  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.
