Oil-water two-phase flow in microchannels: flow patterns and pressure drop measurements.
Understanding and modelling two-phase flows in Microchannels--those with hydraulic diameters smaller than 1 mm--are of considerable interest in several industrial processes involving complex microsystems. Areas of application include chemical engineering (Tice et al., 2003; Shui et al., 2007), biomedical science (Shui et al., 2007), petroleum science (Lenormand et al., 1983) and so on. Significant attention has been focused on gas-liquid two-phase flows in microchannels. However, the flow patterns and corresponding pressure drops of two immiscible liquids in microchannels are still not well understood (Zhao et al., 2006). A number of studies, however, have used two immiscible liquids flowing in microchannels in order to form droplets or plugs (Tice et al., 2003). Droplets have been used in microchannels to carry out and enhance two-phase chemical reactions (Tice et al., 2003). Song et al. (2003) showed that it is possible to form droplets of multiple aqueous reagents in a flow of water-immiscible carrier fluid, transport the droplets through microchannels without dispersion, and mix the contents of the droplets by chaotic advection in winding channels.
Oil-water two-phase flows in microfluidic devices have been successfully employed in creating emulsions commonly used in the chemical and textile industries, food, and many other domains. In these applications, it is necessary to precisely control the droplet size and the polydispersity (Tan et al., in press). Therefore, most investigations of the liquid-liquid flow in microsystems have focused on the droplet size versus liquid physical properties and microsystem geometry.
Recently, the effect of various operating conditions on the flow patterns, slug size, interfacial area, and pressure drops was investigated by Kashid and Agar (2007). Experiments were carried out using different Y -junction mixing elements with various downstream capillaries. The authors showed that the capillary Y-junction dimensions had a significant effect on slug size and thus interfacial area, which increases with decreasing dimensions. Three flow regimes were observed as a function of liquid flow rate: slug flow, droplet flow of water in organic phase, and deformed interface flow. The latter regime is unstable and was observed only at a high ratio of water to cyclohexane flow rate. Water forms long slugs while cyclohexane is present as small droplets. A theoretical prediction of the pressure drop along a slug flow capillary was developed based on the capillary pressure and hydrodynamic pressure drop of the two individual phases.
In the case of pipes of large hydraulic diameter, several studies have been devoted to two-phase flows of immiscible liquids, where it appears that, as for gas-liquid flow, pressure drop is strongly dependent on flow patterns.
The simplest pattern that can be modelled easily is annular flow (Brauner, 1991; Rovinsky et al., 1997; Bannwart, 2001). In this case, the pressure drop differs according to whether the less viscous fluid is in contact with the pipe wall or flows in the centre of the pipe (lubrification effect). However, due to density effects, liquid-liquid patterns in pipes are seldom annular, and other flow patterns are frequently encountered (Fujii et al., 1994; Beretta et al., 1997; Bannwart et al., 2004), namely dispersed, slug, bubbly, and plug flows.
Angeli and Hewitt (2000) studied the effect of wettability on flow patterns. Two horizontal test sections were used, one made of stainless steel and another of acrylic resin. The authors observed a substantial difference in flow patterns and phases distribution between these two tubes. The flow patterns were classified as follows: stratified flow, stratified flow with a layer of drops or three-layer flow, stratified/mixed flow, and dispersed flow (droplets of oil in water or vice versa). The effect of pipe inclination on liquid-liquid two-phase flow patterns, phase holdups, and pressure drops was also studied recently by Rodriguez and Oliemans (2006) and Lum et al. (2006).
In this paper, we present experimental results of two-phase oil-water flows in horizontal microchannels. The following section describes the experimental set-up. Experimental Results Section presents experimental observations of two-phase flow patterns and two-phase pressure drops. The results are interpreted in Discussion Section using the homogeneous and Lockhart-Martinelli models.
EXPERIMENTAL SET-UP AND PROCEDURE
This section presents the experimental set-up used in this study, the wettability characteristics of the microchannels, and the determination of their hydraulic diameters.
A schematic view of the experimental set-up is shown in Figure 1. The 120-mm-long horizontal microchannel constitutes the test section. Two fluids are introduced separately through a T-junction using two calibrated pumps. The mixture is evacuated via a second T-junction. This last one was used for a phase distribution study to be presented in a future report. In the present paper, only the results obtained in the central channel are presented.
[FIGURE 1 OMITTED]
Two sets of microchannels were prepared using two parallel plates made of quartz or glass. For each set, the microchannel was etched using conventional precision technology on one of the two plates, which were then assembled together. Watertightness was ensured by drilling 16 holes distributed symmetrically around the inlet, central, and outlet microchannels. The two plates were then clamped tightly together using screws bolted through the 16 holes.
The fluids used were deionized water and mineral oil (Marcol 82). The physical properties of the mineral oil are given in Table 1.
In order to determine the wettability of the glass and quartz microchannels using oil or water, the contact angle ([theta]) of a liquid droplet placed on a flat sample of glass or quartz was measured by a confocal scanning laser microscope (Salim et al., 2008). The measured contact angles of an oil droplet on a flat sample of quartz and glass were 12[degrees] and 3[degrees], respectively. The measured contact angles of a water droplet on a flat sample of quartz and glass were 42[degrees] and 38[degrees], respectively. Oil is therefore the more wetting liquid for both materials.
Hydraulic Diameter Estimation
The hydraulic diameters [D.sub.h] of the microchannels were determined using two methods:
(1) From image analysis with the following equation:
[D.sub.h] = 4A/P (1)
where A and P are the wetting area and perimeter of the microchannel cross-section, respectively. These parameters were determined by a method using confocal scanning laser microscopy (Salim et al., 2008) as follows. The walls of the microchannels were wetted with an aqueous solution of fluorescein. Stacks of two-dimensional (2D) images were recorded through a 10x Nikon objective with a Biorad Rainbow microscope by steps of 10 [micro]m. Figure 2 shows projections of the stacks of 2D images in the x-y-z space and in the x-z plane. The white voxels and pixels correspond to the film of fluorescent aqueous solution. The perimeter of the microchannels was deduced from the boundary between glass or quartz and the liquid fluorescent film. As seen in Figure 2, the quartz microchannel section is almost square, whereas the glass microchannel section is semicircular. Hydraulic diameters of 793 and 667 [micro]m were obtained for the quartz and glass microchannels, respectively.
[FIGURE 2 OMITTED]
(2) From oil and water single-phase flow:
Oil and water single-phase flow experiments were conducted with quartz and glass microchannels by varying the flow rate and measuring the corresponding pressure drop as indicated in Figure 1. The hydraulic diameter was determined assuming a circular cross-section for each microchannel. The Hagen-Poiseuille equation (Equation 2) was assumed to be valid
[DELTA]P/L = 32[mu]V/[D.sup.2.sub.h] (2)
where [DELTA]P is the pressure drop over the length L, [mu] the dynamic viscosity, V the superficial velocity, and [D.sub.h] is the microchannel hydraulic diameter.
Hydraulic diameter values of 787 and 677 [micro]m were obtained for the quartz and glass microchannels, respectively. These values are in very good agreement with those determined by confocal scanning laser microscopy.
Two-Phase Flow Experiment Procedure
Several experiments were carried out by varying the flow rates of the two fluids. For each experiment, the microchannel was initially saturated with one fluid (fluid 1) at a constant rate. The second fluid (fluid 2) was then injected at a given flow rate. When steady state was reached for each flow rate, the pressure drop, temperatures, and flow rates were measured, and the flow configurations were recorded. The flow rate of fluid 2 was then increased stepwise.
The pressure drop was measured using a differential transducer connected to two liquid-filled pressure taps cemented into holes drilled along the microchannel, as illustrated in Figure 1. The distance between the taps was 40 mm and the first tap was located 50 mm from the microchannel inlet. The temperature of each fluid was measured at the inlet of the T-junction. Video and photography were used to record flow patterns. When the maximum flow rate of fluid 2 was reached, the microchannel was cleaned by injecting dichloromethane ([Cl.sub.2]C[H.sub.2]) in order to remove any residual oil. Air was then injected to dry the microchannel. This procedure was followed in order to ensure reproducibility of the experimental conditions. Subsequently, the microchannel was resaturated with fluid 1, and the experiment was repeated several times at various flow rates. In the case of the quartz microchannel, the range of Reynolds numbers (Re = [rho]V[D.sub.h]/[micro]) for the oil and water were 0.3-9 and 8-400, respectively. For the glass microchannel, Re ranges were 0.32-4.5 and 11-202 for oil and water, respectively.
This section presents the flow patterns observed, the corresponding flow maps, and the two-phase pressure drops measured.
Two-Phase Flow Patterns
Different flow patterns were observed depending on the flow rates and the nature of the first fluid injected into the microchannel. Photographs of the flow configurations are shown in Figures 3-5.
Microchannels Initially Saturated With Oil
Three flow patterns were identified in the case where the microchannel was initially saturated with oil at a constant flow rate, and water flow rate was subsequently increased stepwise (Figure 3). The three patterns are droplet, slug, and annular with the water as the dispersed phase. The transition between different configurations was clear visually. Whether the microchannel material was quartz or glass was found to have no influence on these patterns.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
In contrast to liquid-liquid flow in large channels (Fujii et al., 1994), no isolated drops were observed in the liquid bridges between the slugs. A similar result was found for gas-liquid systems in microchannels (Fukano et al., 2005; Salim, 2006).
The flow maps established from the flow patterns in Figure 3 reveal no difference between quartz and glass microchannels. Then, only one flow map is presented (Figure 6) for both microchannels. The oil superficial velocity is plotted against the water superficial velocity.
The symbols in Figure 6 denote the observed flow patterns for a given oil and water superficial velocity. The black thick lines correspond to the transitions between droplet-slug and slug-annular configurations. The transition between droplet and slug flow occurs at a water volume fraction of about 0.3, indicated by a thin black line. This finding is in agreement with other studies carried out with two immiscible liquids in large channels. literature reports have found that the droplet-slug transition occurs for a dispersed phase volume fraction ranging between 0.2 and 0.3 (Brauner, 1990; Beretta et al., 1997). On the other hand, the transition from slug to annular flow appears at practically a constant water superficial velocity.
Compared to the experimental results of Fujii et al. (1994), the present transition droplet-slug flow takes place for a higher water volume fraction. This may be due to capillary effects, which become more pronounced as channel dimensions decreased.
[FIGURE 6 OMITTED]
The slug-annular transition studied in this work agrees well with that obtained by Fujii et al. (1994) at low oil superficial velocity ([V.sub.o]), although a difference appears with increasing [V.sub.o] (Figure 6). Moreover, the domain of slug flow in the microchannel is smaller compared to the large channel. These results are similar to those obtained with a gas-liquid system. In fact, for a gas-liquid two-phase flow, several studies have shown that the slug-annular transition occurs at higher gas superficial velocity as the hydraulic diameter of the channel decreases (Mishima and Hibiki, 1996; Coleman and Garimella, 1999; Zhao and Bi, 2001) and that the domain occupied by the intermittent flow (slug or churn) becomes smaller as the hydraulic diameter of the channel decreases (Coleman and Garimella, 1999; Triplett et al., 1999).
Microchannels Initially Saturated With Water
When water was injected first into the microchannel, the flow patterns were slightly different depending on whether the microchannel was made of quartz or glass. For the quartz microchannel (Figure 4), we observed droplet, slug, and stratified flows, whereas for the glass microchannel (Figure 5), we observed droplet, semi-stratified, and stratified flows. In both cases, the oil was the dispersed phase. The semi-stratified and stratified configurations arise from the coalescence of the oil droplets and slugs, respectively, giving rise to a continuous film.
Flow pattern maps for both quartz and glass microchannels are shown in Figure 7a and b. The thick black lines represent the transition between droplet and slug for the quartz microchannel and between droplet and semi-stratified flow for the glass microchannel. For the quartz microchannel, the transition between droplet and slug occurs at an oil volume fraction of about 0.3. For the glass microchannel, the transition between droplet and semi-stratified flows occurs at an oil volume fraction of 0.23.
Drop and Slug Velocities
Averaged droplet and slug velocities were determined from flow images recorded at intervals of 0.04 s. The velocity measurement was based on the travel time of each flow pattern between the inlet and outlet of the microchannel. Figure 8 shows a linear relationship between the measured velocity for droplets and slugs and the mixture superficial velocity through the glass microchannel:
[FIGURE 7 OMITTED]
[V.sub.meas] = [C.sub.0] ([V.sub.w] + [V.sub.o]) (3)
where [V.sub.meas] is the measured velocity and [V.sub.w], and [V.sub.0] are superficial velocities of water and oil, respectively. The constant [C.sub.0] depends on the flow pattern ([C.sub.0] = 1.06 for droplets and [C.sub.0] = 1.28 for slugs). Measurements taken with the quartz microchannel yielded the same results. The higher value of [C.sub.0] found for the slug, means that it can move faster than the continuous oil phase because it flows in the centre part of the channel cross-section where the velocity is higher. Consequently, the liquid film surrounding the slug will be deflected toward its downstream.
Equation (3) has been widely used for gas-liquid flows in mini- and microchannels (Fukano et al., 2005). For the gas-liquid co-current flow through horizontal capillary tubes, the value of [C.sub.0] depends on the hydraulic diameter. In fact, at least for the gas-liquid system, it is well known that the value of [C.sub.0] increases as the channel diameter decreases (Fukano et al., 2005). For a hydraulic diameter between 1 and 4.9 mm, the value of [C.sub.0] varies between 1.21 and 1.09 (Fukano et al., 2005).
[FIGURE 8 OMITTED]
Two-Phase Pressure Drops
Figures 9a and b and 10a and b show pressure drops measured during oil-water two-phase flow through the quartz and glass microchannels in the two cases where the microchannel is saturated first with oil (Figure 9) or first with water (Figure 10). In these figures, each curve represents an individual experiment in which the first fluid flow rate was held constant as the second fluid flow rate was increased. The symbols used in the figures represent the different flow patterns as described in two-phase flow pattern section. The results appear to be similar whether the microchannel is made of quartz or glass. However, the oil-water pressure drop depends strongly on whether the microchannel is initially saturated with oil or water. With initial oil saturation (Figure 9), the pressure drop increases at low water superficial velocity and then decreases relatively sharply. Beyond a given value (3 [less than or equal to] [V.sub.w] [less than or equal to] 10 cm/s), the pressure drop then increases almost linearly with water superficial velocity. For microchannels initially saturated with water (Figure 10), however, the two-phase pressure drop always increases with oil superficial velocity. This increase is linear for the oil superficial velocity lesser than about 20 cm/s, beyond this value the pressure drop increases faster (quartz microchannel).
The decrease of the two-phase pressure drop observed at low water superficial velocity with the microchannel initially saturated with oil (Figure 9) was also observed in two-phase flow experiments performed by Charles et al. (1961) in which the more viscous liquid was in contact with the wall of the pipe. This trend was also observed in oil-water emulsion flows in pipes by Sanchez and Zakin (1994) and in porous media by Abdobal et al. (2003). According to Charles et al. (1961), the pressure drop decrease may be attributed to a reduction in the effective viscosity of water-in-oil emulsion at high water content, such that the viscosity is lower than that of the pure oil. However, this process has also been observed in the case of gas-liquid systems. In fact, a number of investigators have reported a pressure drop reduction during vertical and horizontal slug flow in capillary tubes (Morgante and Fabre, 2005). The pressure drop decrease can also take place in the case of a slug-annular transition of gas-liquid flow in horizontal microchannels (Salim, 2006). In gas-liquid systems, some researchers attributed this reduction to the so-called sudden expansion of liquid flow from a liquid film surrounding a long air bubble to a liquid slug following the long air bubble (Fukano et al., 2005).
[FIGURE 9 OMITTED]
Accordingly, as found in the drop and slug velocities part a higher relative velocity exists for the large drops of water 'slugs. Consequently, the kinetic energy of the liquid film 'oil' flowing around the slug dissipates in its wake by mixing the liquid in the wake with the liquid rushing into there with a high kinetic energy. Then, the energy loss is larger in slug flow.
[FIGURE 10 OMITTED]
In this section, we interpret the experimental results of two-phase pressure drops using the homogeneous and Lockhart-Martinelli models. These models are generally used to describe two-phase flows in pipes and have been used by several investigators to describe gas-liquid two-phase flow in microchannels (Kawahara et al., 2002; English and Kandlikar, 2005; Fukano et al., 2005).
The homogeneous model basically considers the flow of the two phases as a single-phase flow, with equivalent physical properties.
The two-phase friction factor is then defined by
[[lambda].sub.m] = 2D[([DELTA]P/L).sub.TP]/[[rho].sub.m][V.sup.2.sub.m] (4)
and the Reynolds number of the mixture by
[Re.sub.m] = [[rho].sub.m][V.sub.m]D/[[mu].sub.m] (5)
where subscript m stands for the mixture, [mu] is the dynamic viscosity, V is the superficial velocity, and [rho] is the mean density. [([DELTA]P/L).sub.TP] is the two-phase pressure drop over the length L.
The mixture superficial velocity is defined by
[V.sub.m] = [V.sub.w] + [V.sub.o] (6)
where [V.sub.w] and [V.sub.o] are the water and oil superficial velocities.
The mixture mean density is defined by
[[rho].sub.m] = [[epsilon].sub.w][[rho].sub.w] + (1 - [[epsilon].sub.w])[[rho].sub.o] (7)
where [[epsilon].sub.w] is the water volume fraction, that is, the volume of water divided by the total volume. For gas-liquid systems, [[epsilon].sub.w] corresponds to the void fraction. As [[epsilon].sub.w] was not measured in our experiments, we used the following equation, which assumes no slip flow condition 'homogeneous flow':
[[epsilon].sub.w] = [Q.sub.w]/[Q.sub.w] + [Q.sub.o] (8)
where [Q.sub.w] and [Q.sub.o] are the volumetric flow rates of water and oil, respectively.
Several models have been proposed to evaluate the dynamic viscosity of the mixture. As expected, the predicted two-phase frictional pressure drop depends on the model employed (Kawahara et al., 2002). It is generally assumed that the dynamic viscosity of the mixture depends on the viscosity of each phase, their volume fractions, the temperature, and the magnitude of the dispersion of one phase in the other. The equations most widely used in the literature for gas-liquid two-phase flow are as follows:
Mc Adams (1954):
[[mu].sub.m] = [(x/[[mu].sub.g] + 1 - x/[[mu].sub.l]).sup.-1] (9)
Cicchitti et al. (1960):
[[mu].sub.m] = x [[mu].sub.g] + (1 - x) [[mu].sub.l] (10)
Dukler et al. (1964):
[[mu].sub.m] = [[epsilon].sub.g] [[mu].sub.g] + [[epsilon].sub.l] [[mu].sub.l] (11)
Beattie and Whalley (1982):
[[mu].sub.m] = [[mu].sub.g] [[epsilon].sub.g] + [[mu].sub.l] (1 - [[epsilon].sub.g]) (1 + 2.5 [[epsilon].sub.g]) (12)
Lin et al. (1991):
[[mu].sub.m] = [[mu].sub.g][[mu].sub.l]/[[mu].sub.g] + [x.sup.1.4] ([[mu].sub.l] - [[mu].sub.g]) (13)
where x = [[rho].sub.g][Q.sub.g]/([[rho].sub.g][Q.sub.g] + [[rho].sub.l][Q.sub.l]) is the mass quality.
The gas-liquid dynamic viscosity models were extended to oil-water two-phase flow by replacing the gas phase by the lower viscous phase, which corresponds to water in the present work.
Similar to laminar single-phase flow, the relationship between the friction factor and Reynolds number in the homogeneous model may be written as follows:
[[lambda].sub.m] 64/[Re.sub.m] (14)
The various two-phase dynamic viscosity models presented above were tested by comparing the results of each model to the theoretical friction factor in Equation (14). The accuracy of each model was evaluated by calculating the mean absolute relative error:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)
and the standard deviation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)
where [[lambda].sub.m,exp] and [[lambda].sub.m,cal] are the friction factors determined experimentally from Equation (4) and theoretically from Equation (14), respectively.
Calculated values of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for experiments with the microchannels initially saturated with oil are given in Table 2. Based on the errors and standard deviations, it appears that the viscosity model proposed by Cicchitti et al. (1960) is the most appropriate for describing the experiments performed with the quartz microchannel. For the glass microchannel, however, the viscosity model proposed by Dukler et al. (1964) gives the lowest values of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Figure 11 shows the friction factor versus the Reynolds number of the mixture for both quartz and glass microchannels, using the viscosity model of Cicchitti et al. (1960) for the quartz and of Dukler et al. (1964) for the glass.
For the experimental results obtained with the microchannels initially saturated with water, the friction factor [[lambda].sub.m] is found to be lower for two-phase flow than for single-phase flow. The same trend was found for both microchannels and then only the results obtained from the quartz microchannel are presented in Figure 12. The dynamic viscosity of the mixture was calculated using the models proposed by Cicchitti et al. (1960) and Dukler et al. (1964) for the quartz and glass microchannels, respectively. The other dynamic viscosity models do not reasonably fit the experimental data.
[FIGURE 11 OMITTED]
[FIGURE 12 OMITTED]
Using a least-squares method, we obtained the following correlations:
For the quartz microchannel:
[[lambda].sub.m] = 34.62/[Re.sup.1.09.sub.m] (17)
For the glass microchannel:
[[lambda].sub.m] = 56.4/[Re.sup.1.26.sub.m] (18)
The Lockhart and Martinelli model (1949) was developed to describe two-phase gas-liquid flow in pipes. This model defines the following parameters:
[[phi].sub.g] = [square root of [([DELTA]P/L).sub.TP]/[([DELTA]P/L).sub.g]] (19)
[[phi].sub.l] = [square root of [([DELTA]P/L).sub.TP]/[([DELTA]P/L).sub.l]] (20)
x = [[phi].sub.g]/[[phi].sub.l] = [square root of [([DELTA]P/L).sub.l]/([DELTA]P/L).sub.g]] (21)
where [([DELTA]P/L).sub.TP] is the two-phase pressure drop, and [([DELTA]P/L).sub.g] and [([DELTA]P/L).sub.l] are the gas and liquid single-phase pressure drops that would be obtained if each phase was flowing alone in the pipe with the same superficial velocity as under two-phase flow conditions.
Taking Equation (2) into account, the Martinelli parameter can be written as
[chi] = [square root of [[mu].sub.l] [V.sub.l]/[[mu].sub.g] [V.sub.g]] (22)
The most commonly used equation linking the gas-phase multiplier and Martinelli parameter for gas-liquid flow in pipes is the Chisholm (1967) correlation:
[[phi].sup.2.sub.g] = 1 + C[chi] + [chi square] (23)
where the value of C depends on whether each phase is laminar or turbulent. Previous investigations have shown that the parameter C also depends on the hydraulic diameter of the pipe (Mishima and Hibiki, 1996; English and Kandlikar, 2005). In the present work, the Lockhart-Martinelli model was modified for liquid-liquid two-phase flow by replacing the gas-phase multiplier by the lower viscous phase multiplier, which corresponds to water in the present work.
For the microchannels initially saturated with oil, the plots of [[phi].sub.w] versus [chi] are superposed in Figure 13. Also included is plot showing the Chisholm (1967) correlation, taking into account the value of the parameter C proposed by English and Kandlikar (2005) for the gas-liquid two-phase flow in a microchannel:
C = 5(1 - [e.sup.-319D]) (24)
where D is the hydraulic diameter of the microchannel in millimeters. Note that, for a channel with a hydraulic diameter of 0.01 m or greater, the value of C approaches the laminar-laminar value proposed by Chisholm (1967) for gas-liquid flow.
The Chisholm correlation fits well with the experimental results of the droplet flow, but overestimates the pressure drop corresponding to the slug and annular flows. The slug and annular flows are well described using an equation of the form
[[phi].sup.2.sub.w] = 1 + [alpha][chi] + [beta][chi square] (25)
where [alpha] and [beta] are constants. The parameter a appears to depend on the microchannel properties. The parameter [beta] is similar for both microchannels. The values of these parameters are determined experimentally and given in Table 3.
[FIGURE 13 OMITTED]
For the microchannels initially saturated with water, Figure 10a and b shows that the two-phase pressure drop can be described as a function of the water and oil single-phase pressure drops:
[([DELTA]P/L).sub.TP] = [([DELTA]P/L).sub.w] + [psi] [([DELTA]P/L).sub.o] (26)
where [([DELTA]P/L).sub.TP] is the two-phase pressure drop, and [([DELTA]P/L).sub.w] and [([DELTA]P/L).sub.o] are the water and oil single-phase pressure drops that would be obtained if each phase was flowing alone in the microchannel with the same superficial velocity as under two-phase flow conditions. In comparison with Equation (25), this correlation suggests that the parameter [alpha] is not needed.
The parameter [psi] seems to be proportional to the oil volume fraction. Then [psi] can be written as
[psi] = [eta][Q.sub.o]/[Q.sub.o] + [Q.sub.w] = [eta][[epsilon].sub.o] (27)
where [eta] depends on the microchannel properties. The parameter [eta] was determined from the experimental results. Therefore, the two-phase pressure drop for each microchannel may be written as follows:
For the quartz microchannel:
[([DELTA]P/L).sub.TP] = [([DELTA]P/L).sub.w] + 0.67[[epsilon].sub.o] [([DELTA]P/L).sub.o] (28)
For the glass microchannel:
[([DELTA]P/L).sub.TP] = [([DELTA]P/L).sub.w] + 0.8[[epsilon].sub.o] [([DELTA]P/L).sub.o] (29)
[FIGURE 14 OMITTED]
In Figure 14a and b, we compare the measured and the calculated pressure drops from the correlations in Equations (28) and (29) for the quartz and glass microchannels, respectively. Assuming the calculated pressure drop is correct, Equations (28) and (29) predict the pressure drop with a mean absolute error of 16% and 18% for the quartz and glass microchannels, respectively.
Two-phase oil-water flow experiments were conducted in horizontal microchannels made of quartz and glass. Two series of experiments were performed. In each case, one fluid was first injected into the microchannel at a constant flow rate. The second fluid was then injected at various flow rates. The corresponding flow patterns were recorded and the resulting two-phase pressure drops were measured. The pressure drops depend closely on three variables: (1) the flow rates, (2) whether water or oil was the first injected fluid, and (3) the type of microchannel material.
In the case where oil was first injected, the patterns observed in both quartz and glass microchannels were droplet, slug, and annular flows with the water as the dispersed phase. When water was injected first, however, the patterns observed were droplet, slug, and stratified flows for the quartz microchannel, and slug, semi-stratified and stratified flows for the glass microchannel. The flow maps constructed from the data show several similarities with both liquid-liquid flow in large channels and with gas-liquid flow in microchannels. Using flow images, we demonstrated that droplet and slug velocities are proportional to the superficial velocity of the mixture, with a proportionality coefficient depending on the flow pattern.
Two-phase pressure drop curves obtained with oil as the first fluid injected into the microchannels were very different from those obtained with the microchannels initially saturated with water. With oil injected first at a given rate, the pressure drop increased with low water flow rates and then decreased. Increasing water flow rate further then increased the pressure drop. When water was injected first into the microchannels, the two-phase pressure drop always increased with the oil flow rate. This increase was linear for the glass channel and almost quadratic for the quartz microchannel.
The experimental results were interpreted using the homogeneous and Lockhart-Martinelli models for flows in pipes. The homogeneous model is based on single-phase flow laws. The weak point of this model is the definition of the dynamic viscosity of the two-phase mixture, as illustrated by the various correlations reported in the literature. We showed that when the microchannels are saturated first with oil, the viscosity models proposed by Cicchitti et al. (1960) and Dukler et al. (1964) are the most successful for describing the experiments performed with the quartz and glass microchannels, respectively. However, the homogeneous model does not allow a good fit with the experimental data obtained with the microchannels initially saturated with water. Nevertheless, we have established empirical correlations relating the friction factor and Reynolds number of the mixture.
Using the Lockhart and Martinelli (1949) approach, we showed that a modified Chisholm (1967) correlation correctly describes the experimental results. This correlation introduces two parameters that depend on the microchannel type and the flow pattern with regard to the first liquid injected in the microchannel.
NOMENCLATURE A wetting area of the microchannel ([m.sup.2]) C constant [C.sub.0] constant [D.sub.h] hydraulic diameter ([micro]m) P microchannel perimeter ([micro]m) Q flow rate ([cm.sup.3]/s) Re Reynolds number V superficial velocity (cm/s) Greek Symbols [alpha] constant [beta] constant [gamma] surface tension (mN/m) [DELTA]P pressure difference (kPa) [epsilon] liquid volume fraction [eta] parameter [theta] gas-liquid-solid contact angle ([degrees]) [lambda] friction factor [mu] dynamic viscosity (mPa s) [rho] liquid density (kg/[m.sup.3]) [psi] Lockart-Martinelli parameter [chi] Martinelli parameter [psi] function Subscripts g gas l liquid m oil-water mixture meas measured o oil TP two-phase flow w water
This work has been supported in part by INPL (Institut National Polytechnique de Lorraine) as a 'projet novateur a risque' grant. The authors wish to thank Gilles Bessaques from UMR G2R and Franck Demeurie from LEMTA for their technical assistance.
Manuscript received November 21, 2007; revised manuscript received June 24, 2008; accepted for publication July 3, 2008.
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Abdelkader Salim, (1,2) *, ([dagger]) Mostafa Fourar, (1) Jacques Pironon (2) and Judith Sausse (2)
(1.) Ecole des Mines de Nancy-LEMTA, Nancy, France
(2.) Nancy-Universite and CNRS, G2R laboratory, Nancy, France
([dagger]) (Present address: Institut de Mecanique des Fluides de Toulouse, Toulouse, France.
* Author to whom correspondence may be addressed. E-mail address: firstname.lastname@example.org
Table 1. Properties of mineral oil Product name MARCOL 82 Density 843 kg/[m.sup.3] Viscosity 30.6 meas at 20[degrees]C Oil-water interfacial tension 30.1 mN/m at 20[degrees]C Table 2. Percentage mean absolute average error and standard deviation for pressure drop values in comparison with various viscosity correlations Quartz microchannel Dynamic viscosity model [MATHEMATICAL [MATHEMATICAL EXPRESSION EXPRESSION NOT REPRODUCIBLE NOT REPRODUCIBLE IN ASCII] (%) IN ASCII] (%) Dukler et al. (1964) 15 10 Cicchitti et al. (1960) 12 8 Lin et al. (1991) 75 7.5 Mc Adams (1954) 80 6 Beattie and Whalley (1982) 148 64 Glass microchannel Dynamic viscosity model [MATHEMATICAL [MATHEMATICAL EXPRESSION EXPRESSION NOT REPRODUCIBLE NOT REPRODUCIBLE IN ASCII] (%) IN ASCII] (%) Dukler et al. (1964) 9.4 4.9 Cicchitti et al. (1960) 10 7.4 Lin et al. (1991) 76 7.9 Mc Adams (1954) 81 5.5 Beattie and Whalley (1982) 115 54 Table 3. Values of [alpha] and [beta] for the quartz and glass microchannels initially saturated with oil Parameter [alpha] [beta] Quartz microchannel 0.26 0.8 Glass microchannel 0.3
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|Author:||Salim, Abdelkader; Fourar, Mostafa; Pironon, Jacques; Sausse, Judith|
|Publication:||Canadian Journal of Chemical Engineering|
|Date:||Dec 1, 2008|
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