Pressure drop of two-phase liquid-liquid slug flow in square microchannels

Networks of microdevices can be used to form, sort, split and recombine droplets by varying the fluidic resistance of the channels. To facilitate design of such systems we propose two models to calculate pressure drop of liquid-liquid slug flow in square microchannels. By approximating a droplet surrounded by liquid film as annular flow, the moving film model includes the velocity profile in the lubricating layer. In the no-film model, the presence of liquid film is neglected. Pressure drop measurements of water-toluene and water-silicone oil slug flow generated in glass/silicon devices of 200 and 400 μm width serve to validate these two models. We found that the droplet viscosity influences the applicability of the models. Good agreement is obtained for water-toluene slug flow, with the average error of 15-20% between the measured and calculated values for both models, proving that the presence of the lubricating film may be neglected for flows with similar viscosities of both phases. On the contrary, both predictions agree poorly with experiments for silicon oil-water flow which we attribute to the lower than expected liquid film thickness around the silicon oil droplets. Therefore we use the moving film model to estimate the thickness of the lubricating layer which we find to lie between 0.5% and 0.75% of the channel width, lower than the assumed 2%. Finally we compare the performance of our models against two correlations adapted from literature. We thus demonstrate that our approach allows reliable pressure drop prediction for liquids with similar viscosities and delivers important information on flow hydrodynamics.