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Experimental and Numerical Investigations of Two-Phase (Liquid-Liquid) Flow Behavior in Rectangular Microchannels Siva Kumar Reddy Cherlo, Sreenath Kariveti, and S. Pushpavanam* Department of Chemical Engineering, Indian Institute of Technology Madras (I.I.T. Madras), Chennai 600036, India
The interaction between kinetics and mass-transfer effects is determined by the flow regime in liquid-liquid multiphase microreactors. The operating conditions under which the various flow regimes such as slug flow and stratified flow occur in liquid-liquid systems has not been extensively studied and is not well-understood. The effect of operating conditions on slug length for instance is not well-known. The present study focuses on microreactors fabricated in Perspex (poly(methyl methaacrylate) (PMMA)), which are essentially microchannels with a rectangular cross-section. Experiments are carried out for a wide range of flow rates, channel sizes, and fluid systems with varying properties. Two different kinds of flow regimes, slug flow and stratified flow, are experimentally observed, and these are predicted using numerical simulations. We divide the space of operating conditions (the two liquid flow rates) into different regions such that in each region the flow regime is distinct. The dependence of slug length on flow rates and other parameters such as channel size, viscosity, surface tension, and contact angle have been determined and are quantitatively compared with predictions of simulations. 1. Introduction Miniaturization of devices has applications in several emerging technological areas, such as chemical synthesis,1 environmental monitoring2 of small concentrations of contaminants, microseparation processes (liquid-liquid3 and solid-solid4), nanoparticle synthesis,5 and polymerization reactions.6 The progress of chemical reactions in multiphase systems is determined by the interaction between the kinetics and masstransfer effects. Several chemical reactions (for example nitration of benzene and toluene) are limited by these effects. These transport limitations can be overcome by miniaturization. This is mainly useful in liquid-liquid reactions and gas-liquid systems where mass-transfer limitations from one phase to another play a vital role in determining the progress of reactions. These microsystems are operated typically at low Reynolds numbers, and the flow regimes of these multiphase systems can hence be characterized elegantly. It is necessary to know the conditions under which the different flow regimes associated with two- phase flows occur since this will enable us to exploit the intrinsic features of the system and help us optimize and control their performance when they sustain reactions. Burns and Ramshaw7 analyzed an immiscible liquid-liquid two-phase flow system in a microchannel. They found that the flow of the two phases was stratified with a planar interface for a wide range of operating conditions. For some operating conditions they observed slug flow behavior and found that this had a significant effect on mass-transfer rates. Here a slug of one phase is surrounded by a slug of the other phase. Each slug occupies the entire cross-section of the channel. Burns and Ramshaw8 in a later work extensively analyzed slug flow behavior in liquid-liquid systems. They studied the effect of mass transfer across liquid-liquid systems and analyzed emulsification of liquid phases. They studied how vortex motion within a slug could improve mass transfer across an interface. This was exploited to help control fast reactions which are mass transfer limited and which exhibit runaway behavior. These * To whom correspondence should be addressed. E-mail:
[email protected]. Tel.: +91-44-22574161. Fax:+91-44-22570509.
reactions include nitration, hydrogenation, sulfonation, and oxidation of organic compounds. Microreactors are intrinsically safe for carrying out these potentially hazardous reactions as they have a low inventory and possess a high surface area to volume ratio. The length of slugs depends critically on viscosity, flow velocity, geometry, and surface properties. Burns and Ramshaw8 and Dessimoz et al.9 analyzed an acid-base reaction in a L-L system. Acetic acid was taken with kerosene in the organic phase, and sodium hydroxide was taken in the aqueous phase. The acid was soluble in water, and sodium hydroxide was insoluble in the organic phase. Consequently the reaction could take place only in the aqueous phase. A global masstransfer coefficient was estimated. They mainly observed slug flow and stratified flow behavior in their experiments. Song and Ismagilov10 discuss how millisecond kinetics for fast reactions can be determined when mixing is slow and dispersion is high using slug flow conditions. Nisisako et al.11 studied formation of droplets in a simple PMMA fabricated micro-T-channel. They experimentally characterized droplet sizes and the production rate of drops in a T-shaped channel under different operating conditions, i.e., flow rates of continuous and discrete phases. However the droplets were not monodisperse. Kobayashi et al.12 analyzed silicon-based microchannels to form monodisperse droplets. In this work an injection type method was used in which the dispersed phase enters the continuous phase through a 200 µm length channel having an ellipsoidal-shaped mouth. This method helped in the formation of monodisperse droplets. The shape and aspect ratio of the channels determined the formation of droplets. They determined the critical aspect ratio (major axis/minor axis) to be around 3 to form droplets. Using this method they obtained a variation of less than 5% in droplet sizes. Zhao et al.13 have analyzed different liquid-phase-liquidphase flow patterns in rectangular microchannels experimentally. They showed how the different flow regimes depended on various dimensionless numbers. Kashid and Agar14 have analyzed hydrodynamic characteristics of slug flow in a capillary poly(tetrafluoroethylene) (PTFE). In a later study Kashid et al.15 have analyzed internal circulations in a slug of a microreactor. They used a two-phase model and carried out computational
10.1021/ie900555e 2010 American Chemical Society Published on Web 12/09/2009
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fluid dynamics (CFD) simulations based on a finite-element technique using a moving reference frame. On the theoretical front Brackbill et al.16 introduced a continuum approach for modeling surface tension. This forms the basis of the volume of fluid (VOF) approach for solving problems where the interface between the two fluids has to be determined by the flow conditions. Qian and Lawal17 have applied a VOF model using FLUENT successfully and compared the theoretical predictions with experimental data. The system analyzed consisted of long channels so that they could determine how the size of the different slugs varied with different operating conditions. Taha and Cui18,19 have used a VOF approach in FLUENT to study two-phase flow behavior and compared the results with experimental observations. They however restrict their analysis to the interaction of one slug of gas with one slug of liquid. Many of the situations described above are for simple T-shape or straight channels. Hydrodynamic behavior in curved microchannels has been analyzed by Kumar et al.20 In applications involving mass transfer and reactions, slug length in a two-phase flow system determines the performance of the system. However information on slug length variation with different parameters such as flow rate, viscosity, fluid properties, channel size, and contact angle is not sufficiently understood. In the present study we have considered channels with a rectangular cross-section. The different flow regimes in liquid-liquid two-phase flows are determined experimentally, and these are compared with predictions of numerical simulations. We use the VOF model in FLUENT to predict the different flow regimes in microchannels under varying operating conditions. We quantitatively compare the slug lengths obtained from experiments with the predictions from simulations. We also investigate the flow characteristics as a function of channel size and fluid properties. Our objective is to obtain insight and predictive capability of the flow behavior of the system to help in optimal design of different applications. The paper is organized as follows. Section 2 discusses the experimental details and methodology followed. Section 3 discusses the details of the algorithm used in the numerical simulations. Section 4 discusses the results obtained using simulations and experiments. We have a final section where we summarize the results of the work done. 2. Experimental Methodology The T-shaped microchannels made of Perspex (PMMA) used in this work were fabricated using computer numerical controlled (CNC) technique. The channel has a width of 590 µm and a depth of 500 µm. The hydraulic diameter (dh) of this channel is 0.54 mm. Each of the two symmetric inlet channels is 15 mm long, and the mixing channel has a length of 70 mm. The upper surface of the channel is closed with a polymer sheet (a transparent cellophane tape). Although the top surface is different from PMMA, it is also an hydrophobic surface so we expect the flow behavior to be the same as that of a PMMA channel. Kerosene and water are sent through the two symmetric inlet channels. The flow in the straight limb of the microchannel is observed through an optical microscope (Carl Zeiss Axioskope MAT2) fitted with a charge-coupled device (CCD) camera (Redlake Model ES 2093). The flow rates of the two fluids are maintained in the range of 5-350 mL/h using syringe pumps supplied by ASCOR (Model AP12). A second channel with a square cross-section of side of 1 mm (dh, 1 mm) was also fabricated and analyzed. The lengths of the inlet channel and mixing channel were 15 and 70 mm,
Figure 1. Schematic diagram of the dh ) 0.54 mm microchannel with the coordinate system used in the simulations.
respectively. Experiments were performed with various systems such as hexanol-water, octane-water, coconut oil-water, and kerosene-water. The kerosene-water system was extensively analyzed and used as a reference for comparison with other systems. Kerosene was chosen as the organic phase since it does not dissolve PMMA. It completely wets Perspex, whereas water makes a contact angle of 77° with Perspex. The contact angle measurements were carried out with a goniometer. One inlet of the channel was fed with water containing a fluorescent dye, sodium fluorescene (C20H10O5Na2; molecular weight, 376.279; supplied by Hi Media Chemicals), and the other inlet was fed with kerosene containing Sudan 3 for visualization. The sodium fluorescene dye is excited by blue light, and it emits green light. This dye is preferred over rhodamine because it does not adhere to the walls of the Perspex channels. The fluorescent dye was used with water to enhance the contrast between the two fluids. Each experiment was carried out at least twice to ensure reproducibility. Stability of the regimes was checked by disturbing the flow rates and verifying if the flow regime observed persisted after the disturbance was removed. The disturbance was usually a step change in the flow rate which was reversed after some time. All experiments are performed in T-shaped Perspex channels. In the slug-flow regime the slug lengths were determined by analyzing the digitized images after calibration. Across the surface of the slug there is a sharp change in the intensity value. The slug length was determined by tracking this sharp variation of intensity across pixels. The change in intensity is used to determine the location of the interface and calculate the slug lengths. The sizes of 50 slugs were measured after steady state was attained and their mean value was determined and is reported for each operating condition. 3. Simulations Hydrodynamics of two phase flow systems where the interface is determined by the flow conditions can be studied using the VOF approach. This feature is available in the commercial software FLUENT where wall adhesion and surface tension effects can be included. In this approach the surface tension force along the interface is considered as a body force in the region where the interface exists. Several workers have used the VOF approach in the past for simulating the hydrodynamic behavior in microchannels (Qian and Lawal17 and Taha and Cui18,19). The geometry used for the simulations of the dh ) 0.54 mm channel is shown in Figure 1. The entire geometry was meshed in Gambit using a hexahedral mesh. The dimen-
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sionless equations which describe the flow in the microchannel are the equation of continuity and momentum ∇·u ) 0
(1)
1 1 1 ∂u + ∇·uu ) -∇p (∇·∇u) + + F (2) ∂t Re Fr We We follow the approach outlined in Brackbrill et al.16 and treat the interfacial force between the two fluids as a body force. This gives rise to the last term on the right hand side in eq 2. In the VOF approach we use an indicator whose concentration Rk describes the nature of the fluid present. This is initialized as being unity when a cell is completely occupied by one phase and zero when it is completely occupied by another phase. Its distribution with space and time is obtained by solving ∂Rk + u·∇Rk ) 0 ∂t
(3)
The density and viscosity of the fluid used in the above equations are those of a mixture and are given by F ) ∑RkFk and µ ) ∑Rkµk. The dimensional groups which describe the system behavior are Re ) Fr )
dhVFw µw
Simulations were carried out for both two- and threedimensional cases. For the 2D case the depth of the channel (along the y-axis) was assumed to be infinity and we have considered velocity variations along the width (z-axis) alone, while for the 3D case velocity variations along the depth and width have been considered. For the simulations we consider a T-shaped channel with a depth of 590 µm and a width of 500 µm. The entrance length of a channel which ensures fully developed flow given by Dombrowski et al.22 is Le ) 0.379 exp(-0.148Re) + 0.055Re + 0.26 dh
2
V gdh
FV dh ) Re × Ca σ To obtain the contact angle of kerosene-water on Perspex, we use the Young-Laplace equation for the air-water interface, air-kerosene interface, and water-kerosene system, as shown below 2
We )
σsa - σsw - σaw cos θaw ) 0
(4)
σsa - σsk - σak cos θak ) 0
(5)
σsw - σsk - σwk cos θwk ) 0
(6)
From these equations we obtain σwk cos θwk ) σak cos θak - σaw cos θaw
Figure 2. Images of slugs obtained at kerosene flow rates of (a) 10, (b) 20, and (c) 40 mL/h and a constant water flow rate of 10 mL/h in a dh ) 0.54 mm channel (white slug is the aqueous phase).
(7)
Taking the surface tension of the water-kerosene system as 0.045 N/m (Zhao et al.13), for the air-water system as 0.072 N/m, and for the air-kerosene system as 0.026 N/m (Sonmez and Cebeci21) and the contact angle for the air-kerosene system as 0° and that for the air-water system as 77°, the contact angle for the water kerosene system is obtained as 77.48°. This value of the contact angle is used in our simulations when we compare the predictions with experimental data unless mentioned otherwise. The angle between the interface and the wall contained in the kerosene phase is the contact angle referred to. The values of density of water and kerosene used in the simulations are 998 and 780 kg/m3. The viscosities of both water and kerosene were taken to be 0.001 Pa s. The time step for the integration used is 10-5. In each time step 50 iterations were found to be sufficient for convergence, i.e., to ensure that the residuals were lower than 10-5. At the inlet we have used the velocity inlet as boundary conditions, while at the exit we have used the outflow as boundary conditions. This combination of boundary conditions is recommended for liquid systems since it ensures mass conservation. Here all mass entering the system is guaranteed to leave the system.
(8)
This relationship is used to determine the entrance lengths Le of the inlet channels. At the lower flow rates corresponding to an Re ) 20, Le ) 0.74 mm, and for the higher flow rates when Re ) 300, Le ) 4.6 mm. The length of the channels used in the experiments is 70 mm and so is sufficiently long to ensure fully developed flow. To save computational time, we have chosen the length for the inlet channel to be lower than 70 mm in our simulations. However they were sufficiently long to ensure fully developed flow. For instance for the 2D simulations in the 0.54 mm channel at the lower Re, the inlet channel length was 3 mm and the mixing channel length was 10 mm. A total of 9560 cells are created and 20 outlet cells are used. For 3D simulations 50625 hexahedral cells were used at the lower Reynolds numbers for the above geometry. For higher flow rates we have carried out only 3D simulations. The inlet channel length was chosen as 5 mm, and the mixing channel length as 20 mm. A total of 157696 hexahedral cells are used for the higher Re and the geometry described. For simulations of the channel with dh ) 1 mm, the inlet channel length was 4 mm and the mixing channel length was 25 mm, and we have used 27200 cells for the 2D simulations. In all cases it was ensured that the criteria of fully developed flow is well-satisfied. The length of the mixing channel used in the simulations was chosen to be lower than that in actual experiments to reduce computational effort. 4. Results and Discussions To observe the flow behavior, experiments were carried out in a 0.54 mm dh channel at different flow rates. At low flow rates of the two fluids we observe slug flow behavior. The experimental images of the observed slugs are shown in Figure 2. The figure depicts images for three different kerosene flow rates of 10, 20, and 40 mL/h, respectively, when the water flow rate is held constant at 10 mL/h. The water slugs are bright while the kerosene phase is dark in the images.
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Figure 3. Numerical predictions of slug-flow regime at contact angles of 78 and 1°, kerosene flow rates of 10 and 20 mL/h, and a costant water flow rate of 10 mL/h (red color indicates water slugs and blue color kerosene): (a) contact angle of 78° and kerosene flow rate of 10 mL/h; (b) contact angle of 78° and kerosene flow rate of 20 mL/h; (c) contact angle of 1° and kerosene flow rate of 10 mL/h; (d) contact angle of 1° and kerosene flow rate of 20 mL/h.
Figure 4. Dependence of water slug length on kerosene flow rate at a constant water flow rate (10 mL/h). Comparison of experiments with simulation predictions at two contact angles.
The images of the slugs from simulations at kerosene flow rates of 10 and 20 mL/h and water flow rate of 10 mL/h are shown in Figure 3 for contact angles of 78 and 1°, respectively. These results help us understand how sensitive the shape of the interface is to the choice of the contact angle used in the simulations. It also helps us understand the effect of the contact angle on slug length. For instance at a contact angle of 78° the interface is almost perpendicular to the walls (Figure 3a,b), while at a contact angle of 1° the interface is in the form of a smooth curved surface (Figure 3c,d). An extreme value of 1° was chosen for the lower contact angle to clearly bring out the difference in the interface shape. We see that the water slug lengths decrease as we increase the kerosene flow rate. To quantitatively verify the predictions of the simulations with the experimental results, the variation of the experimentally determined water slug lengths with the flow rate of kerosene as observed in the microchannel (dh ) 0.54 mm) is shown in Figure 4. The slug length was determined by tracking the variation of intensity across pixels in the axial direction. The change in the intensity is used to determine the slug interface. The distance between the two interfaces yields the slug length. This approach gives a more accurate measurement of slug length. Lengths are calculated for 50 slugs for each flow rate and are averaged. We observe that the slug length of water decreases with an increase in the kerosene flow rate when the water flow rate is fixed at 10 mL/h. This is to be expected since
Figure 5. Pressure profiles obtained from simulations along the central axial line for 2D (dashed line) and 3D (solid line).
at steady state the volume fraction of water in the channel would decrease when its relative flow rate decreases. The results of two-dimensional simulations carried out in FLUENT for the flow rates used in the experiments are also shown in Figure 4. This allows us to obtain a quantitative comparison between the trends obtained in the experiments and the numerical predictions of the simulations. Results obtained using a contact angle of 78° (1°) is shown as open squares (triangles) in Figure 4. The predictions of the simulations agree well with those of the experimentally determined values at high flow rates of kerosene. The slug lengths were found to increase with a decrease in the contact angle. This increase in the slug lengths is more at low flow rates of kerosene. Consequently the slug length predictions using a contact angle of 1° agrees better with the experimental data than a prediction with a contact angle of 78°. The slugs lengths were determined by varying the kerosene flow rate in steps of 10 mL/h. The experiments for the determination of the slug lengths are carried out until a maximum flow rate of 60 mL/h beyond which the sensitivity of the slug length is low. The slug length calculations discussed so far are based on 2D simulations. We have also performed 3D simulations to check the dependency of slug length on flow rates. The predictions of slug length based on 2D simulations were found to agree very closely with those of 3D simulations. To get a quantitative estimate of the pressure variation in the microchannel, pressure profiles are drawn along the central axial line that is z ) 0.295 mm for the 2D simulations and z ) 0.295 mm and y ) 0.25 mm for the 3D case. The two pressure profiles are shown in Figure 5 (solid line for 3D and dashed line for 2D).The calculated pressure change across the interphase in 3D simulations is found to be 69 Pa, and that for the 2D case is found to be 35 Pa. These values are consistent with the predictions of the Young-Laplace equation, which is 63.4 Pa (where we use ∆p ) 2σ cos θ/R with R ) 0.295, which is half the width of channel). The pressure drop across the interface using a 3D simulation is approximately two times that obtained using a 2D simulation since for the 3D simulations we have two radii of curvature which are finite, while in the 2D case one of the radii of curvature is infinity and does not contribute to the pressure drop. The operating conditions under which the various flow regimes occur as determined by experiments are shown in Figure 6a. We depict the experimentally obtained flow regimes of slug
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Figure 7. Transition of slug flow to stratified flow and slug flow for contact angle of 78° for (a) each flow rate of 60 and (b) 100 mL/h; (c) contact angle of 45° at each flow rate ) 100 mL/h; (d) contact angle of 45° at each flow rate ) 200 mL/h.
Figure 8. Experimental images of stratified flow when flow rates of the two fluids are equal: (a) 150 and (b) for 300 mL/h. Figure 6. (a) Flow regime map obtained from experiments and simulations in terms of flow rates of the two fluids (0, 2, experimental and simulation slug flow, respectively; O, b, experimental and simulation stratified flow, respectively). (b) Dimensionless representation of flow regime map in terms of Weber numbers.
flow (open rectangle) and stratified flow (open circle) in it. The results of the flow regimes obtained by simulations for various flow rates have been shown as a filled triangle for slug flow and filled circle for stratified flow in the same figure. The slug flow regime is obtained for the case when the flow rates of the two fluids are sufficiently low while the stratified flow regime occurs when both the flow rates are sufficiently high. As the flow rate of the fluids is inc,reased the inertial effects dominate over the surface forces and we observe the stratified flow regime. A dimensionless plot is depicted in terms of Weber numbers of kerosene and water in Figure 6b. The transition region from slug flow to stratified flow occurs beyond Wewater ) 0.1 and Wekerosene ) 0.1. This flow regime map plotted in terms of dimensionless numbers is consistent with the results of Zhao et al.13 The static contact angle is different from the dynamic contact angle which depends on the capillary number,23 Ca, and static contact angle. This can be obtained from θd ) θs[1 + (32Ca/ θs3)]; here θs represents the static contact angle, and θd represents the dynamic contact angle. Ca represents the capillary number. The dynamic contact angle increases with increasing velocity (and Ca). So at higher flow rates there is a significant difference in dynamic contact angle and the static contact angle. To study the influence of contact angle on the transition in the flow regime, we have carried out simulations for two contact angles of 45 and 78°. The results are shown in Figure 7, where we depict the volume fraction contours along the center plane (y ) 0.25 mm). Slug flow changes to stratified flow at a flow rate between 60 and 100 mL/h of each fluid when a contact angle of 78° is used. The flow regime observed in the experiments at 100 mL/h still shows slug-flow behavior. To
Figure 9. Experimental images of slugs in the 1 mm square microchannel for different kerosene flow rates: (a) 10, (b) 20, (c) 30, (d) 40, and (e) 60 mL/h at constant water flow rate of 10 mL/h.
understand this discrepancy, we have carried out simulations with a contact angle of 45°. The predictions now show a slug flow regime at 100 mL/h of each flow rate and stratified flow at 200 mL/h, consistent with experimental observations. We conclude that the flow regime is very sensitive to the contact angle at the transition region. Experimental images of stratified flow are shown in Figure 8 for kerosene and aqueous flow rates of 150 and 300 mL/h, respectively. 4.1. Effect of Channel Size on Slug Length and Flow Regime. To determine the effect of channel size on the slug length, we have carried out experiments in two different geometries. The first one is the channel discussed so far with dh ) 0.54 mm, and the second is a microchannel with a square cross-section with a side of 1 mm (dh, 1 mm). Experimentally obtained images of the slug flow regime are shown in Figure 9 for kerosene flow rates of 10, 20, 30, 40, and 60 mL/h, respectively, at a water flow rate of 10 mL/h. A quantitative comparison of the experimental results of slug lengths with numerical predictions is shown in Figure 10 for
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Figure 12. Experimental images of slugs captured when the flow rate of each phase is 10 mL/h: (a) kerosene-water and (b) coconut oil-water systems in a 1 mm channel.
Figure 10. Comparison of experimental slug lengths with simulation prediction with two different contact angles for the kerosene-water system in a 1 mm square channel.
Figure 13. Dependency of slug length on the organic phase flow rate for two different channel sizes and liquid-liquid systems (kerosene-water and coconut oil-water).
Figure 11. Dimensionless representation of the flow regime map in terms of Weber numbers in a 1 mm channel for the kerosene-water system.
this channel. The water slug lengths are clearly decreasing as we increase the kerosene flow rate, and the experimental results are in reasonable agreement with the prediction of simulations. Here again we see that the simulations underpredict the slug lengths when we use a contact angle of 78°. There is an increase in the predictions of the slug lengths when the contact angle is reduced to 1°, resulting in better agreement with experimental data. The flow regime map obtained in terms of the dimensionless Weber number is depicted in Figure 11. Here again we see that the transition from slug flow to stratified flow occurs beyond a critical value of 0.1. It must be kept in mind that the Re for the two flow regime maps of Figures 11 and 6b are different and they also vary as we move in each region. 4.2. Effect of Fuid Properties (Surface Tension and Viscosity) on Slug Length. 4.2.1. Viscosity Effect. Experiments have also been performed using two different systems (coconut oil-water) and (kerosene-water) in the two different channels. Coconut oil is significantly more viscous than kerosene. The water slugs observed in the kerosene system are bigger than that in the coconut oil system, as shown in Figure 12. We attribute this to the effect of the lower viscosity of the kerosene-water system. For the same flow rate and the same system the Reynolds number is lower in the bigger geometry, and hence this leads to the formation of longer slugs in the bigger geometries. The experimentally determined slug lengths for the two systems and
Figure 14. Dependence of water slug length on surface tension as obtained from simulations in a 1 mm square channel.
geometries are shown in Figure 13. In both geometries the coconut oil-water system has a smaller slug compared to the kerosene-water system. This decrease in slug length is attributed to the effect of viscosity. 4.2.2. Surface Tension Effect. We now investigate using simulations the sensitivity of the slug lengths to the surface tension of a system. For this we have performed simulations of a liquid-liquid system using the properties of kerosene and water and varied the surface tension from 5 to 120 mN/m. The simulations predict that there is no significant change in the slug length when the surface tension is changed, as shown in Figure 14. For this simulation the two flow rates were fixed at 10 mL/h. A similar conclusion was obtained by Qian and Lawal.17 To determine if the insensitivity of the slug length to the surface tension as predicted by the simulations is indeed correct, we have carried out experiments using different fluids having different surface tensions in a 1 mm channel. The selected organic fluids are hexanol and octane, while the inorganic phase was chosen as water. The surface tensions of hexanol-water
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tension. Slug length was found to increase with surface tension. The reason for this mismatch between the experimental finding and the simulation prediction is attributed to the fact that in the simulations the viscosity was kept constant as the surface tension was changed. However, in the experiments both the surface tension and the viscosity of the two systems vary simultaneously. Literature Cited
Figure 15. Comparisons of experimental results with numerical predictions of aqueous slug lengths in a 1 mm channel depicting the effect of viscosity and surface tension.
and octane-water are 6.28 and 50.8 mN/m, respectively. The viscosities of hexanol and octane are 4 and 0.5 cP, respectively. Thus the system with a higher surface tension is associated with a lower viscosity. The measured experimental slug lengths for different flow rates of the organic phase are shown in Figure 15 when the aqueous flow rate was fixed at 10 mL/h. From the figure it is seen that for each flow rate there is a significant difference in the slug lengths of the two systems. The slug length is found to increase as the surface tension increases and the viscosity decreases. The predictions from the simulations when a contact angle of 1° is used are depicted in the same figure for a ready comparison. 5. Summary and Conclusions The present study has analyzed the behavior of a liquid-liquid two-phase flow in a microchannel. A variety of liquid-liquid two-phase systems was examined experimentally. The nature of the flow was visualized using an epi-fluoroscent microscope. These flow regimes were validated with numerical simulations based on the VOF method using a commercial package FLUENT. The experimental observations of the kerosene-water system are consistent with that predicted by FLUENT. For a quantitative validation of the modeling results, slug lengths were calculated from the images and the results were compared with the simulation predictions. As far as the slug lengths are concerned, both 3D simulations and 2D simulations give comparable results. It was found that the simulations are sensitive to the contact angle at the region of transition from slug flow to stratified flow. The flow-regime map gives us an indication of the nature of the flow and can be used as long as the fluids are water and kerosene and the material of construction is Perspex. To study the effect of various parameters on the flow behavior, we have varied the size of the channel and the properties of the fluids such as viscosity and surface tension. The slug lengths were found to increase with the size of the channel for a given fluid system. The slug lengths were found to decrease with an increase in the viscosity of the system. As far as surface tension is concerned from simulations it was observed that the slug length does not change with surface tension in a significant way. However experiments showed that there is a significant dependency of the slug length on surface
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ReceiVed for reView April 6, 2009 ReVised manuscript receiVed August 22, 2009 Accepted November 12, 2009 IE900555E
