Numerical Simulations of Liquid−Liquid Flows in Microchannels

Aug 20, 2010 - investigations of drop/slug formation and flow regimes for liquid-liquid (oil-water) flow in microchannels. The Volume of Fluid (VOF) m...
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Numerical Simulations of Liquid-Liquid Flows in Microchannels Richa Raj, Nikita Mathur, and Vivek V. Buwa* Department of Chemical Engineering, Indian Institute of Technology-Delhi, New Delhi 110 016, India

Liquid-liquid flows in microchannels are important to microreactors/microfluidic devices that are used to carry out liquid-liquid reactions, extractions, emulsifications, etc. In this work, we report numerical investigations of drop/slug formation and flow regimes for liquid-liquid (oil-water) flow in microchannels. The Volume of Fluid (VOF) method was used to simulate the dynamics of water drop/slug formation in silicon oil, and the predicted drop/slug shapes/lengths were compared with previous literature measurements [Garstecki et al., Lab Chip 2006, 6, 437-446]. The effects of flow rates of water and oil phases (0.019-0.417 and 0.004-0.14 µL/s, respectively), channel size, liquid-liquid distributor (T-junction and Y-junction), and liquid viscosity on liquid-liquid flow regimes and slug lengths were investigated. The predicted drop/slug formation dynamics/slug lengths agreed satisfactorily with the aforementioned Garstecki et al. literature measurements for Qwater/Qoil in the range of 0.1-1.7. However, for Qwater/Qoil > 1.7, unlike the (long) slug flow reported in the aforementioned Garstecki et al. literature, a parallel flow was observed in the numerical simulations. The effect of wall adhesion (contact angle) on the flow regimes and slug lengths was also investigated. The experimentally validated computational model will be useful to simulate mixing, transport processes, and chemical reactions in microchannels. 1. Introduction Microreactors/microfluidic devices involve the flow of fluids through channels with characteristic dimensions of 1, slug lengths were found to increase. The ratio Wwater/Woil was found to be a very important parameter in transition of the slug detachment mechanism, e.g., from a squeezing mechanism to a shearing mechanism. Kashid and Agar17 also studied the effect of main channel size on the slug volume for a Y-junction circular microchannel and found the slug volume to increase with increasing diameter of the main channel. Kashid et al.18 performed two-dimensional (2-D) simulations of the liquid-liquid slug flow in a microchannel to investigate liquid recirculation in the continuous-phase and dispersed-phase slugs. In their simulations, the shape of the slug of both phases was assumed to be fixed and the slugs were modeled to be stationary with a moving wall boundary condition. Kashid et al.8 reported preliminary 2-D simulations of flow of a water-cyclohexane system through a Y-junction using the VOF method. In their work, they qualitatively showed that the formation of liquid slugs can be simulated if the surface tension and wall adhesion forces are correctly taken into account. Wu et al.19 performed 2-D simulations of a liquid-liquid flow in a cross-junction rectangular microchannel using the latticeBoltzmann method. They investigated the effects of Ca and the Weber number (We) on the drop/slug formation mechanism. Khasid et al.20 performed 2-D VOF simulations of liquid-liquid slug flow through a T-junction microchannel for Ca < 0.01 and validated the results using the experiments of Tice et al.21 The present state of the art on numerical simulations of liquid-liquid flows indicates that, in most of the previous work, fixed slug size/shapes were assumed and recirculation in the slugs was studied. A few studies exist that have reported 2-D simulations of drop/slug formation dynamics; however, they are often limited to demonstrate of applicability of different

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numerical methods (VOF, level set, lattice-Boltzmann) to simulate liquid-liquid flows in microchannels and report only qualitative results. To predict the curvature effects correctly, three-dimensional (3-D) simulations are necessary. To make further progress in this area, it is imperative to perform 3-D simulations of drop/slug formation dynamics including the surface tension and wall adhesion forces. Furthermore, it is necessary to verify the predictive capabilities of the numerical methods to simulate drop/slug formation in different flow regimes for a wide range of operating and design parameters. Moreover, the predictive capabilities of the numerical methods to simulate the liquid film between the slug and the channel wall are not well understood. Gupta et al.13 performed axissymmetric simulations of air-water flow in a circular microchannel. In their work, a stable liquid film was obtained on grid refinement near the wall and the predicted liquid film thickness was in accordance with the Breherton’s law.22 Kashid et al.20 investigated the effect of wetting behavior on the film thickness qualitatively by specifying different contact angles. In the present work, we performed numerical simulations of liquid-liquid (silicon oil-water) flow in microchannels using the VOF method. The objective of the present work was to verify the predictive capabilities of the VOF method to simulate experimentally observed flow regimes and to predict the drop/ slug shapes/lengths for a wide range of flow rates, fluid properties, and channel and distributor geometry. The dynamics of drop/slug formation in different flow regimes was investigated and the predictions were validated using the measurements of Garstecki et al.1 The effects of Qwater (0.001-0.12 µL/s) and Qoil (0.01-0.5 µL/s), continuous-phase liquid viscosity (10 and 100 mPa s), interfacial tension (36.5-109.5 mN/m), and channel size on the flow regimes and slug length was studied, and the predictions were verified using the measurements of Garstecki et al.1 The effect of distributor type (T-junction vs Y-junction) was also investigated. The effect of wall adhesion force on flow regimes was verified by specifying different contact angles. 3. Computational Model In this study, the VOF method23 was used to simulate the dynamics of drop/slug formation of water (dispersed-phase) in silicon oil (continuous phase) in a rectangular 3-D microchannel under laminar flow conditions. The fluids were modeled as incompressible and Newtonian. 3.1. The VOF Method. In the VOF method, a marker function (volume fraction) is used to identify the underlying fluid phases. If Rq is the volume fraction of the qth phase in a computational cell, then the expression Rq ) 1 implies that the computational cell is completely filled with phase q, Rq ) 0 implies that the computational cell has no phase q, and a value of Rq in the range of 0-1 implies that the cell contains the interface between phases p and q. A single set of mass and momentum conservation equation is solved throughout the domain: ∂ (F) + ∇ · (FVj) ) 0 ∂t

(1)

∂ b + (∇V b)T)] + Fg b+b F (FV b) + ∇ · (FV bb V ) ) -∇p + ∇ · [µ(∇V ∂t

(2) where F and µ are the volume-fraction-weighted density and viscosity, respectively, which are defined as F ) RqFq + (1 - Rq)Fp

(3)

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µ ) Rqµq + (1 - Rq)µp

(4)

b) used in eq 2 was calculated The surface tension force (F (using the FLUENT 6.3 User Manual) as

[

b F)σ

Fκnˆ (1/2)(Fp + Fq)

]

(5)

where σ is the coefficient of surface tension, nˆ the surface normal, and κ the local surface curvature, which is calculated as24 κ ) ∇ · nˆ

(6)

where nˆ ) n/|n| and n ) ∇ · Rq. The geometric reconstruction scheme,25 based on piecewise linear interpolation,26 was used for the reconstruction of the interface. In the VOF approach, the reconstructed interface is advected by solving an advection equation for Rq. For phase q, the advection equation is written as ∂ (R F ) + ∇ · (RqFqb V q) ) 0 ∂t q q

Figure 1. Microchannel geometry and computational grid.

(7)

The wall adhesion force was also taken into account by specifying the three-phase contact angle, as nˆ ) nˆw cos θw + ˆtw sin θw

(8)

where nˆw and ˆtw are the unit vectors normal and tangential to the wall, respectively. It was assumed that the contact line maintains a constant (static) contact angle (θw), independent of the velocity and the direction of the contact line movement. The combination of this contact angle with the normally calculated surface normal one cell away from the wall determines the local curvature of the surface, and this curvature is used to adjust the body force term in the surface tension calculation. 3.2. Numerical Solution. Equations 1, 2, and 7 were solved using the commercial flow solver FLUENT v6.3 (Ansys, Inc., USA). The spatial derivatives were discretized using the QUICK scheme,27 while a first-order implicit method was used for the discretization of the temporal derivatives. The Pressure Implicit with Splitting of Operator (PISO) algorithm28 was used for the pressure-velocity coupling in the solution of the momentum equation. The solution domain consists of a 3-D T-junction microchannel, as shown in Figure 1. A typical computational mesh is also shown in Figure 1. Four different geometries of the T-junction microchannel were considered, for which measurements of slug length were reported by Garstecki et al.1 (see Table 1) for different Qwater/Qoil ratios in the range of 0.15-5.0. A time step of 1 × 10-6 s was used for simulations. Silicon oil (Foil ) 930 kg/m3, µoil ) 0.01 Pa s) and water (Fwater ) 1000 kg/m3, µwater ) 0.001 Pa s) were used as the working fluids. The interfacial tension between the two phases was taken to be 0.0365 N/m. Liquid inlets were modeled as velocity inlets, the outlet was modeled as the outflow, and a no-slip boundary condition was imposed at the channel walls. The effect of wall adhesion taken into account by specifying a static contact angle of 140°. The length of the inlets were taken as 2.5 times the width of the inlets (Wwater and Woil) (Lwater ) 125-250 µm and Loil ) 125-250 µm) such that the flow became fully developed. Simulations were also performed by specifying a parabolic velocity profile at the inlets, and it was found that the predicted slug formation time and slug lengths were same in both cases.

Table 1. Channel Configurations Considered in the Present Work geometry

Woil (µm)

Wwater (µm)

H (µm)

A B C D

100 100 50 100

50 100 50 50

33 33 33 79

The simulations were also performed to verify the adequacy of the outlet boundary conditions by imposing pressure outlet and outflow boundary conditions and it was observed that predicted slug length was not influenced by the outlet boundary condition. Therefore, in all of the further simulations, a uniform velocity was imposed at the inlets and the outflow boundary condition was imposed at the outlet. 4. Results and Discussions 4.1. Preliminary Simulations and Experimental Validation. Preliminary simulations were performed to investigate the slug formation mechanism for the flow of silicon oil and water in a T-junction microchannel with Qwater ) 0.14 µL/s and Qoil ) 0.083 µL/s (geometry A). A comparison of predicted and measured1 slug shapes is shown in Figure 2. This figure shows that the slug formation take place in four stages: (1) the dispersed phase (water) enters the main channel; (2) the water slug grows and spans almost the entire cross-section of the main channel; (3) the slug elongates downstream and the neck connecting it to the inlet thins; and (4) finally, the neck breaks and the slug flows downstream. The predicted slug shapes were in satisfactory agreement with the experimentally observed slug shapes1 (see Figure 2). The predicted slug formation time (6.4 ms) was in good quantitative agreement with the measured slug formation time (7 ms). Further simulations were carried out to study the effect of grid resolution on the predicted slug shapes and lengths for Qwater ) 0.14 µL/s and Qoil ) 0.408 µL/s (geometry A). The simulations were performed using a coarse grid (51 260 cells), a medium grid (72 960 cells), and a fine grid (102 816 cells). The predicted slug formation times were 5.4, 6.4, and 6.6 ms for the coarse, medium, and fine grids, respectively. The corresponding slug lengths were 253, 325, and 322 µm, respectively. The predicted slug formation time and slug length for medium and fine grids were almost independent of grid resolution and were in a quantitatively good agreement with

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Figure 2. Dynamics of slug formation: comparison of experimental (Garstecki et al.1 (reprinted with the permission from ref 1; copyright Royal Society of Chemistry (RSC), 2006)) and simulated slug shapes (Qwater ) 0.14 µL/s, Qoil ) 0.083 µL/s, geometry A).

Figure 3. Effect of channel length on the predicted drop shapes (a) Qwater/ Qoil ) 0.343 and (b) Qwater/Qoil ) 3.96. For each panel, (i) Lchannel ) 1600 µm and (ii) Lchannel ) 4000 µm (geometry A).

the experimental slug formation time (7 ms) and slug length (300 µm). Therefore, all further simulations were performed using a grid resolution corresponding to the medium grid. The adequacy of the channel length was investigated by performing simulations in channels with lengths of 1600 µm (standard case) and 4000 µm (geometry A). The predicted drop/ slug shapes for the flow rate ratios of Qwater/Qoil ) 0.343 (Qwater ) 0.14 µL/s) and 3.96 (Qoil ) 0.028 µL/s) are shown in Figures 3a and 3b, respectively. In the above simulations, the drop/ slug detached at the T-junction was found to attain its steady shape within a distance of ∼3.5Woil downstream from the T-junction. For Qwater/Qoil ) 0.343, the formation periods for successive drops were 1.4, 1.2, 1.2, and 1.2 ms. This shows that the drop formation period (and, therefore, the slug length) remains constant for the second drop onward and are not influenced by the increase in the channel length. For Qwater/Qoil ) 3.96, unlike the experimentally observed slug flow, a parallel flow was observed in both simulations (channel lengths of 1600 µm (standard case) and 4000 µm; see Figure 3b). Thus, no improvement in the predictions was achieved with the increase in the channel length. Therefore, all further simulations were performed with a channel length of 1600 µm. 4.2. Effect of Qwater and Qoil. Garstecki et al.1 reported different flow regimes (viz, drop, slug, and long slug), as a function of Qoil and Qwater, for oil-water flow in a T-junction microchannel. They also reported the drop/slug shapes and lengths for different flow regimes. Numerical simulations were

Figure 4. Effect of Qoil on experimental (Garstecki et al.1 (reprinted with the permission from ref 1; copyright Royal Society of Chemistry (RSC), 2006)] and simulated flow regimes at a constant Qwater value of 0.14 µL/s (geometry A): (a) Qoil ) 0.408 µL/s (Qwater/Qoil ) 0.343), (b) Qoil ) 0.124 µL/s (Qwater/Qoil ) 1.129), and (c) Qoil ) 0.019 µL/s (Qwater/Qoil ) 7.179).

performed to study the effect of Qoil (0.01-0.5 µL/s) on the flow regimes and drop/slug length for a constant Qwater value of 0.14 µL/s. A comparison of predicted and measured1 drop/ slug shapes for Qwater/Qoil ratios of 0.343, 1.129, and 7.179 is shown in Figure 4. It can be seen that the observed drop flow (at Qwater/Qoil ) 0.343) and slug flow (at Qwater/Qoil ) 1.129) could be qualitatively well predicted (see Figures 4a and 4b). However, at Qwater/Qoil ) 7.179, the long slug flow regime reported by Garstecki et al.1 could not be predicted, even qualitatively, compared to the parallel flow regime observed in the simulations. The flow regimes depend on Ca (the ratio of viscous force and interfacial tension force) and We (the ratio of inertial force and interfacial tension force). The viscous force plays an important role in the slug formation dynamics above a critical Ca value of Cacr ≈ 1 × 10-2).1 At low values of Qoil, Ca < Cacr (1.575 × 10-3-8.3 × 10-3), the role of viscous force becomes insignificant and the slug formation mechanism is governed by interfacial tension force (Wewater ) 9.776 × 10-3). As a result, the formation of long slugs was observed.1 At higher

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Figure 5. Effect of Qoil on the slug length at a constant Qwater value of 0.14 µL/s (geometry A).

Figure 6. Effect of Qwater on experimental (Garstecki et al.1 (reprinted with the permission from ref 1; copyright Royal Society of Chemistry (RSC), 2006)) and simulated flow regimes at a constant Qoil value of 0.028 µL/s (geometry A): (a) Qwater ) 0.004 µL/s (Qwater/Qoil ) 0.143), (b) Qwater ) 0.05 µL/s (Qwater/Qoil ) 1.8), and (c) Qwater ) 0.111 µL/s (Qwater/Qoil ) 3.96).

values of Qoil, viscous force becomes significant (Ca ) 1.02 × 10-2-3.4 × 10-2) and results in the formation of slugs of smaller length or drops. The predicted slug lengths were in a good quantitative comparison with the measurements for Qwater/ Qoil < 1.13 (see Figure 5). For Qwater/Qoil > 1.13, a parallel flow was observed unlike the long slug flow reported by Garstecki et al.1 The possible reason for the observed disagreement seems to be the wall adhesion (contact angle and surface roughness) effects (see section 4.3 for further discussion). The effect of Qwater (0.001-0.12 µL/s) on the flow regimes and drop/slug lengths was investigated for a constant Qoil (0.028 µL/s). A comparison of predicted and measured1 drop/slug shapes for Qwater/Qoil ratios of 0.143, 1.8, and 3.96 is shown in Figure 6. It can be seen that the observed drop flow regime (at Qwater/Qoil ) 0.143) could be predicted qualitatively well (see Figure 7a). However, for Qwater/Qoil ) 1.8 and 3.96, the slug

Figure 7. Effect of Qwater on the slug length at a constant Qoil value of 0.028 µL/s (geometry A).

and the long slug flow regimes reported by Garstecki et al.1 could not be predicted, even qualitatively, compared to the parallel flow regime observed in the simulations. At Qoil ) 0.028 µL/s (Ca ) 2.323 × 10-3), the viscous force is insignificant and, hence, the slug length is dependent only on Qwater. The slug lengths were found to increase with increasing Qwater. A quantitative comparison of the measured and predicted slug lengths for Qwater/Qoil < 1 is shown in Figure 7. 4.3. Effect of Contact Angle. The effect of wall adhesion force on the flow regimes and slug lengths was investigated by performing simulations at Qwater/Qoil ) 0.343 (Qoil ) 0.408 µL/ s, geometry A), using different values of wall contact angles (60°, 90°, 120°, 140°, 160°, 180°). As shown in Figure 8, a parallel flow was observed in simulations performed using the contact angle values of 60° and 90° (see Figures 8a and 8b). In the simulation performed using a contact angle of 120°, the formation of slugs was observed in the initial period. However, the observed slug flow was eventually found to transit to a parallel flow (see Figure 8c). For simulations performed using the contact angle of 140°, a stable drop flow regime was observed (see Figure 8d). With further increases in contact angle to 160° and 180°, the drop size found to be marginally influenced and a stable drop flow regime was found to prevail (see Figures 8e and 8f). In all above simulations, a static contact angle was specified and its variation with the contact line velocity and the effect of surface roughness was ignored. Since a static contact angle that has been specified in the present simulation is seen to have a significant influence on the observed flow regimes, the parallel flow observed at high Qwater/Qoil ratio (Qwater/Qoil > 1.13) seems to be a result of inadequate account of the wall adhesion effects. The effect of contact angle was also investigated for Qwater/Qoil of 1.8 (Qoil ) 0.028 µL/s, geometry A). For the simulation performed with θw ) 180°, a stable slug flow was observed, unlike the parallel flow observed at θw ) 140°. However, the measured slug length (330 µm) was significantly higher than the predicted slug length (267 µm). For Qwater/Qoil ) 5.0, no improvement in the flow regime was observed with increase in θw from 140° to 180° and a parallel flow was observed at both θw ) 140° and 180° (unlike the long slug flow regime observed by Garstecki et al.1). Because of a lack of experimental data on the dependence of contact angle on the three-phase contact line velocity and surface roughness, and also because of the inadequacy of the appropriate computational models to account for the above-mentioned effects, it

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Figure 8. Effect of contact angle on drop/slug formation (geometry A), Qwater ) 0.1399 µL/s, Qoil ) 0.408 µL/s, Qwater ) 0.1399 µL/s, Qoil ) 0.343): (a) 60°, (b) 90°, (c) 120°, (d) 140°, (e) 160°, and (f) 180°.

Figure 9. Effect of channel size and T-junction geometry on the predicted drop/slug shapes: (a) geometry A, (b) geometry B, and (c) geometry C (Qwater ) 0.14 µL/s).

is difficult to quantify these effects; further work is needed to address these issues. 4.4. Effect of Channel Size. The effect of channel size on the drop/slug lengths was investigated by performing the simulations for four different T-junction microchannels (see Table 1) for Qwater/Qoil ratios in the range of 0.15-5.0 at constant Qwater (0.14 µL/s). The predicted drop/slug shapes are shown in Figure 9 for different Qwater/Qoil values. A quantitative comparison between predicted and experimental drop/slug lengths is shown in Figure 10. For all channel geometries and for Qwater/ Qoil < 0.5 (Ca > Cacr ≈ 1 × 10-2), the drop/slug length was found to be independent of the channel size and the predicted slug lengths were in a satisfactory agreement with the experimental drop/slug lengths with the absolute deviations in the range of 10%-15%. For Qwater/Qoil > 1, a parallel flow was observed for channels configurations with H ) 33 µm (geom-

etries A, B, and C) against the experimentally observed slug flow regime (not shown here). Although slug flow was observed in numerical simulations of oil-water flow through a channel (geometry D) for Qwater/Qoil >1, the slug lengths were significantly overpredicted. Further investigations are needed to understand the reasons for obtaining a parallel flow or for overpredicting the slug lengths for Qwater/Qoil > 1. 4.5. Effect of Viscosity and Surface Tension. The effect of µoil on the slug shape and length was investigated by performing the simulations for two values of µoil (10 and 100 mPa s) for a T-junction microchannel (geometry A). As seen from Figure 11, the slug length was found to decrease marginally with increasing µoil from 10 mPa s to 100 mPa s. The decrease in the slug length can be attributed to the increase in the shear force on the dispersed phase segment resulting in an early detachment. The predicted and experimental slug lengths were

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Figure 10. Effect of channel size and T-junction geometry on the predicted slug length.

Figure 11. Effect of µoil on the predicted slug length (geometry A).

in quantitatively satisfactory agreement with the measurements of Garstecki et al.1 The effect of surface tension on the drop/ slug length was investigated by performing simulations for Qwater/Qoil ) 0.343 for T-junction microchannel (Qwater ) 0.14 µL/s, Qoil ) 0.408 µL/s, Ca ) 1.12 × 10-2-3.4 × 10-2, geometry A) for the different values of surface tension (36.5, 73, and 109.5 mN/m). The predicted slug lengths were 115, 124, and 132 µm, respectively, for surface tensions in the range of 36.5-109.5 mN/m. Further simulations were carried out for Qwater/Qoil ) 0.715 for the above-mentioned values of surface tension (Qwater ) 0.022 µL/s, Qoil ) 0.028 µL/s, Ca ) 7.75 × 10-4-2.32 × 10-3, geometry A) and the predicted slug lengths were found to be 216, 254, and 259 µm, respectively. This

shows that the slug length is independent of interfacial tension for the range of Ca values considered in the present work. 4.6. Effect of Distributor. The effect of distributor on the slug formation dynamics and the slug length was investigated for three distributors: cross-flow T-junction, coflow T-junction, and Y-junction microchannels (geometry B). The slug formation mechanism was found to be the same for all three distributors, as shown in Figure 12. The predicted slug lengths were 159, 156, and 157 µm, respectively, and these were found to be almost independent of the distributors type for Qwater/Qoil ) 0.343 (Qwater ) 0.14 µL/s, Qoil ) 0.408 µL/s; Ca ) 3.4 × 10-2). For Qwater/Qoil ) 0.686 (Qwater ) 0.14 µL/s, Qoil ) 0.204 µL/s, Ca ) 1.7 × 10-2), the predicted slug lengths were 174, 180, and

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to simulate the mixing and mass transfer in microchannels, it is necessary to investigate the issues related to the film thickness. Note that a thin liquid film was observed in most of the simulations performed with Ca > Cacr (∼1 × 10-2). However, for small vales of Ca ( 1.7, a parallel flow regime was obtained, unlike the long slug regime observed experimentally.1 Possible reasons for the observed disagreement seem to be inadequate modeling of the wall adhesion (surface wettability and roughness). • The wall adhesion was found to influence the drop/slug formation mechanism strongly and must be taken into account for accurate prediction of the slug formation mechanism in different flow regimes. • The predicted drop/slug lengths were found to be almost independent of the continuous phase viscosity for Ca < Cacr and also independent of the interfacial tension for the range of Ca values considered in the present work. • For Ca > Cacr, the predicted drop/slug lengths were found to be independent of the channel size and also independent of the inlet distributor type for the range of Ca values considered in the present work. Further work is needed to predict the formation of long slugs observed for Qwater/Qoil > 1.7. To extend the computational model

Notations Ca ) capillary number; Ca ) µoilUoil/σ Dh ) hydraulic diameter (m) F ) surface tension force per unit volume (kg/(m2s 2)) g ) gravity (m/s2) H ) height of the channel (m) L ) length (m) nˆ ) unit surface normal vector p ) pressure (Pa) Q ) flow rate (µL/s) Re ) Reynolds number; Re ) FUDh/µ ˆt ) unit vector tangential to wall We ) Weber number; We ) U2DhF/σ W ) width of the inlet (m) U ) superficial velocity of fluids (m/s) V ) velocity (m/s) Greek Letters µ ) viscosity (Pa s) R ) marker function (volume fraction) F ) density (kg/m3) σ ) coefficient of surface tension (N/m) κ ) local surface curvature θ ) contact angle (°) Subscripts/Superscripts ) critical p, q ) phases w ) wall cr

Acronyms SDS ) sodium dodecyl sulfate VOF ) Volume of Fluid method

Acknowledgment The financial support from the Department of Science & Technology, New Delhi, is gratefully acknowledged. Literature Cited (1) Garstecki, P.; Fuerstman, M. J.; Stone, H. A.; Whitesides, G. M. Formation of droplets and bubbles in a microfluidic T-junction-scaling and mechanism of breakup. Lab Chip 2006, 6, 437–446. (2) Chung, P. M. Y.; Kawaji, M. The effect of channel diameter on adiabatic two-phase flow characteristics in micro channels. Int. J. Multiphase Flow 2004, 30, 735–761. (3) Triplett, K. A.; Ghiaasiaan, S. M.; Abdel Khalik, S. I.; Sadowski, D. L. Gas liquid two-phase flow in microchannels Part I: Two-phase flow patterns. Int. J. Multiphase Flow 1999, 25, 377–394. (4) Xiong, R.; Bai, M.; Chung, J. N. Formation of bubbles in a simple co-flowing micro-channel. J. Micromechan. Microeng. 2007, 17, 1002– 1011. (5) Yu, Z.; Hemminger, O.; Fan, L. S. Experiment and lattice Boltzmann simulation of two-phase gas-liquid flows in microchannels. Chem. Eng. Sci. 2007, 62, 7172–7183.

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ReceiVed for reView March 15, 2010 ReVised manuscript receiVed June 28, 2010 Accepted July 30, 2010 IE100626A