Article pubs.acs.org/IECR
Two-Phase Flow in Microchannels: The Case of Binary Mixtures Shahnawaz Molla, Dmitry Eskin, and Farshid Mostowfi* Schlumberger DBR Technology Center, 9450 17th Avenue, Edmonton, T6N 1M9, Alberta, Canada ABSTRACT: Pressure measurements for segmented gas−liquid flows revealed a constant pressure gradient when the gas phase gradually expanded along the channel due to a substantial pressure drop (1500−1600 kPa). The segmented flow was formed by miscible gas and liquid hydrocarbons. A fully saturated liquid (pressurized liquid with dissolved gas) near the bubble point was introduced to the channel. Gas bubbles emerged from the liquid phase due to a reduction in local pressure when the fluid traveled through the channel. The gas phase expanded from nearly 0% up to 70% void fraction as the segmented flow accelerated along the channel. A novel, nonintrusive, in situ pressure measurement was used to accurately determine the pressure profile in the channel. To measure the void fraction and local velocity throughout the channel, a high-speed imaging technique was used. Finally, five different available models were used to describe the experimental results. The models considered the liberation of the gas phase from the saturated liquid as well as the subsequent variations in viscosity using a thermodynamic model.
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INTRODUCTION Recently, gas−liquid flows in microchannels have drawn considerable attention. For example, phase transition of refrigerants from liquid to gas−liquid flow in microchannels has been successfully used to develop effective heat sinks.1,2 Another innovative application of gas−liquid flow in microchannels can be found in monolith reactors and microreactors,3−5 where segmented flow of gas and liquid (also referenced as “slug flow”, “Taylor flow”, or “bubble-train flow”) is employed to control fluid mixing and gas−liquid mass transfer. In a slug flow, the liquid slugs act as tiny reaction chambers with reduced axial dispersion of the reacting species.6,7 Given that applications such as microreactors require controlled production of liquid slugs and gas bubbles for optimal mixing and mass transfer, slug flows have been studied extensively to predict the pressure drop, liquid film thickness, and void fraction in a channel.8,9 Several researchers have developed sensitive pressure measurement techniques for measuring the pressure drop caused by moving droplets through microchannels.10−14 In these studies, the local pressure and pressure fluctuations during drop formation were measured across short channel lengths (∼10 mm), either by measuring the curvature of emerging droplets at a T-junction (Laplace sensor10) or by detecting the displacement of an interface between two immiscible liquids flowing through two parallel channels (microfluidic comparator11,14). Recently, Orth et al.13 have developed a novel multiplexed pressure sensing technique with PDMS membranes, which operated as pneumatically tunable microlenses under pressure. Using this technique, they measured the linear pressure profile in laminar flows. These techniques have the sensitivity necessary to detect small pressure changes when a secondary phase (droplets, biological cells, etc.) enters the channel and increases the hydrodynamic resistance. These techniques are suitable for microfluidic applications working at relatively low pressure ( 0.99) to 80% of the channel length. This pressure distribution was analogous to the incompressible flow. The predictions of the axial pressure distribution from different models showed good agreement, except for the pressure drop calculated by the MullerSteinhagen and Heck model, which was slightly higher than the other models.
Table 2. Range of Flow Conditions Studied in the Simulation Reynolds Number mixture
liquid, ReL
gas, ReG
C1−C10 C1−C12
30−120 21−32
38−61 37−45
pressure-dependent fluid properties predicted by the EOS calculations. The EOS calculations predicted considerable change in the viscosity of the liquid phase in the two-phase flow that occurred below saturation pressure. The calculated values of fluid viscosity (Figure 3) and density as a function of pressure were used as fluid property references in the pressuredrop calculation. In the simulation, the long serpentine channel was divided to short segments, each 10% of the channel’s total length, to calculate the pressure drop in the slug flow with the variation of fluid properties and void fraction. The pressure drop in each segment was sufficiently small to assume uniform fluid properties in the flow within the segment. The pressure at the inlet of the microchannel and the mass flow rate were taken from the experiments, and the simulation was conducted to estimate the pressure drop in the microchannel flow under conditions similar to those in the experiments. Fluid properties were calculated based on the average pressure in the short segment. The pressure drop in each segment was calculated in an iterative manner with the following steps: (1) The inlet pressure and the mass flow rate (constant along the channel) were defined at the inlet of the first segment. A pressure drop across the segment was assumed; i.e., the pressure at the end of the segment was approximated. The mean pressure in the segment then was calculated based on the pressures at the inlet and the end of the segment. (2) The average gas/liquid volume fraction (void fraction) and the fluid properties in the segment were calculated at the mean pressure using the EOS model. The liquidphase and gas-phase velocities were also calculated.
Figure 4. Simulated pressure profiles for the flow of (a) the C1−C10 mixture, mass flow rate of G = 320 kg/(m2 s) and (b) the C1−C12 mixture, mass flow rate of G = 350 kg/(m2 s). The different frictional pressure drop models used in the calculations are shown in the legends. The temperature used in the calculation is 22 °C. 946
dx.doi.org/10.1021/ie301860u | Ind. Eng. Chem. Res. 2013, 52, 941−953
Industrial & Engineering Chemistry Research
Article
the Zhang−Mishima, Lee−Lee, and Lockhart−Martinelli models, the pressure gradient increased monotonically as long as the gas-volume fraction was relatively small (0.7−0.8) and increased significantly (>20%) when the gas volume fraction was >0.7. This rapid increase in the pressure gradient in the two-phase flow explains the deviation from the linear pressure drop in the channel. The pressure gradient increase of the C1− C12 mixture exceeded 25% as the value of the gas-volume fraction in the channel reached 0.8. The pressure gradient calculated by the Muller-Steinhagen and Heck model was noticeably higher than the pressure gradient calculated using the other models. The pressure-drop in the microchannel was also calculated using the semiempirical model (eqs 15 and 16). With the pressure decrease along the channel, the gas volume fraction (void fraction) of the mixtures increased, as shown in Figure 2, and the viscosity of the liquid phase in the channel increased simultaneously, as illustrated in Figure 3. A constant slug length (Ls = 32Dh) is used for this simulations. It will be shown later that the influence of slug length variation on the pressure gradient was not significant. The value of the adjustable parameter a in eq 16 was 0.69 as in our previous work. The simulated pressure profile for the flow of the C1−C10 mixture is shown in Figure 6a for parameter values used in Figure 4a. Similar to Figure 4, the calculated total pressure drop is shown vs the scaled channel length. The model predicts a linear pressure drop in the flow direction up to the end of the channel where the gas volume fraction is 0.85. This result agrees well with the data obtained from the previous analysis based on Lockhart−Martinelli approach. The reason behind possible deviations becomes clear by analyzing the variation of the mean pressure gradient in the channel. Figure 6b shows the variation of the pressure gradient (solid line) calculated (eq 15), as a function of gas volume fraction and corresponding fluid properties. The pressure gradient increases with increasing gas volume fraction (up to 0.65) by maximum 7% in this case. The effect of this change on the local pressure is not significant,
The pressure profile in the channel began to deviate from linearity near the exit of the long channel. Correlation of the pressures at that location with the corresponding gas-volume fraction at that pressure (Figures 2 and 4) showed that the deviation occurred when the gas-volume fraction in the flow was >0.75. A gas-volume fraction of ≥0.75 was calculated at pressures below 500 kPa, based on the EOS calculation. The calculation was valid for both mixtures. An increase in the gas-volume fraction resulted in a significant viscosity increase of the liquid phase (20%−40%), which caused a larger frictional pressure drop in the flow. The pressure gradients for the flow of the C1−C10 mixture with different gas-volume fractions are shown in Figure 5. Based on
Figure 5. Pressure gradient in the C1−C10 mixture flow. The horizontal axis shows the variation of gas-volume fraction within the channel. The different frictional pressure drop models used in the calculations are shown in the legends. All parameters are the same as those given in the previous figure.
Figure 6. (a) Pressure profiles simulated with the semiempirical model for C1−C10 mixture flow, mass flow rate G = 320 kg/(m2 s) and (b) variation of the pressure gradient as a function of volume fraction in the channel. Contributions of the two terms in eq 16 to the total pressure gradient are shown. 947
dx.doi.org/10.1021/ie301860u | Ind. Eng. Chem. Res. 2013, 52, 941−953
Industrial & Engineering Chemistry Research
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to a 1.1-mm-thick glass wafer. The channel had uniform rectangular cross sections along its length (W ≈ 117 μm, H ≈ 58 μm, from SEM measurement). The pressure drop in the channel was measured using 10 equally spaced membrane cavities that were connected to the main channel. The membrane formed a thin wall (100 μm thick) separating the channel from the outside, and, when subjected to local pressure inside the microchannel, the membrane protruded outward, which was used to measure the local pressure in the channel. Using the embedded membranes, it was possible to achieve an accuracy of 40 kPa in pressure measurements. Each membrane was calibrated individually prior to running the experiments. The calibration procedure for the pressure measurement and imaging technique is described in ref 22. The liquid−gas mixtures (C1−C10 and C1−C12) were prepared in pressurized sample bottles. The pure gas phase was injected into a given volume of liquid until it was saturated with the gas at a specified pressure and temperature. During the experiment, the sample was injected at high pressure (2860 kPa, p > psat) from the sample bottle using an ISCO 500D syringe pump (ISCO, USA). The channel exit was at atmospheric pressure. The saturated liquid flow rate from the sample bottle was regulated by the syringe pump and flow was monitored for 15 min before every measurement to ensure stable conditions. Pressure measurements and video recordings were acquired simultaneously. Experimental Results. Experiments were conducted to study the pressure drop for the two binary gas−liquid systems. Decane (n-C10H22) and dodecane (n-C12H24), procured from Sigma−Aldrich (USA) and used as-supplied, were used as the liquid phase (see Table 3 for physical properties) and methane
because this occurs along a relatively long distance ( 0.98). The pressure at the inlet of the test section was varied (for C1−C10, 1732−2662 kPa; for C1−C12, 2159−2792 kPa) to create different gasvolume distributions in the channel. Notably, the linear trend was consistently observed in all the experiments with slug flow over a wide range of gas-volume fractions in the channel. The void fractions, corresponding to the pressure profiles with the highest inlet pressures in Figure 10, are shown in Figure 9. The pressure measurements show a good repeatability as indicated by the error bars. As the pressure decreased in the direction of the flow, the gas phase expanded and gradually occupied a larger space in the channel for both the C1−C10 and C1−C12 mixtures. Consequently, the liquid-volume fraction decreased along the channel. The gas-volume fractions (in the test section as shown in Figure 8a) varied from 0.25 to 0.7 in the C1−C10 mixture and from 0.1 to 0.7 in the C1−C12 mixture.
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COMPARISON WITH MODEL PREDICTIONS The experimental pressure profile was compared with model predictions with the experimental parameters (inlet pressure, mass-flow rate) used as input to the pressure-drop model. First, the gas-volume fractions for the two mixtures were compared with the EOS model predictions as shown in Figure 11. The plots show the variation of the gas-volume fraction with pressure in the channel. The experimental data for the slug flow 950
dx.doi.org/10.1021/ie301860u | Ind. Eng. Chem. Res. 2013, 52, 941−953
Industrial & Engineering Chemistry Research
Article
Figure 12. Comparison of pressure measurements from all experiments with (a) Lee−Lee model predictions and (b) semiempirical model predictions. The solid line represents the parity line.
showed good agreement with the model predictions, which assume the equilibrium distribution of the gas and liquid phases in the mixture. The close agreement indicates the enhanced mixing properties in the gas−liquid slug flow. The deviation at lower pressure range (
