of electrodes, reagent could be dispensed from that channel into droplets in the main microfluidic channel without the use of valves. The application of an electrical field also destabilizes the interface between phases, leading to fusion of the passing droplet with the injected reagent. The amount of fluid injected into passing droplets may be tuned by adjusting the pressure in the dispensing channel as well as the velocity of the passing droplets. Using this device, researchers were able to add reagent selectively into passing droplets at a rate of 10,000 droplets per second [30]."},{"_id":"3a749055616cbc410c000026","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":6.125,"parentId":null,"content":"#Methods for Droplet Splitting"},{"_id":"3a74b0f4616cbc410c000032","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a749055616cbc410c000026","content":"#Droplet Fission Basics [http://www.sciencedirect.com/science/article/pii/S0165993609002647 - @y21]\nDroplet fission has been a very important issue in droplet-based microfluidics systems. It generally includes the following aspects: reducing the droplet volume; controlling the concentration of chemicals inside the droplets [33]; and, producing arrays of droplets for high-throughput (Fig. 6) [34]. \nFission of droplets can be carried out controllably by hydrodynamic stress and a bifurcating junction. When the two-phase fluids in the main channel flow toward a bifurcating junction, the droplet is affected by the pressure and the shear strain arising from the flow. As long as the forces surpass the interface tension, fission occurs, so decreasing the inlet width of the main channel or constricting the channels at the branching points can increase the forces on a droplet and lead to its split [35]. The relative sizes of daughter droplets depend on the symmetry of the flow. If the flow is fully symmetric, equal forces will be exerted onto the two halves of the mother droplet, resulting in the creation of two equal-sized daughter droplets [34,36]. For asymmetric flow, the forces on the two halves of the mother droplet are proportional to the droplet surface area exposed to those stream lines, and the mother droplet tends to break up into two unequal daughter droplets. The volume of the daughter droplet therefore depends not only on channel resistances but also the volume of the mother droplet [33]. Under asymmetric flow, daughter droplets with different concentrations would be produced from a primary droplet if the concentration gradient of mother droplet was retained until fission occurred [33]."},{"_id":"3a756edf616cbc410c000039","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":2,"parentId":"3a749055616cbc410c000026","content":"##Passive Fission Methods\nPassive splitting of droplets involves appropriate continuous fluid and droplet velocity and also incorporate different channel geometries."},{"_id":"3a7580a1616cbc410c00003a","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a756edf616cbc410c000039","content":"###Geometry-Mediated Splitting [http://www.springer.com/cda/content/document/cda_downloaddocument/9781461432647-c1.pdf - @springer]\nLink et al. developed two simple methods to induce droplet fission, using only the geometry of the microchannels. In one device, a simple bifurcation of the main microfluidic channel is introduced in order to split droplets. Through experimentation, it was determined that droplet fission would occur at this bifurcation if the droplet is plug-like: that is, when the length of the droplet in the microchannel is greater than the circumference on the edge of the droplet. The droplet splits evenly if the resistances of the two daughter channels—downstream of the bifurcation— have the same fluidic resistance. Since fluidic resistance is proportional to microchannel length, according to the Hagen-Poiseuille equation, changing the length of one of the two daughter channels allows droplets to split unevenly. In this way, the volume ratio of the daughter droplets produced by the fission can be changed. Another design proposed by the group employed a large post near the middle of a microfluidic channel to induce droplet fission (Fig. 2.6a-d). By adjusting the position of this large post in the microchannel, the ratio of sizes of daughter droplets can be changed [33]. \nBuilding on this technology, another group used a repeating bifurcation structure to split a single parent droplet into 8 or 16 daughter droplets of nanoliter volumes. The bifurcation structure consists of a T-shaped junction, where the parent microfluidic channel meets the daughter microfluidic channels at an angle of 901. This group observed asymmetric splitting of droplets despite symmetric channel designs, in devices containing consecutive bifurcations. It was hypothesized that asymmetric droplet breakup was due to a high surface tension pressure relative to the pressure drop in the microchannel. They determined that asymmetric splitting in bifurcating junctions can be minimized by keeping the surface tension low, for example, by adding surfactants to the system, or increasing the flow rate through the device [34].\nUtilizing a different bifurcation design, a single droplet was split into 128 monodispersed droplets. In this design, the parent microfluidic channel splits into daughter channels at an angle of 451 forming a Y-shaped bifurcation junction (Fig. 2.6e). Hsieh et al. found that using a bifurcation channel angle of 451 reduced the asymmetric breakage of droplets, when compared to a design using an angle of 901. In addition, the use of droplet fission for a new application—the production of a large number of PEG microspheres—was demonstrated [35]. \nAnother approach to combating the problem of asymmetric droplet splitting involved the use of syringe pumps to withdraw fluid evenly from multiple outlets. In a device that split a single droplet into 8, fluid was withdrawn from 7 of the 8 outlets at 1/8 the rate of the inlet flow. The eighth outlet of the device was left open to remove any excess fluid from the device. This technique minimized the pressure differences between the outlet channels and as a result, the device produced droplets with a size coefficient of variation of 9.38% [31]. \nFinally, a liquid sample can be split into nanoliter volume plugs by feeding the liquid into a main channel that splits into several smaller, daughter channels. The liquid fills each smaller channel until it reaches a valve. Mielnik et al. used a hydrophobic valve to arrest the flow of fluid into each daughter channel, while a waste channel was placed downstream of the daughter channels to drain excess fluid [36]. Once filled, each daughter channel contains 335 nL of fluid that can be metered out of each channel for further processing. The series of daughter channels effectively splits a single sample plug into eight smaller plugs. Using this technique, a single nucleic acid sample from a patient was split into ten smaller plugs, and each plug could be screened against a different reagent, allowing simultaneous screening for multiple viruses [37]. "},{"_id":"3a75842e616cbc410c00003b","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":3,"parentId":"3a749055616cbc410c000026","content":"##Active Fission Methods\nActive splitting gives the opportunity to control splitting more precisely than the possibilities available passive methods. However, systems that utilize active fission require further control electronics."},{"_id":"3a758b17616cbc410c00003c","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a75842e616cbc410c00003b","content":"###Droplet Splitting Using Electrical Fields, Heat and Lasers[http://www.springer.com/cda/content/document/cda_downloaddocument/9781461432647-c1.pdf - @springer]\nWhile the aforementioned devices have the ability to split a droplet reliably into daughter droplets, the fission product volumes are constrained by the fixed geometry of these devices. Thus, several devices employing electrical fields, heat, and lasers have been developed to achieve more control over the droplet fission process and allow for dynamic adjustment of the daughter droplet volumes. In addition, such methods have the ability to \"switch\" droplets completely to one outlet or another, in lieu of executing droplet fission, so that only selected droplets may be divided if necessary. These additional functionalities come at the cost of a more complex device, but may be desirable or necessary, depending on the system's application. \nThe throughput of droplet fission can be raised dramatically through the use of electric fields to split droplets. Link et al. used a device similar in geometry to the previously developed passive devices with bifurcating junctions, but added electrodes to charge and induce droplet splitting. Electrodes are placed under the two daughter channels after the bifurcation junction, and an electrical field is established between them. Uncharged droplets enter the bifurcation junction and the electrical field. The droplets polarize in the field and divide at the bifurcation (Fig. 2.7a-c). Simultaneously, opposite charges are induced on the two daughter droplets. Additionally, the authors noticed that at higher electrical fields, no droplet splitting occurred and the entire parent droplet was diverted to one of the daughter channels. Such a phenomenon could be used to remove erroneous droplets, or control the number of volume of daughter droplets produced in a bifurcating design. While this technique allows high throughput of up to 100,000 Hz, the use of electrical fields may preclude the use of this technique for some applications where reagents may be damaged by electrical fields [24].\nDroplets may also be divided using a technique known as electrowetting-ondielectric (EWOD). In this technique, electrical potentials are applied to specific points on a dielectric surface in order to induce movement of droplets by changing the wetting ability and contact angle of the fluid. Numerous groups have demonstrated the use of EWOD for droplet splitting [38, 39], however, the detailed mechanism and use of this technique is beyond the scope of this text. \nOne unique method for inducing droplet splitting involves the use of a laser. To use this technique, a microfluidic channel containing a post near the middle of the channel is used. In the absence of the laser, droplets split evenly around the post and form two daughter droplets of equal volume. However, when the laser is applied to one side of the post, the droplet is induced to split asymmetrically. Heat from the laser causes a local increase in the surface tension on the droplet, which prevents forward movement of the droplet past the laser [40]. The laser acts to block the droplet, and can affect the volume of the daughter droplets produced based on the length of time that the laser is applied in this position. As with the electrical fields, a droplet can be \"switched\" into a single channel instead of divided, by increasing the laser power used [16]. Although novel, this technique may not deliver as high a throughput as the technique in which electrical fields were used to split droplets, and may suffer from the same biocompatibility issue as well. However, the use of a laser provides even greater control over the volume of daughter droplets produced and may prove useful in devices where very precise manipulation of droplets is required. \nFinally, microheaters integrated into microfluidic chips have been used to control droplet splitting and \"switch\" droplets to one of multiple downstream channels. In a technique similar to EWOD, Darhuber et al. used a technique called thermocapillary actuation, combined with chemical patterning of the surface of the device, to induce droplet splitting (Fig. 2.7d-g). The technique consists of stretching a fluid over a set of microheaters, activating the heaters sequentially to draw the fluid out, and then selectively turning off microheaters to induce splitting of the fluid [41]. Another group used an integrated microheater, positioned beneath one of the daughter channels (downstream of a bifurcation junction) to provide control over the volume of daughter droplets produced, as well as to allow switching of the droplet from one daughter channel to another. When the heater is turned on, a viscosity gradient is created and the viscosity of continuous phase in the heated daughter channel decreases. The fluidic resistance in the heated daughter channel is decreased owing to this decrease in viscosity. When a droplet reaches the bifurcation junction, a larger daughter droplet is produced in the heated daughter channel due to the difference in viscosity and interfacial tension between the two branches. By adjusting the temperature of the heater, different daughter droplet volumes can be produced. In addition, the use of an integrated microheater does not preclude the use of biological materials, since the heater works sufficiently for dividing droplets at 361C. At slightly higher temperatures, the droplet does not split at the junction, but the entire droplet is carried or switched to the daughter branch containing the heater, providing a simple sorting mechanism [42]."},{"_id":"3a6ff0808bda8f38d0000025","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":6.25,"parentId":null,"content":"#Investigation of Droplets Merging\nGenerally, the need of optical microscope systems are evident.\n[@TODO]"},{"_id":"3a74910e616cbc410c000027","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":6.4375,"parentId":null,"content":"#Investigation of Droplets Splitting\n[@TODO]"},{"_id":"3a746869616cbc410c000017","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":6.625,"parentId":null,"content":"#Key Application Areas of Microfluidics [http://en.wikipedia.org/wiki/Microfluidics - @wikipedia]\nMicrofluidic structures include micropneumatic systems, i.e. microsystems for the handling of off-chip fluids (liquid pumps, gas valves, etc.), and microfluidic structures for the on-chip handling of nano- and picolitre volumes.[8] To date, the most successful commercial application of microfluidics is the inkjet printhead. Significant research has been applied to the application of microfluidics for the production of industrially relevant quantities of material.[9]\nAdvances in microfluidics technology are revolutionizing molecular biology procedures for enzymatic analysis (e.g., glucose and lactate assays), DNA analysis (e.g., polymerase chain reaction and high-throughput sequencing), and proteomics. The basic idea of microfluidic biochips is to integrate assay operations such as detection, as well as sample pre-treatment and sample preparation on one chip.[10][11]\nAn emerging application area for biochips is clinical pathology, especially the immediate point-of-care diagnosis of diseases. In addition, microfluidics-based devices, capable of continuous sampling and real-time testing of air/water samples for biochemical toxins and other dangerous pathogens, can serve as an always-on \"bio-smoke alarm\" for early warning."},{"_id":"3a746d75616cbc410c000018","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a746869616cbc410c000017","content":"##Continuous-flow microfluidics [http://en.wikipedia.org/wiki/Microfluidics - @wikipedia]\nThese technologies are based on the manipulation of continuous liquid flow through microfabricated channels. Actuation of liquid flow is implemented either by external pressure sources, external mechanical pumps, integrated mechanical micropumps, or by combinations of capillary forces and electrokinetic mechanisms.[12][13] Continuous-flow microfluidic operation is the mainstream approach because it is easy to implement and less sensitive to protein fouling problems. Continuous-flow devices are adequate for many well-defined and simple biochemical applications, and for certain tasks such as chemical separation, but they are less suitable for tasks requiring a high degree of flexibility or ineffect fluid manipulations. These closed-channel systems are inherently difficult to integrate and scale because the parameters that govern flow field vary along the flow path making the fluid flow at any one location dependent on the properties of the entire system. Permanently etched microstructures also lead to limited reconfigurability and poor fault tolerance capability.\nProcess monitoring capabilities in continuous-flow systems can be achieved with highly sensitive microfluidic flow sensors based on MEMS technology which offer resolutions down to the nanoliter range."},{"_id":"3a747009616cbc410c000019","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":2,"parentId":"3a746869616cbc410c000017","content":"##Droplet-based microfluidics [http://en.wikipedia.org/wiki/Microfluidics - @wikipedia]\nDroplet-based microfluidics as a subcategory of microfluidics in contrast with continuous microfluidics has the distinction of manipulating discrete volumes of fluids in immiscible phases with low Reynolds number and laminar flow regimes. Interest in droplet-based microfluidics systems has been growing substantially in past decades. Microdroplets offer the feasibility of handling miniature volumes of fluids conveniently, provide better mixing and are suitable for high throughput experiments.[14] Exploiting the benefits of droplet based microfluidics efficiently requires a deep understanding of droplet generation,[15] droplet motion, droplet merging, and droplet breakup[16]"},{"_id":"3a74726e616cbc410c00001a","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":3,"parentId":"3a746869616cbc410c000017","content":"##Digital microfluidics [http://en.wikipedia.org/wiki/Microfluidics - @wikipedia]\nAlternatives to the above closed-channel continuous-flow systems include novel open structures, where discrete, independently controllable droplets are manipulated on a substrate using electrowetting. Following the analogy of digital microelectronics, this approach is referred to as digital microfluidics. Le Pesant et al. pioneered the use of electrocapillary forces to move droplets on a digital track.[17] The \"fluid transistor\" pioneered by Cytonix[18] also played a role. The technology was subsequently commercialized by Duke University. By using discrete unit-volume droplets,[15] a microfluidic function can be reduced to a set of repeated basic operations, i.e., moving one unit of fluid over one unit of distance. This \"digitization\" method facilitates the use of a hierarchical and cell-based approach for microfluidic biochip design. Therefore, digital microfluidics offers a flexible and scalable system architecture as well as high fault-tolerance capability. Moreover, because each droplet can be controlled independently, these systems also have dynamic reconfigurability, whereby groups of unit cells in a microfluidic array can be reconfigured to change their functionality during the concurrent execution of a set of bioassays. Although droplets are manipulated in confined microfluidic channels, since the control on droplets is not independent, it should not be confused as \"digital microfluidics\". One common actuation method for digital microfluidics is electrowetting-on-dielectric (EWOD). Many lab-on-a-chip applications have been demonstrated within the digital microfluidics paradigm using electrowetting. However, recently other techniques for droplet manipulation have also been demonstrated using Surface Acoustic Waves, optoelectrowetting, mechanical actuation,[19] etc."},{"_id":"3a7473a9616cbc410c00001b","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":4,"parentId":"3a746869616cbc410c000017","content":"##DNA chips (microarrays) [http://en.wikipedia.org/wiki/Microfluidics - @wikipedia]\nEarly biochips were based on the idea of a DNA microarray, e.g., the GeneChip DNAarray from Affymetrix, which is a piece of glass, plastic or silicon substrate on which pieces of DNA (probes) are affixed in a microscopic array. Similar to a DNA microarray, a protein array is a miniature array where a multitude of different capture agents, most frequently monoclonal antibodies, are deposited on a chip surface; they are used to determine the presence and/or amount of proteins in biological samples, e.g., blood. A drawback of DNA and protein arrays is that they are neither reconfigurable nor scalable after manufacture. Digital microfluidics has been described as a means for carrying out Digital PCR."},{"_id":"3a7474fd616cbc410c00001c","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":5,"parentId":"3a746869616cbc410c000017","content":"##Molecular biology [http://en.wikipedia.org/wiki/Microfluidics - @wikipedia]\nIn addition to microarrays biochips have been designed for two-dimensional electrophoresis,[20] transcriptome analysis,[21] and PCR amplification.[22] Other applications include various electrophoresis and liquid chromatography applications for proteins and DNA, cell separation, in particular blood cell separation, protein analysis, cell manipulation and analysis including cell viability analysis [23] and microorganism capturing.[11]"},{"_id":"3a74765e616cbc410c00001d","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":6,"parentId":"3a746869616cbc410c000017","content":"##Evolutionary biology [http://en.wikipedia.org/wiki/Microfluidics - @wikipedia]\nBy combining microfluidics with landscape ecology and nanofluidics, a nano/micro fabricated fluidic landscape can be constructed by building local patches of bacterial habitat and connecting them by dispersal corridors. The resulting landscapes can be used as physical implementations of an adaptive landscape,[24] by generating a spatial mosaic of patches of opportunity distributed in space and time. The patchy nature of these fluidic landscapes allows for the study of adapting bacterial cells in a metapopulation system. The evolutionary ecology of these bacterial systems in these synthetic ecosystems allows for using biophysics to address questions in evolutionary biology."},{"_id":"3a747738616cbc410c00001e","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":7,"parentId":"3a746869616cbc410c000017","content":"##Microbial behavior [http://en.wikipedia.org/wiki/Microfluidics - @wikipedia]\nThe ability to create precise and carefully controlled chemoattractant gradients makes microfluidics the ideal tool to study motility, chemotaxis and the ability to evolve / develop resistance to antibiotics in small populations of microorganisms and in a short period of time. These microorganisms including bacteria [25] and the broad range of organisms that form the marine microbial loop,[26] responsible for regulating much of the oceans' biogeochemistry."},{"_id":"3a7478d1616cbc410c00001f","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":8,"parentId":"3a746869616cbc410c000017","content":"##Cellular biophysics [http://en.wikipedia.org/wiki/Microfluidics - @wikipedia]\nBy rectifying the motion of individual swimming bacteria,[27] microfluidic structures can be used to extract mechanical motion from a population of motile bacterial cells.[28] This way, bacteria-powered rotors can be built.[29][30]"},{"_id":"3a7479f6616cbc410c000020","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":9,"parentId":"3a746869616cbc410c000017","content":"##Optics [http://en.wikipedia.org/wiki/Microfluidics - @wikipedia]\nThe merger of microfluidics and optics is typical known as optofluidics. Examples of optofluidic devices :\nTuneable Microlens Array[31][32]\nOptofluidic Microscopes [33][34][35]"},{"_id":"3a747b12616cbc410c000021","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":10,"parentId":"3a746869616cbc410c000017","content":"##Acoustic droplet ejection (ADE) [http://en.wikipedia.org/wiki/Microfluidics - @wikipedia]\nAcoustic droplet ejection uses a pulse of ultrasound to move low volumes of fluids (typically nanoliters or picoliters) without any physical contact. This technology focuses acoustic energy into a fluid sample in order to eject droplets as small as a millionth of a millionth of a liter (picoliter = 10−12 liter). ADE technology is a very gentle process, and it can be used to transfer proteins, high molecular weight DNA and live cells without damage or loss of viability. This feature makes the technology suitable for a wide variety of applications including proteomics and cell-based assays."},{"_id":"3a747c8c616cbc410c000022","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":11,"parentId":"3a746869616cbc410c000017","content":"##Fuel cells [http://en.wikipedia.org/wiki/Microfluidics - @wikipedia]\nMicrofluidic fuel cells can use laminar flow to separate the fuel and its oxidant to control the interaction of the two fluids without a physical barrier as would be required in conventional fuel cells.[36][37][38]"},{"_id":"3a747dd9616cbc410c000023","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":12,"parentId":"3a746869616cbc410c000017","content":"##A tool for cell biological research [http://en.wikipedia.org/wiki/Microfluidics - @wikipedia]\nMicrofluidic technology is creating powerful tools for cell biologists to control the complete cellular environment, leading to new questions and new discoveries.[39] Many diverse advantages of this technology for microbiology are listed below:\nSingle cell studies [40]\nMicroenvironmental control: ranging from mechanical environment [41] to chemical environment [42]\nPrecise spatiotemporal concentration gradients [43]\nMechanical deformation\nForce measurements of adherent cells\nConfining cells [44]\nExerting a controlled force [44][45]\nFast and precise temperature control [46][47]\nElectric field integration [44]\nCell culture [48]\nPlant on a chip and plant tissue culture [49]\nAntibiotic resistance: microfluidic devices can be used as heterogeneous environments for microorganisms. In an heterogeneous environment is easier for a microorganism to evolve. This can be useful for testing the acceleration of evolution of a microorganism / for testing the development of antibiotic resistance."},{"_id":"3a747f42616cbc410c000024","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":13,"parentId":"3a746869616cbc410c000017","content":"##Future Directions [http://en.wikipedia.org/wiki/Microfluidics - @wikipedia]\nOn-chip characterization:[50]\nMicrofluidics in the classroom: On-chip acid-base titrations [51]"},{"_id":"3a6fedaf8bda8f38d0000024","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":7,"parentId":null,"content":"#Applications of Droplets Merging\n[@TODO]\nThere are several biological application that contains proper reaction timing, etc..."},{"_id":"3a7491c5616cbc410c000028","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":8,"parentId":null,"content":"#Application of Droplets Splitting\n[@TODO]"},{"_id":"3a7493aa616cbc410c000029","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":9,"parentId":null,"content":"#Compatison of Merging Techniques\n[@TODO]"},{"_id":"3a74942a616cbc410c00002a","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":10,"parentId":null,"content":"#Comparison of Splitting Techniques\n[@TODO]"},{"_id":"3a7494a8616cbc410c00002b","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":11,"parentId":null,"content":"#Suggestion for Droplet Merging Subsystem\n[@TODO]"},{"_id":"3a75c6f4616cbc410c000044","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a7494a8616cbc410c00002b","content":"##Goal of Merging\nMerging of droplets deals not only with volume modification but also can mix reagents of different droplet types."},{"_id":"3aaac5e11e4334527800004f","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1.5,"parentId":"3a7494a8616cbc410c00002b","content":"##Fusion of droplets [http://www.ncbi.nlm.nih.gov/pubmed/15269794 - @168]\nTo coalesce two or more droplets in the microfludic channels \nrequires the removal of the continuous phase separating them. When two droplets come into close contact, a thin liquid bridge forms between the droplets due to the attractions between molecules. The high curvature meniscus formed around the bridge creates an imbalance of the surface tension that quickly coalesces the two droplets.43 To form the initial contacts between droplets, fluid between droplets must be removed. This can be achieved through expanding the channel junction as shown in Fig. 11a. The volume fluid between droplets can also be reduced through setting faster droplet generation rate. \nWe have experimented with the three different channel geome- tries as shown in Fig. 11 containing either a straight expansion, a tapered expansion, or a flow rectifying design in which droplets are focused and fused in the middle of the junction by balancing the net shear forces. Droplet fusion in the rectangular expansion design works at a limited range of rates and sizes determined by the length and the width of the expansion. The tapered expansion, which is equivalent to a series combination of rectangular ones, works at a wider range of sizes and rates but can allow undesired multiple fusions. Among the three designs, the flow rectifying design provides the most flexibility in fusing droplets as demonstrated in Fig. 12. Simultaneous fusion of three or more droplets have also been observed with this design. The mechanism of this type of fusion qualitatively agrees with mechanism described by Niko- layev et al.,44 in which the fusion of two droplets initiates an internal flow inside the droplet that induces additional coalescence of surrounding droplets. \nThe flow rectifying design allows the fluid volume between drops to be separated at controllable rates, whereas other designs provide fixed rates based on the width of the expansion. In the flow rectifying design, the separating fluid volume flows into the upper and lower channels at a rate controlled by the resistance of the identical upper and lower channels. This allows equal fluid volume to be removed by the upper and lower channels, but does not generate net force along the vertical axis. By controlling the separating flow rates, the speed at which droplets approach each other at the junction can be tuned to allow desired droplet fusion to occur. \nIn a more complex system involving fusion of different types of droplets, each type of reactant inside the fused droplet can be arranged in order. An example of such mixing is shown in Fig. 13, in which if the dye droplet enters the junction first, the dye content becomes more concentrated at the head of the fused droplet and visa versa. \nAs demonstrated in an earlier section, droplet fission can be used to control the chemical concentration of each daughter droplets. Since fission is perpendicular to the direction of flow, the chemical concentrations distributed to the daughter droplets are dependent on the chemical gradient of the mother droplet oriented in the direction of flow. The chemical gradient generated using co-flow stream is parallel to the direction of flow, while the chemical gradient generated after droplet fusion in flow rectifying design is perpendicular to the direction of flow. This provides additional freedom to control how the partial concentrations of the chemicals in the original droplet divide among the daughter droplets. "},{"_id":"3a75caa0616cbc410c000045","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":2,"parentId":"3a7494a8616cbc410c00002b","content":"##Chosen Parameters\n"},{"_id":"3a7495a5616cbc410c00002c","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":12,"parentId":null,"content":"#Suggestion for Droplet Splitting Subsystem\n[@TODO]"},{"_id":"3a75be92616cbc410c000042","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a7495a5616cbc410c00002c","content":"##Goal of Splitting\nThe final goal of microdroplet splitter is an.\nIt needs first to be simply fabricated and easily tested in laboratory."},{"_id":"3aaabd071e4334527800004e","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1.5,"parentId":"3a7495a5616cbc410c00002c","content":"##Control of droplet fission [http://www.ncbi.nlm.nih.gov/pubmed/15269794 - @168]\nDroplet break-up events can be used to reduce the size of generated \ndroplets. For droplets generated with chemical gradients,4 the reaction time and chemical concentration in each of the daughter droplets depend on the fission mechanism. \nThe mechanism for droplet break-up in immiscible shearing flows has been thoroughly investigated.37-41 Essentially, droplet break-up occurs when the viscous stress exerted by the continuous phase induces a critical asymmetric stress on the droplet causing an imbalance of the surfacing tension.37 This is generally described by the capillary number, here defined as Ca = hv/g,35 where h is the viscosity of the oil phase, v is the velocity of the droplet entering the junction, and g is the interfacial tension between water and oil. When Ca is greater than the critical capillary number (Ccr), droplet fission occurs. Since Ccr depends on the type of shear strain exerted by the flow, Ccr required to produce droplet fission can be varied accordingly by changing the input flow rates of the mother channel Q0 and the output flow rates of the two daughter channels (Q1 and Q2) as shown in Fig. 1. Since the droplet moves at about the same velocity as the continuous oil phase, v of droplet is equal to the ratio of the applied oil flow rate to the cross sectional area. Previous studies on symmetric break-up conditions by Link et al.35 showed that the critical capillary number varies according to Ccr = ae0(1/ e02/3 21)2, where a is a dimensionless constant equal to 1 for square hannels, and e0 is the initial extension ratio which expressed using variables from Fig. 1 is Ld/pWi. \nWhen the flow is fully symmetric, the forces exerted on the two halves of the mother droplet are equal, and if the droplet is not breakable by the flow, the droplets are randomly distributed into the daughter channels. In the case when the droplet is breakable by flow, droplet fission creates two equal sized daughter droplets as shown in the insert of Fig. 2. The three inlet dimensions studied here all have channel heights, h, equal to 40 mm, and consist of one square channel cross section and two rectangular channel cross sections with widths Wi equal to 70 mm and 100 mm, respectively. In comparing the square and rectangular channel, the equivalent width of a square with same cross section is used to determine the extension ratio for rectangular channels. The results are shown in Fig. 2. For square channel the criteria for droplet break-up agrees strongly with Link et al.35 For channels with different geometries, Ccr with a = 1 does not predict droplet break-up. In general we found that when the height of the channel is constant, the range of breakable droplet sizes decreases with increasing inlet channel width as indicated by the observed smallest droplet breaking \ndiameter shown in Table 1. Under a constant Qo, decreasing the inlet width of the channel increases the shear stress exerted on the droplet. As a result when the width of the mother channel is narrow, smaller minimum break-up diameter is observed. \nUnder asymmetric flow, the streamlines divide according to the flow rates inside the daughter channels. When a droplet traveling along the center of the channel, reaches the bifurcating junction, the pressure and shear forces that pull the droplet into each daughter channel are proportional to the droplet surface area exposed to those stream lines. If the forces are larger than the surface tension of the droplet, it splits into two drops of unequal sizes. \nIn designing the asymmetric junction, the inlet width and the height of the channel are minimized to be 40 mm to allow the widest range of breakable droplet sizes. The width difference of the daughter channels are used to vary the bifurcating flow. By \ncontrolling the respective width ratio (Wd1/Wd2) to be 30 mm/60 mm, 30 mm/90 mm, and 30 mm/120 mm, the flow bifurcates according to the following (Q1/Q2) ratios: 1/1.8, 1/2.1, and 1/2.2 \nThe range of minimum breakable droplet size for asymmetric flow is presented in Table 2 as a set of extensional numbers with an upper limit of eu, for droplets that break and a lower limit of el, for droplets that don't break. The upper and lower limits of these extensional numbers would show up in the lower right corner of Fig. 2 indicating that the break-up under these asymmetric conditions occur at a much higher extensional number than under symmetric break-up conditions. This agrees with qualitative observation of Link et al.,35 and is consistent with other previous studies, which showed that critical capillary number increases as flow becomes more asymmetric.37-40 \nSince the lengths of a droplet in channel is directly proportional to its volume, the volume ratio of the daughter drops under asymmetric fission can be determined by the length ratio of the two daughter drops. Previous observations by Song et al. and Link et al., suggested that daughter droplet volume is inversely propor- tional to the resistance of the channels. Our data suggested that daughter droplet volume depends on both the channel resistances and the volume of the mother drop. In Fig. 3, the ratios of larger-to- smaller daughter droplets (LS/LD) after asymmetric fission indicated that the ratio of daughter droplet volumes changes with the size of the mother drop. If the ratio is independent of the sizes of the mother droplets, then the smaller daughter droplet in the bottom photo of Fig. 3 would be smaller than the corresponding daughter droplet in the upper photo. While we did not specifically verify the droplet volume ratio that is equivalent to the ratio of channel resistances,35 it appears from Fig. 3 that ratio decreases with decreases in mother droplet size, which suggests that the daughter volume ratio identical to ratio of bifurcating flow is achievable for smaller droplet sizes. \nFor many biological assays, it is desirable to rapidly sort biological samples into various volumes and concentrations for analytical and combinatorial purposes. This is often difficult and cumbersome with current electrode-based droplet platforms, as it would require programmed synchronization of many electrodes to process a single stream of droplets13 In the droplet fission system presented here, a single bifurcating junction can create two organized streams of droplets with sizes controlled by the design of the bifurcating flow. With multiple bifurcating junctions, parallel streams of controlled liquid volume in droplets can be rapidly analyzed. Droplets with diameters approaching ~ 1 mm or less, can also be generated during near critical break-up conditions. These droplets are generated through multiple asymmetric fission junc- tions using the channel shown in Fig. 4. "},{"_id":"3a75c44a616cbc410c000043","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":2,"parentId":"3a7495a5616cbc410c00002c","content":"##Chosen Parameters\n"},{"_id":"3a749753616cbc410c00002e","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":12.5,"parentId":null,"content":"#Future of the Project\n[@TODO]"},{"_id":"3a74960c616cbc410c00002d","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":13,"parentId":null,"content":"#Conclusion"},{"_id":"3a759d5b616cbc410c000041","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":1,"parentId":"3a74960c616cbc410c00002d","content":"##Summary [http://www.springer.com/cda/content/document/cda_downloaddocument/9781461432647-c1.pdf - @springer]\nAlthough many varied and creative strategies have been devised for the manipulation of droplets—including the combination, separation, mixing, and sorting of these droplets—the potential for integration of these techniques into a complete processing device is what would eventually revolutionize the field and change the paradigm of how biological and chemical assays are carried out. Attempts to combine several droplet manipulation steps on chip have been successful for the execution of biological assays, but these techniques often depend on off-chip equipment for sample preparation or droplet storage [29]. The transition of microfluidic devices from a pursuit largely backed by academic labs to one endorsed and supported by industry will rely on the continued integration of multiple droplet processing steps in a single device. With the continued development of integrated microfluidic devices for droplet processing will come a reduction in processing time due to automation, a decrease in contamination potential by reducing manual handling steps, and a reduction of the cost of assays and reactions, due to a minimal consumption of all reagents involved. "},{"_id":"3a74983b616cbc410c00002f","treeId":"38c8d03272f07c8c8b00001d","seq":1,"position":14,"parentId":null,"content":"#Acknowledgements\n[@TODO]"}],"tree":{"_id":"38c8d03272f07c8c8b00001d","name":"Splitting and Merging in Microfluidics","publicUrl":"thesis-1-4-aidn5h-splitting-and-merging-in-microfluidics-ett-mahara-2013-14-1-uf"}}