Localized electric field induced transition and miniaturization of two-phase flow patterns inside microchannels.

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Localized Electric Field Induced Transition and Miniaturization of Two-Phase Flow Patterns inside Microchannels

Abhinav Sharma,1 Vijeet Tiwari,1 Vineet Kumar,1 Tapas Kumar Mandal,*1,2 Dipankar Bandyopadhay*1,2 1

Department of Chemical Engineering, Indian Institute of Technology Guwahati, India. 2

Centre for Nanotechnology, Indian Institute of Technology Guwahati, India

*

Author to whom correspondence to be addressed.

Email: [email protected],

[email protected]

Abstract Strategic application of external electrostatic field on a pressure-driven two-phase flow inside a microchannel can transform the stratified or slug flow patterns into droplets. The localized electrohydrodynamic stress at the interface of the immiscible liquids can engender a liquiddielectrophoretic deformation, which disrupts the balance of the viscous, capillary, and inertial forces of a pressure-driven flow to engender such flow morphologies. Interestingly, the size, shape, and frequency of the droplets can be tuned by varying the field intensity, location of the electric field, surface properties of the channel or fluids, viscosity ratio of the fluids, and the flow-ratio of the phases. Higher field intensity with lower interfacial tension is found to facilitate the oil droplet formation with a higher throughput inside the hydrophilic microchannels. The method is successful in breaking down the regular pressure-driven flow

Received:09-Feb-2014; Revised: 01-Jul-2014; Accepted: 10-Jul-2014 This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1002/elps.201400066. This article is protected by copyright. All rights reserved.


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patterns even when the fluid inlets are exchanged in the microchannel. The simulations identify the conditions to develop interesting flow morphologies such as, (i) an array of miniaturized spherical or hemispherical or elongated oil drops in continuous water phase, (ii) ‘oil-in-water’ microemulsion with varying size and shape of oil droplets. The results reported can be of significance in improving the efficiency of multiphase microreactors where the flow patterns composed of droplets are preferred because of the availability of higher interfacial area for reactions or heat and mass exchange.

Key words: microchannel; electric field; multiphase flow; flow patterns.

1 Introduction Recent advances in the technologies are experiencing a paradigm shift from the macro to the microscale because of the advantages such as portability, faster analysis and response times, superior process control, multi-tasking by parallelization of events in a compact space, and disposability. For common engineering practices the microscale devices are now more preferred because they can handle significantly less amount of samples for analysis, ensuring the availability of higher surface to volume ratio for the mass or momentum exchange [1–6]. In this context, the flow morphologies of the microscale multiphase flows have been studied extensively for their prominence in the biological analyses [1, 2], microchip technologies [3], microfluidic devices [4], flow cytometry [5], and microreactors [6]. The flow physics in the highly confined microchannels is rather unique due to the dominance of the capillary and frictional forces over the inertial and the gravitational influences [7, 8]. The two-phase microscale flows have also drawn considerable scientific attention because the interplay between the governing forces can lead to interesting transitions in the flow patterns [9-13]. A

This article is protected by copyright. All rights reserved.


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host of fascinating flow behaviors has been reported in the literature, which include the pathways to form drop or bubble dispersions [4, 9], ordered to chaotic transitions of interfacial patterns [14], folding and swirling of the flow-threads [15-17], production of liquid vesicles [18], mixing [19], and particle synthesis [20]. A number of review articles ably summarize the open issues related to the microscale multiphase flows [21-26]. The multiphase flows inside the microfluidic devices can largely be divided into liquid-liquid and gas-liquid configurations in which the latter is perhaps the most widely studied and well understood [27-32]. In comparison, the liquid-liquid configurations have drawn much less attention until in the recent times even though they are associated with some exciting flow behaviors [33-36]. The weaker capillarity at the interface combined with the characteristic viscosity or density stratification have enabled the liquid-liquid configurations to be separated from the similar gas-liquid systems. While the gas to fluid viscosity or density ratio is always less than unity for the gas-liquid configurations, the same is not always true for the liquidliquid flows. Further, the interfacial tension of the liquid-liquid configuration is at least an order of magnitude lower than the similar gas-liquid systems. In addition to this, the external field induced transport behaviors of the liquid-liquid flows find important applications in microscale pumping, mixing, separation, reaction, heat and mass transfer [37-43]. Recent works indicate that the influence of an external electric field can cause interesting transitions in the liquid-liquid multiphase flow patterns due to the electrohydrodynamic (EHD) stress at the interface originating from the accumulation of induced dipoles or free charges [44-55]. The studies reflect that the use of external electrostatic field can certainly, (i) cause a dielectrophoretic deformation at the interface of a two-phase configuration to develop unique flow patterns, (ii) alter the surface to volume ratios of the morphologies, and (iii) regulate the residence time of the different flow patterns inside the channel. Importantly, these features can easily be exploited to improve the efficiency of the microscale mixers, emulsifiers,



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reactors, and heat-exchangers. However, until now the major challenges have been the developments of, (a) experimental methodologies to fabricate and characterize these configurations and (b) computational techniques for the theoretical analyses. A number of recent works suggest that the field induced two-phase flows can be explored through experiments combined with computations. For example, the Poisson’s equation for the electric field coupled with the Stokes equation for the flow are solved using a boundaryintegral technique [48] to analyze the experimental results on the electric field induced breakup of droplets [44]. The electric field induced deformation of the drops having leaky dielectric, perfectly dielectric, and constant charge properties have also been studied employing the finite element or finite volume methods [49-52]. In such computations, the free-surface is tracked through either volume-of-fluid (VOF) or level-set (CLSVOF) method, while the Lattice-Boltzmann method (LBM) is found to be devoid of the complexities associated to the interface tracking methods [53]. Previous studies indicate that the phasefield method can be another alternative to accurately track the spatiotemporally deforming interfaces at lesser computational cost [55-62]. Importantly, until now, most of the computational studies focus on the field induced deformation of the stationary flow configurations. The influence of external field on the evolving flow morphologies in the microfluidic devices requires far more attention because they can significantly improve the efficiency of different microscale processes [46, 54]. A very recent experimental study [63] demonstrates the size of the dispersed droplets inside a flow-focusing microchannel can be controlled with the help of an external alternating current (AC) electric field. In particular, the regimes of dispersed droplet production were obtained by tuning the conductivity of the dispersed phase and the frequency of the electric field at lower potentials. In the present study, we computationally explore the strategies to disintegrate the pressuredriven flow patterns into miniaturized droplets with the help of a direct current (DC) external



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electric field inside the ‘T’ shaped microchannels. Figure 1 schematically shows the geometry considered in which the inlets allow the immiscible fluids to enter into the flow domain and pass through the outlet. To generate the electric field, a pair of electrodes is strategically placed along the channel walls in the downstream from the ‘T’ junction of the channel. The pair of electrodes helps in developing the local EHD stress at the liquid-liquid interface when the fluids move inside the channel. The EHD governing equations and boundary conditions are solved employing finite element method while the phase field method is incorporated to track the deforming interface. The study highlights that the localized electric field can indeed lead to droplet flow patterns under the flow conditions where a pressure-driven flow develops stratified, slug, or plug flow patterns. To emphasize the advantage of the proposed methodology, we also present a parametric study with the variations in the flow rate, viscosity, dielectric constant, contact angle of the fluids on the channel wall, interfacial tension between the fluids, and the intensity of the electric field. The method is found to be successful in breaking the regular pressure-driven flow patterns into a number of interesting flow morphologies such as, an array of spherical or hemispherical or elongated oil drops in continuous water phase, and ‘oil-in-water’ microemulsion. The strategies discussed in this study are versatile in a sense that they can easily be integrated with any microdevice without disturbing the main course of action.

2 Materials and methods 2.1 Governing Equations: Figure 1 shows the geometry of a ‘T’ shaped microchannel with the locations and dimensions of the inlets, outlet, and the electrodes for the electric field. The liquid phases are assumed to be perfectly dielectric, immiscible, Newtonian, and incompressible. The gravitational force is acting in the negative y-direction. The following



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continuity and equations of motion have been employed to describe the motion of the ith phase inside the microchannel,

  ui  0 ,

(1)

  ui  ui  ui   pi     τi  Mi   fst   g .

(2)

Here, the subscript i = 1 denotes oil phase and 2 denotes the water phase. The over-dot symbol denotes the time derivative. The notations u i , i , i , and pi denote the velocity vector, density, viscosity, and pressure of the ith phase. The notation g is the acceleration due





to gravity vector and the constitutive relation for a Newtonian fluid is, τi  i ui  uiT . The surface tension force is defined as a product of the chemical potential G and the gradient of the phase field (  ) as, f st  G . The phase field method has been employed to track the interface [62, 64, 65]. The surface tension force is determined by minimizing the total free energy inside fluid domain, which is expressed as a function of the phase field variable (  ),

1   F      f      2  dV . 2  V

(3)

Where, V is the volume of the liquid domain consisting of both oil and water phase. The total free

energy,

F   ,

is

described

in

terms

of

the

double

well

potential,

f     / 4 N 2  2  1 , and surface energy. In order to calculate the surface energy, the 2





mixing energy density is evaluated as,    3 N  / 2 2 where  is the surface tension and the parameter N determines the thickness of the diffused interface between the fluids. The chemical potential is defined as

a derivative of the free

energy functional,

G  F      2    2  1 / N 2  . The phase field transport equation is written in the form of Cahn-Hilliard equation as,



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  ui       G  .

(4)

The transport variable for the phase field (  ) acquires a value of 1 in the water and 1 in the oil phase and  is the mobility of the interface. The physical properties i , i , and  i of the ith

phase

are

employed

to

  0.5  1 1     2 1    ,

evaluate

the

interfacial

  0.5 1 1     2 1    ,

properties

as, and

  0.5 1 1      2 1    . The volume fractions are defined as the functions of the phase field variable as, V f 1  0.5 1    and V f 2  0.5 1    . The typical characteristic times for the electrical field, magnetic field, and a friction dominated flow are, tE   i 0 /  i , tM  i 0 i l 2 , and tP  i l 2 / i , respectively. Here, l is the characteristic length scale, which can be the diameter of the channel (~ 10-4 m). For the dielectric fluids, the typical magnitudes for the electrical conductivity,  i is ~10-6 - 10-9 S m1

, the magnetic permeability, i 0 is ~10-6 S m-1, and the dielectric permeability,  i 0 is ~10-

11

C2 N−1 m−2. The parameter space ensures that, tP  tE  tM , for which the electrostatic

approximation remains valid [66]. Further, the magnitude of the dimensionless number,

   0 E0 / el n0 K  1, ensures that the fluids are electrically neutral under the influence of the external electrostatic field [66]. The typical order of magnitudes for the electric field intensity ( E0 ), charge of an electron (e), and the ionic concentration ( n0 K ) can be considered as, ~106 V m-1, ~10-19 C and ~1020, respectively. In the absence of any magnetic field, the irrotational (   Ei  0 ) electric field (Ei) is expressed in terms of the electric potential (Vi) as, Ei  Vi , which leads to the governing Laplace equation for the electrostatic field, 2Vi  0 , following the Gauss’s law (   Ei  0 ). The Maxwell’s stress for the electric field is, Mi   0 i Ei  Ei  0.5  Ei  Ei  I  , where I refers to the identity tensor.



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Here the symbols  0 and  i are the permittivity of the free space and the dielectric constant of the ith layer. 2.2 Boundary Conditions: Constant potential boundary conditions are enforced at the electrodes as, Vi = 0, at the cathode and, Vi = V0, at the anode. Uniform velocity normal to the cross-sections are employed at the horizontal and the vertical inlets, vi = U. The default pressure outlet boundary condition is enforced at the outlet. The walls of the channels are assumed to be partially wetting and impermeable. The equilibrium contact angle of the water droplet confined by the oil phase resting on the channel wall (θ) is set to three different values, 45°, 90°, and 135° to study the effect of wettability. 2.3 Solution Methodology: We consider two-dimensional (2-D) microchannels of 100 µm widths and three-dimensional (3-D) microchannels of square (100 µm × 100 µm) crosssections. The length of the microchannel from the inlet to the outlet is 1.4 mm. The electrodes are placed 200 micron downstream from the ‘T’ junction having length, 50 µm in 2-D and area 50 µm × 100 µm in 3-D. The 2-D (3-D) geometry is divided into 7260 (46962) quadrilateral (tetrahedral) elements to obtain the grid independent solutions. The unsteady governing equations together with the boundary conditions are solved using the commercially available COMSOL multiphysics software based on the finite element method [65]. In this method, the spatial terms of the governing equations are initially discretized to obtain an ordinary differential equation (ODE) in time, which is time-marched to obtain the evolution of the flow patterns. We employ the built-in Galerkin least-square (GLS) method, stabilized through streamline and crosswind diffusions, to discretize nonlinear convective diffusion equations. The second order elements for velocity and first order elements for pressure are used for the accurate calculations of the gradients. The incremental pressure correction scheme for the segregated predictor-corrector method is employed to obtain the velocity and pressure profiles for the incompressible flow. The backward Euler scheme is utilized for



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consistent initialization in time and a second-order accurate backward difference method is employed for time-marching with a local error control. Time step size between 10-4 and 10-3 seconds is found to be optimum for a converged solution. The dimensional parameters used in the simulations are in the range of oil-water flows,  j ~ 1000 kg/m3,  j ~ 0.001 – 0.02 Pa s,  j ~ 2.2 - 80, d j ~ 0.0001 - 0.1 m,  ~ 0.0058 - 0.0258 N/m, and V ~ 150 - 300 V. 2.4 Model validation: Previous experiments [67] identified the effect of an external electric field on the coalescence of a suspended water droplet inside a continuous oil medium into a bulk water layer. As a benchmark, we validate the numerical method to solve the governing equations with appropriate boundary conditions for the same configuration, following a previous computational work [68]. The axisymmetric geometrical domain shown in the Supplementary Figure 1 represents a cylinder of radius 8 mm and height of 20 mm in which water is filled until 3 mm from the bottom and the rest of the geometry is filled with silicone oil. In the beginning of the simulation, a water droplet of 1.5 mm radius is placed in such a manner that its boundary coincides with the oil-water interface. The physical properties employed for the simulations are mentioned in the figure caption, which is same as the previous computational work [68]. The figure shows the spatiotemporal evolution of the coalescence of the water droplet into the bulk water phase driven solely by gravity [row (a)] and under the coupled influence of electric field and gravity [row (b)], when the field intensity is 2.67 × 105 Vm-1. The numerical results for the coalescence using the present model match closely with the previous experimental [67] and numerical [68] observations, which confirms the accuracy of the method employed in the present study.

3 Results and discussion The pressure-driven two layer flows inside the microchannels often develop stratified or slug or plug flow patterns. Transforming these flow regimes into droplets can improve the



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efficiency of reactions or the heat and mass exchanges in the microfluidic devices, because of the availability of larger interfacial area per unit volume. Further, the larger frictional influence due to the contact of flow features to the wall in the stratified or slug flow regimes reduces the throughput of the processes. In comparison, the droplets suspended in a continuous phase show a faster kinetics because they can pass on easily through the continuous medium facing a lesser frictional resistance. The present study primarily focuses on the two important aspects of the liquid-liquid flows, (i) developing the miniaturized flow patterns having higher surface to volume ratio, and (ii) increasing the throughput by improving the frequency of these flow patterns. In this direction, we first identify the conditions to develop stratified or slug or large plug flow morphologies in a two-phase flow by varying the oil to water flow ratio ( Q = v1 v2 ). Following this, a localized electric field is generated in the microchannel through the electrodes to disintegrate the larger flow patterns into droplets. Interestingly, the jump in the EHD stress can deform the oil-water interface into interesting shapes. For example, a spherical droplet can deform into a prolate shaped spheroid under the influence of an external electric field with the axis directed along the field [69-72]. The transformation of a spherical droplet into a prolate shaped spheroid has been termed as liquid dielectrophoretic (L-DEP) deformation in which a non-uniform electric field exerts force on the induced dipoles accumulated at the soft-interface to cause deformation [69-72]. The LDEP phenomena resemble closely to the solid particle dielectrophoresis with the exception that the soft interface of the liquid droplet deforms while migration takes place. Figure 2 shows a similar transition in the morphologies of an oil droplet translating in a continuous water phase and exposed to an external electrostatic field inside a hydrophilic microchannel. The simulation shows that, as the droplet enters into the zone of the electric field exposure, the circular shape progressively distorts into an elongated one with the major axis aligned



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towards the electrodes. The repulsion between the accumulated induced dipoles at the interface helps in deforming the surface of the droplet. Following this, as it translates to the middle portion of the electrode, the elongated droplet forms an ‘oil plug’. The hydrophilic nature of the channel walls ensures that the oil phase never stick to the channel walls. The droplet regains the circular shape when it translates out of the zone of electric field exposure. The figure confirms that the size and shape of the flow patterns inside a microchannel can be altered with the help of localized external electrostatic field. We employ this phenomenon to transform the regular pressure-driven flow regimes in the following section. Image (a) in Figure 3 shows that spatiotemporal dynamics of a pressure driven oil-water system, which develops a steady state stratified flow when water (oil) enters horizontally (vertically) with a flow ratio, Q = 1. It is well known that for a multiphase microfluidic reactor the stratified flows are undesirable because of the availability of the lesser interfacial area as compared to the droplet driven flows. Images (b) – (f) show that under the influence of a local electric field at the downstream of the same channel can indeed transform the stratified flow patterns to slugs, plugs, and droplets with the increase in the electric field intensity, Ψ, from 2 MVm-1 to 6 MVm-1. The simulations show that under the influence of the external field, the oil phase with lower dielectric permittivity becomes locally elongated at the zone where electrodes are placed to form an ‘oil plug’ showing an L-DEP phenomenon. Following this, the pinned oil plug in between the electrodes experiences a pressure from the inlet flows, which helps in producing the slugs in the downstream of the electrodes at lower values of Ψ, as shown in the image (c). Images (d) – (f) suggest that with increase in Ψ, gradual transitions from slug to plug to droplet morphologies take place. Increase in the Ψ escalates the concentration of the induced dipoles across the oil-water interface which in turn develops larger EHD stress to produce the oil droplets. A still higher Ψ than the values reported in the present work are expected to develop much smaller features with faster



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throughput. Figure 3 shows a simple method to transform a stratified flow into droplet flow pattern under the influence of an external electric field, applied locally at the downstream of a microchannel. Figure 4 shows the change in the frequency of the droplets (f – solid line, plotted at the left yaxis) and the cumulative length of the interfacial contact between the phases (Li – broken line, plotted at the right y-axis) with the change in the parameters Ψ,  r ,  , and  r . The equivalent dimensionless electric capillary number (CaE = l 0 2  2 /  ) [72] is plotted at the top of the x-axis. The parameter f is a measure of the throughput and Li is a measure of the available interfacial area for mass and momentum exchange, which is the total length of the oil-water interface at the downstream of the electrodes. The plot (a) shows that f increases significantly with increase in Ψ (higher CaE) whereas Li initially reduces and then increases with Ψ (broken line, triangular symbols). While Li is ~ 1 mm for a stratified pressure-driven flow in the downstream of the electrodes, it becomes ~ 1.5 mm for the droplet flow patterns. The plot suggests the availability of higher surface to volume ratio together with higher throughput at higher values of Ψ and CaE. The throughput is facilitated because the smaller droplets pass through the middle of the channel exerting a much lesser frictional influence. In addition, a larger Ψ and dielectric contrast (  2  1 ) across the interface develops larger Maxwell’s stress at the interface, which eventually transforms the stratified flow to the droplet flow patterns. Plot (b) shows that f and Li both increase with an increase in the dielectric contrast between the fluids (increase in Ca and decrease in  r ). Plot (c) shows that increase in the interfacial tension (decreasing CaE) imparts a stronger stabilizing influence against the destabilizing electric field force, which leads to reduction in Li and f. Plot (d) shows that with increase in  r , Li initially increases and then reduces whereas f progressively reduces. The Supplementary Figures 2 – 4 depict the flow morphologies with the variation



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in  r ,  , and  r to corroborate the results shown in Figure 4. Images (a) – (g) in the Supplementary Figure 2 depict that the reduction in the dielectric contrast can cause a reduction in the EHD stress across the interface and enforce a transition from a droplet to the stratified flow. Images (a) – (e) in the Supplementary Figure 3 show a transformation from slug to droplet flow regime with reduction in γ when, Q = 1 and Ψ = 3 MVm-1. It may be noted here that addition of surfactant to any of the phases can indeed reduce the interfacial tension to the limit discussed in the figure. The images show that the reduction in γ can cause a net reduction in the stabilizing influence at the interface, which can enforce drop formation at a much smaller value of Ψ. Images (a) – (e) in the Supplementary Figure 4 display that the size and frequency of the droplets can also be controlled by tuning the viscosity ratio of the phases, r  2 / 1 . The images show that at lower value of  r , the time required for droplet breakup is smaller, the sizes of the droplets are smaller, and the droplet frequency is higher. Concisely, the Figures 3, 4 and Supplementary Figures 2 – 4 together highlight the importance of Ψ,  2 ,  , and  2 on the transition of flow patterns, their size and shape, and throughput. Supplementary Figure 5 summarizes the effects when the locations of the inlet fluids are exchanged. Image (a) shows a steady stratified flow morphology of a pressure driven oilwater system when water (oil) enters vertically (horizontally) with a flow ratio, Q = 1 inside a hydrophobic microchannel. Image (b) shows that application of a local external field in the same channel can transform the stratified flow patterns to slugs when the electric field intensity Ψ is 3 MVm-1. Images (b) – (d) show a reduction in the size of the slug patterns with increasing the field intensity from 3 MVm-1 to 5 MVm-1. We observe that increase in the field intensity can yield plugs or even droplet flow patterns. Image (d) shows that as the water layer enters the zone of electric field exposure, the interface deforms into a water plug showing a phenomenon similar to L-DEP. A comparison between Figure 3 and This article is protected by copyright. All rights reserved.


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Supplementary Figure 5 uncovers that the oil droplets can be formed at a much lower field intensity when introduced from vertical inlet of a hydrophilic (θ = 45o) channel whereas the formation of water droplets requires a much larger field intensity when introduced from the vertical inlet of a hydrophobic (θ = 135o) channel. Supplementary Figure 6 summarizes the influences of the ratio of the oil to water flow rate (Q) and the equilibrium contact angle (θ). The sets (a) – (c) show the effect of Q and the columns (I) – (III) show the effect of θ on the flow patterns. The rows (i) – (iii) in the image sets summarize the flow patterns, which develop for a pressure-driven flow. The row (iv) shows the change in the flow pattern due to the application of the localized electric field. In most of the situations the pressure-driven flows show a stratified flow at the steady state. A comparison between the sets (a) – (c) highlight that the application of the localized electric field helps in, (A) breaking down the flow patterns into smaller fragments for almost all values of Q; (B) the flow patterns with oil droplets inside a continuous water medium is more common when the channel wall is hydrophilic (θ = 45˚) [rows (a) – (c), column (I), and image (iv)]; (C) the droplet size can be reduced by tuning the Q in which Q = 0.1 produces a collection of small droplets for all values of θ; (D) interesting hemispherical oil droplet patterns issuing out of the channel are observed when the wall is partially wetting (θ = 90˚) and Q = 0.5 [row (b), column (II), and image (iv)]; (E) for hydrophobic channels (θ = 135˚) the stratified pressure-driven stratified flows are broken into water slugs at higher values of Q [rows (b) and (c), column (III), and image (iv)]. The simulations are performed at a moderate value of Ψ = 3 MVm-1. Flow patterns with further smaller surface area and higher throughput can be expected with increase in the field intensity and reduction in the interfacial tension. The 3-D simulations in the images (a) and (b) in the Supplementary Figure 7 display the change in the size of the oil droplet with the change in Q inside a hydrophilic microchannel at 3 MVm-1. The similarity in the flow regimes alongside the time scale predicted for the drop



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formation in this figure corroborates the accuracy of the predictions from the 2-D simulations shown in the Figure 3. Further, the flow patterns observed in the simulations in Supplementary Figure 7 show a similar trend as observed in a previous experimental work [54]. The experiments demonstrated the effects of flow rates and the voltage applied on the mono-disperse droplet formation in square channels for a two-phase system of corn oil and glycerin. Herein, with the help of numerical simulations we identify a set of parameters, which can lead to different flow regimes with variable sizes, shapes, and frequencies. Supplementary Figures 6 and 7 together highlight the importance of a localized external electric field in developing diverse flow regimes inside hydrophilic to hydrophobic microchannels for wide range of oil to water flow rates. Figure 5 displays interesting examples where a localized electric field can generate oil in water emulsion. The microchannel in the image (a) possesses multiple vertical inlets of different sizes in which oil is introduced through the left most horizontal inlet and smaller vertical inlets in the middle of the geometry. The water is introduced through the left most vertical inlets. Electric field is generated locally in the downstream of both the larger and smaller vertical inlets. The simulation images show that at steady state the left most inlet produces oil droplet under the influence of the electric field. With progress in time, as the droplet moves downstream, a pair of oil droplets also joins the stream as the smaller vertical inlets also produce a pair of droplets under the influence of the electric field. This leads to the formation of a collection of dispersed oil droplets in continuous water phase at the downstream of the channel. Image (b) shows that if multiple microchannels similar to the image (a) are integrated together, an ‘oil in water’ emulsion can be produced at the outlet.

4 Concluding remarks



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A comprehensive study has been performed on the localized electric field driven transitions of flow patterns of two-phase pressure-driven flows inside ‘T’ shaped microchannels. A series of 2-D and 3-D simulations are performed to uncover the following things, (i) The regular pressure-driven stratified, slug, and plug flow patterns can be broken into smaller plugs or droplets with the help of a localized electric field, which can be integrated independently from the outside of the channel. The dielectrophoretic deformation of the oilwater interface originating from localized EHD stress is found to disturb the balance between the frictional, capillary, and inertial influence to engender these flow patterns. (ii) The flow ratio of the liquids, dielectric contrast across the interface, interfacial tension, intensity of the electric field, viscosity ratio of the fluids, and hydrophobic or hydrophilic nature of the channel walls are found to have significant influence on the flow pattern, feature size, and throughput. Flow of liquids with lower interfacial tension inside a hydrophilic channel with a smaller oil to water flow ratio is found to be the suitable combination for the miniaturized oil droplet formation at higher field intensity. (iii) Introduction of the oil phase from the vertical inlet of the ‘T’ shaped hydrophilic channel is found to be more favorable to form oil microdroplets at the lower electric field intensities. The field intensity requirement is larger to break the stratified flow patterns when water is introduced vertically inside a hydrophobic channel. (iv) Example simulations show the steps to produce an ‘oil in water’ microemulsion exploiting this phenomenon in which a collection of oil droplets are dispersed into a continuous water phase. In summary, the study displays some interesting pathways to develop droplet flow inside a microfluidic device by locally perturbing a pressure-driven flow with the help of an external electrostatic field. The results can motivate future experiments related to the field induced flow inside microfluidic devices.



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Acknowledgments The authors gratefully acknowledge the financial support from DST-SERB, grant no. SR/S3/CE/0079/2010 and DST-FIST, grant no. SR/FST/ETII-028/2010. Discussions with Dr. Trung-Dung Dang are also gratefully acknowledged.

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Figure 1. A 2D schematic diagram of the ‘T’ shaped microchannel employed for the simulations. The direct current (DC) electric field is generated at the electrodes placed 0.2 mm downstream of T-junction. The channel is 0.1 mm wide, which is also the electrode separation distance.



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Figure 2. Droplet deformation under the local influence of non-uniform electric field. A stationary oil droplet is suspended in a continuous water phase moving with a velocity 0.005 ms-1. The droplet passes from a region free of electric field (left side) to the region with electric field exposure (center) and then again translates out of the electric field region (right side). The other necessary parameters for the simulation are,  = 0.0058 Nm-1, r  10 , θ = 45o, and Ψ = 1.4 MVm-1. Images correspond to the time, (a) 0 s, (b) 0.002 s, (c) 0.008 s, and (d) 0.016 s.



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Figure 3. Influence of the external electric field intensity (Ψ) on the flow morphologies of a pressure driven oil-water flow with oil entering from the vertical inlet. Image (a) show the morphologies for the pressure driven flow without external electric field at, t = 0.2 s. Images (b) – (f) show the steady state morphologies where Ψ is 2 MVm-1, 3 MVm-1, 4 MVm-1, 5 MVm-1, and 6 MVm-1, respectively. The morphologies are observed at the same time interval, t = 0.2 s. Other parameters taken for this study are, θ = 45o, r  10 , γ = 0.01 Nm-1 and Q = 1. The darker (lighter) shade shows the water (oil) phase.



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Figure 4. Sensitivities of different dimensional and non-dimensional parameters. The plot (a) shows variations in the interfacial contact length (Li – right side of y-axis) and frequency of the structures passing through the outlet (f – left side of y-axis) with Ψ where  1 = 2.2,

 2 = 80, θ = 45o, r  10 , γ = 0.01 Nm-1, and Q = 1. The top side of x-axis in the plots (a) – (c) shows the corresponding electric capillary number CaE. Plot (b) shows the variations in Li and f with the ratio of dielectric constant,  r  1 /  2 where Ψ = 3 MVm-1,  1 = 2.2, r  10 , θ = 45o and Q = 0.5. Plot (c) the variations in Li and f with interfacial tension, γ, where Ψ = 3 MVm-1, θ = 45o,  1 = 2.2,  2 = 80 and Q = 0.5. Plot (d) shows the variations in Li and f with the viscosity ratio, r  1 / 2 , where Ψ = 3 MVm-1, θ = 45o, γ = 0.0058 Nm-1,  1 = 2.2,

 2 = 80, and Q = 0.5.



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Figure 5. Strategies to prepare oil in water microemulsion. In the images (a) and (b) water inlets are marked as ‘W-I’ and the oil inlets are marked ‘O-I’. The fluids exit from the outlet located towards the right and the symbols ‘+’ and ‘–’ on the images denote the location of the anodes and cathodes. The dimensions of the inlets, outlet, and the electrodes are provided on the image. At all the inlets of image (a) and (b) Q = 0.1. In the images (a) and (b), at the left pair of electrode Ψ = 3.3 MVm-1, at the right pair of electrode Ψ = 3 MVm-1, θ = 45o,

 1 = 2.2,  2 = 80, r  10 , and  = 0.0058 Nm-1. The darker (lighter) shade shows the water (oil) phase.


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