LIQUID LIQUID MIXTURES FLOW IN MICROCHANNELS. Ben-Ran Fu

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1 LIQUID LIQUID MIXTURES FLOW IN MICROCHANNELS Ben-Ran Fu Green Energy and Environment Research Laboratories, Industrial Technology Research Institute, Taiwan; and Department of Engineering and System Science, National Tsing Hua University, Hsinchu, Taiwan ICETI-J1009_SCI No. 13-CSME-49, E.I.C. Accession 3507 ABSTRACT This study constitutes an experimental and numerical investigation into the single-phase flow of liquid liquid mixtures and of water in uniform, converging and diverging microchannels. The experimental results for the pressure drop in three microchannels show good agreement with both theoretical predictions and CFD simulation results. The numerical velocity profiles in microchannels are also presented and show excellent agreement with the analytical velocity profiles. In addition, the pressure distribution prediction for the converging and diverging microchannels is also consistent with that obtained through the CFD results. Keywords: pressure drop; velocity profile; pressure distribution. M ELANGE D UN FLUX LIQUIDE LIQUIDE DANS DES MICROCANAUX RÉSUMÉ Cet article constitue une recherche expérimentale et numérique de l écoulement monophase de mélange liquide-liquide et eau dans des microcanaux convergents et divergents. Les résultats expérimentaux de la perte de charge dans trois microcanaux démontrent une bonne concordance tant dans les prédictions théoriques que les résultats de simulation CFD. Le profil de la vitesse numérique dans les microcanaux est aussi présenté et démontre un excellent accord avec le profil de la vitesse analytique. En outre, la prédiction de la distribution de pression pour les microcanaux convergents et divergents est aussi consistante avec les résultats obtenus par le système CFD. Mots-clés : perte de charge ; profil de vitesse ; distribution de la pression. Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No. 3,

2 1. INTRODUCTION The single-phase flow of a liquid or gas in uniform microchannels has been studied by many researchers in recent years. It is of interest and significance to understand the transport phenomena of hydrodynamics, especially the pressure drop, through microchannels. However, the microchannels used in the literature normally had a uniform cross-sectional area, in the shape of a rectangle, circle, triangle, or trapezoid. Recently, the fluid flow in a microchannel with a varying cross-sectional area has been of significant interest for many applications such as boiling heat transfer for microelectronics cooling [1], condensation heat transfer [2], microchannel heat exchangers [3], chemical reactions in microfluidic devices [4, 5], biotechnology [6], and micromixers [7], as well as in fundamental studies of adiabatic single-phase flow [8] and two-phase flow [9]. However, liquid liquid mixture flows in microchannels have usually been reported in relation to mixing performance tests [10, 11], whereas the pressure drops of such liquid liquid mixture flows in microchannels have rarely been studied. This study presents the single-phase pressure drops of liquid liquid mixtures (solutions of sulfuric acid, H 2 SO 4, and sodium bicarbonate, NaHCO 3 ) and water in rectangular silicon-based microchannels with uniform and varying cross-sectional areas as determined experimentally and numerically. In the liquid liquid mixture experiments, each solution enters separately at a specific flow rate from an entrance port and flows through a rectangular front channel. The two liquid streams subsequently meet at the intersection of the two connecting microchannels and the main channel. The main and two front channels form a Y-shaped test section, which is widely employed in the literature as a micromixer. The sulfuric acid may react with the sodium bicarbonate to produce CO 2 bubbles if the concentration is high enough or the flow rate is low enough. This reaction is as follows: H + + HCO 3 CO 2 + H 2 O. In this study, the concentrations of both solutions are low enough and the flow rate is high enough to prevent any chemical reaction in the microchannels. Thus, simple-phase flow prevails. The pressure drops under various conditions are measured and compared with theoretical predictions and numerical solutions. The flow field and pressure distribution in the main channels are also studied numerically. This information is of significant interest in relation to the removal of CO 2 bubbles in a micro-sized direct methanol fuel cell. 2. EXPERIMENT DETAILS 2.1. Experimental Setup A schematic diagram of the experimental setup is shown in Fig. 1. This consists of the Y-shaped test section with two front channels and the main channel with a uniform, converging, or diverging cross-sectional area; a syringe pump (KD Scientific 200); a data acquisition system (YOKOGAWA MX100); and a pressure measurement system. The syringe pump uses two syringe tubes to drive the two solutions into different inlet chambers simultaneously (or DI water only), as shown in Fig. 2. The two liquid streams meet at the intersection of the two front channels and the main channel. The mixtures output from the test section are drained to a container on an electronic balance, which might make it possible to calibrate the flow rate of each fluid before an experiment. The pressure taps are located near the inlet or outlet chamber at a connecting tube made of glass. The dimension of these connecting tubes is much larger than the test channels. Therefore, the pressure losses through the connecting tubes are estimated to be negligibly small. The differential pressure transducer (Huba 692) used in the present study has a short response time of s, and the sampling rate for the pressure drop measurements is set at 100 Hz. The present study employs aqueous solutions of sulfuric acid and sodium bicarbonate as the working fluids. These solutions are driven simultaneously by the syringe pump at the same flow rate. The total volumetric flow rates (Q total ) are controlled in the range from to m 3 /s. Three concentrations C are investigated for the two solutions at the inlet before mixing: 0.25, 0.50, and 0.75 mol/l. The flow rate is relatively high and the concentration is relatively low for both solutions to prevent a chemical 632 Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No. 3, 2013

3 Fig. 1. Schematic of experimental apparatus. Fig. 2. Test section layout. reaction in the ain channel. A chemical reaction between H 2 SO 4 and NaHCO 3 will produce CO 2 and may cause the flow to become two phase. Indeed, Fu et al. [5] employed these two solutions to explore two-phase flow due to chemical reactions. The single-phase flow of deionized water in the Y-shaped test sections is also studied, and the total volumetric flow rate of water (Q total ) is also controlled in the range from to m 3 /s Fabrication of Test Section The schematics of the Y-shaped test sections are shown in Fig. 2. The width of the uniform microchannel is 675 µm, whereas it varies linearly from 1500 µm to 210 µm for the converging microchannel and from 210 µm to 1500 µm for the diverging one, resulting in a convergence or divergence angle of The length and depth of the main channel are 20 mm and 100 µm, respectively. The mean hydraulic diameter of the main microchannel is approximately 174 µm in all cases. Both the front channels have uniform crosssectional areas. Bulk micromachining and an anodic bonding process were used to fabricate the test section. The microchannels and inlet and outlet chambers are etched using deep reactive-ion etching stopped at the box layer of the SOI wafer, which results in an accurate depth of 100 µm. Therefore, a theoretical pressure Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No. 3,

4 drop prediction could be obtained with high accuracy. Direct writing using excimer laser micromachining technology is used for the through holes under the inlet and outlet chambers. The top surface is covered with Pyrex #7740 glass using anodic bonding. 3. METHOD FOR CFD SIMULATIONS Numerical simulations of two fluid mixtures and water flow in the Y-shaped test sections are performed using commercial software (CFD-ACE+). Each simulation uses 225,792 cells for each type of microchannel. Grid independence tests are conducted with various quantities of cells, i.e., 37,632, 75,264, 150,528, 225,792, and 301,056 cells. The results reveal that the deviation in the velocity distribution and pressure drop between 225,792 and 301,056 cells is only about 0.5%. The boundary condition at the inlet is fixed at a constant mass flow rate, corresponding to the experimental conditions. Moreover, a constant pressure condition (P = 0) is applied at the outlet, and no-slip conditions are applied on all the channel walls. CFD-ACE+ is used to solve the steady-state momentum and continuity equations for the fluid flowing in the Y-shaped test sections. The convergence criterion of simulations is applied when the normalized residuals for the velocity and pressure decrease to a value of RESULTS AND DISCUSSION 4.1. Pressure Drop As stated in the section on the experimental setup, taps for the pressure differential transducer are located near the inlet and outlet chambers. Therefore, the measured pressure drop could be considered to be the pressure drop between the inlet and outlet chambers. The total pressure drop ( P) is composed of the frictional pressure drop ( P f ) through the channels, acceleration pressure drop (1/2ρ(Vout 2 Vin 2 )), and minor pressure loss ( P loss ) due to a change in the cross-sectional area. This is expressed as P = P f ρ(v 2 out V 2 in) + P loss. (1) Because the microchannels are relatively small, the mean Reynolds number (Re) ranges from 11.8 to 174 in the main channel. The flow in a microchannel is assumed to be laminar, and the frictional pressure drop can be approximately evaluated using the following equation [12]: P f = L 0 ( 1 2 ρv (x)2 f (x) 1 D H (x) ) dx, (2) where L is the length of the channel, ρ is the density of the liquid or mixture, V is the mean velocity of the fluid, f is the friction factor, D H is the hydraulic diameter of the microchannel, and x is the flow direction. Assuming that the Hagen Poiseuille equation is applicable for a rectangular channel with varying cross-sectional area, the frictional factor can be evaluated using the equation reported in the literature [13]. The minor pressure losses ( P loss ) are evaluated using the following equation: P loss = k 1 2 ρv 2, (3) where k is a loss coefficient. In the present study, the inlet and outlet configuration losses are considered. The loss coefficients for the inlet and outlet are typically 0.5 and 1.0 [14], respectively. In addition, the hydrodynamically developing flow may be important in the microchannel, and the pressure loss associated with the flow developing in the entrance region of the microchannel should be considered [15]. The loss coefficients for the flows developing in the front channel are 1.07, 0.83, and 1.43, because of the size effect [16], for the uniform, converging, and diverging microchannels, respectively. 634 Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No. 3, 2013

5 Fig. 3. Experimental pressure drop data for (a) uniform, (b) converging, and (c) diverging microchannels. Figure 3 shows the experimental pressure drop data ( P Exp ) in the test sections as a function of the inlet concentration (water or mixture) and volumetric flow rate. The figure clearly shows that the pressure drop increases approximately linearly with an increase in the flow rate, as well as with the concentration. At a given flow rate, the total pressure drop increases with an increase in the inlet concentration. This is because the viscosity of each solution increases with its concentration. For each test section, the maximum pressure drop difference between the water flow and mixture flow with C = 0.75 mol/l is about 15% because of the different viscosities. Comparisons of the total pressure drops between the experimental measurements and theoretical predictions ( P Th ) are shown in Fig. 4. This figure shows that the deviation between the theoretical value and experimental data for the total pressure drop is within 10% for P > 10 kpa. The relative deviations become much more significant for P < 10 kpa because the relative uncertainty of the experimental measurement becomes higher for lower pressure drops. Figure 5 shows comparisons of the total pressure drops for a mixture flow with C = 0.75 mol/l among the experimental, theoretical, and CFD simulation results as a function of the volumetric flow rate. These figures clearly show that the agreement among the experimental, theoretical, and CFD simulation results is within 10%. These comparisons demonstrate the good quality of the experimental data and numerical solutions reported in the present study. Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No. 3,

6 Fig. 4. Comparisons of total pressure drops between experimental data and theoretical predictions. Fig. 5. Comparisons of total pressure drops among experimental, theoretical, and CFD simulation results in (a) uniform, (b) converging, and (c) diverging microchannels. 636 Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No. 3, 2013

7 Fig. 6. Velocity profiles in microchannels at z = 0 and different axial locations (x/l) for water flow with Q total = m 3 /s: (a) uniform, (b) converging, and (c) diverging microchannels Velocity Distribution For the main channel with a uniform cross section, the analytical fully developed velocity profile is available in the literature. For a steady-state, fully developed, laminar, and incompressible flow, the exact solution of the velocity distribution in the rectangular channel with a y a and b z b can be expressed as [17] ( u(y,z) = 16a2 µπ 3 dp ) [ dx ( 1) (n 1)/2 1 cosh(nπz/2a) ] cos(nπy/2a) n=1,3,5,... cosh(nπb/2a) n 3, (4) where dp/dx is the pressure gradient along the flow direction and a negative constant. Figure 6 shows the velocity profiles of the numerical results in the main channel at z = 0 and different axial locations (x/l) in the flow direction for Q total = m 3 /s. At the intersection of the front channels and main channel (x/l = 0), the two streams from the front channels merge. Therefore, two velocity peaks are shown. The analytical velocity profiles, calculated from Eq. (4) with z = 0 and Q total = m 3 /s, are also shown in Fig. 6 to validate the numerical solution. The numerical velocity profiles demonstrate good agreement with the analytical velocity profiles, with a deviation of about 1.4%. As shown in Fig. 6a, the velocity profiles are overlapping, except for x/l < 0.03, indicating that the flow is fully developed after x = 0.03L. Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No. 3,

8 Fig. 7. Pressure distribution in microchannels at Q total = m 3 /s for C = 0.75 mol/l. The velocity profiles in the converging and diverging microchannels keep changing in the flow direction owing to the variation in the flow s cross section. In the converging microchannel, the velocity distribution evolves from a two-stream profile at the intersection into a parabolic one with an increase in the peak velocity along the flow direction because of the decreasing cross-sectional area. In contrast, in the diverging microchannel, the velocity profile evolves from a two-peak distribution into a parabolic one with a decrease in the peak velocity along the flow direction. It is also interesting to note that the velocity profile at x/l = 0.6, where the cross-sectional area is coincident with the mean value of the converging microchannel, agrees very well with the analytical solution for a uniform channel with the same cross-sectional area as the mean value. The same degree of agreement is also demonstrated for the diverging microchannel at x/l = 0.4, where the mean cross-sectional area is located. These good agreements may justify using the Hagen Poiseuille equation to evaluate the pressure drop through a converging or diverging microchannel Pressure Distribution It is interesting to examine the pressure distribution along the flow direction in microchannels. Figure 7 shows the numerical simulations of the pressure distribution at the centerline in the main channel along the flow direction at z = 0 for a mixture flow with C = 0.75 mol/l and Q total = m 3 /s. The pressure distribution predicted from Eqs. (1 3) for converging and diverging microchannels is also shown in Fig. 7, and shows good agreement with the CFD results. This demonstrates that Eqs. (1 3) may give reasonable predictions of the pressure drop for a two-solution mixture flow in a microchannel with a varying cross-sectional area. Although such an analysis using Eqs. (1 3) seems simple and straightforward, there is no real implementation of such an analysis in the literature for the pressure drop in a microchannel with a nonuniform cross-sectional area. For the uniform microchannel, the figure clearly shows a linear pressure distribution with a constant and negative slope, indicating that the flow is fully developed. Moreover, in the converging microchannel, the pressure decreases slowly at the beginning but rapidly near the exit. Conversely, in the diverging microchannel, the pressure decreases very rapidly near the entrance but slowly near the outlet. Notably, a steep pressure drop is seen near the entrance (0 < x/l < 0.1) in the diverging microchannel. This may have significant implications for the movement of a bubble in a diverging microchannel. A bubble in a diverging microchannel moves easily in the forward direction, but moves with difficulty in the backward direction, especially near the entrance because of the steep pressure gradient there. 638 Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No. 3, 2013

9 5. CONCLUSIONS This study constitutes an experimental and numerical investigation into the single-phase flow of liquid liquid mixtures and water in Y-shaped microchannels with uniform, converging, and diverging crosssectional areas. Very good agreement, within 10%, was obtained between the theoretical pressure drop predictions using the Hagen Poiseuille equation, the experimental data, and the CFD simulation results. For the uniform microchannel, the velocity profile evolved from a two-peak velocity profile at the intersection between the front channels and main channel (x/l = 0) into a fully developed velocity profile for x/l It showed excellent agreement with the analytical fully developed velocity profile. For the converging and diverging microchannels, the velocity profiles continued to develop from two-peak distributions into parabolic velocity profiles in the axial distributions because of the changes in the channels cross sections. Moreover, the numerical velocity profile at a local position with the mean cross-sectional area, i.e., x/l = 0.6 and 0.4 for the converging and diverging microchannels, respectively, agreed very well with an analytical solution that assumed a uniform cross section at that particular location. Unlike the linear pressure distribution in the main channel with a uniform cross section, the pressure fell slowly in the converging microchannel near the entrance and rapidly near the exit. Conversely, the pressure decreased rapidly in the diverging microchannel near the entrance and slowly near the outlet. Such a pressure distribution may enable the forward flow of a bubble in a diverging microchannel. ACKNOWLEDGEMENTS This work was supported by the National Science Council of Taiwan under contract No. NSC E MY3, and the author would like to express his gratitude to the Geothermal Technology Department at the Industrial Technology Research Institute. REFERENCES 1. Fu, B.R., Tsou, M.S. and Pan, C., Boiling heat transfer and critical heat flux of ethanol water mixtures flowing through a diverging microchannel with artificial cavities, International Journal of Heat and Mass Transfer, Vol. 55, pp , Kuo, C.Y. and Pan, C., Two-phase flow pressure drop and heat transfer during condensation in microchannels with uniform and converging cross-sections, Journal of Micromechanics and Microengineering, Vol. 20, , Liu, T.L., Fu, B.R. and Pan, C., Boiling two-phase flow and efficiency of co- and counter-current microchannel heat exchangers with gas heating, International Journal of Heat and Mass Transfer, Vol. 55, pp , Fu, B.R. and Pan, C., Simple channel geometry for enhancement of chemical reactions in microchannels, Industrial & Engineering Chemistry Research, Vol. 49, pp , Fu, B.R., Tseng, F.G. and Pan, C., Two-phase flow in converging and diverging microchannels with CO 2 bubbles produced by chemical reactions, International Journal of Heat and Mass Transfer, Vol. 50, pp. 1 14, Hsieh, S.S. and Liou, J.H., DNA molecule dynamics in converging-diverging microchannels, Biotechnology and Applied Biochemistry, Vol. 52, pp , Sun, C.L. and Sie, J.Y., Active mixing in diverging microchannels, Microfluidics and Nanofluidics, Vol. 8, pp , Duryodhan, V.S., Singh, S.G. and Agrawal, A., Liquid flow through a diverging microchannel, Microfluidics and Nanofluidics, in press, doi: /s , Hwang, J.J., Tseng, F.G. and Pan, C., Ethanol-CO 2 two-phase flow in diverging and converging microchannels, International Journal of Multiphase Flow, Vol. 31, pp , Xia, H.M., Wang, Z.P., Koh, Y.X. and May, K.T., A microfluidic mixer with self-excited turbulent fluid motion for wide viscosity ratio applications, Lab on a Chip, Vol. 10, pp , Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No. 3,

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