Volume-of-fluid simulations in microfluidic T-junction devices: Influence of viscosity ratio on droplet size

Abstract: We used volume-of-fluid (VOF) method to perform three-dimensional numerical simulations of droplet formation of Newtonian fluids in microfluidic T-junction devices. To evaluate the performance of the VOF method we examined the regimes of drop formation and determined droplet size as a function of system parameters. Comparison of the simulation results with four sets of experimental data from the literature showed good agreement, validating the VOF method. Motivated by the lack of adequate studies investigating the influence of viscosity ratio ({\lambda}) on the generated droplet size, we mapped the dependence of drop volume on capillary number (0.001 < Ca < 0.5) and viscosity ratio (0.01 < {\lambda} < 15). We find that for all viscosity ratios investigated, droplet size decreases with increase in capillary number. However, the reduction in droplet size with capillary number is stronger for {\lambda} < 1 than for {\lambda} > 1. In addition, we find that at a given capillary number, the size of droplets does not vary appreciably when {\lambda} < 1, while it increases when {\lambda} > 1. We develop an analytical model for predicting droplet size that includes a viscosity-dependent breakup time for the dispersed phase. This improved model successfully predicts the effects of viscosity ratio observed in simulations. Results from this study are useful for the design of lab-on-chip technologies and manufacture of microfluidic emulsions, where there is a need to know how system parameters influence droplet size.