Analytical and numerical study on droplet breakup in microfluidic T-junction

Droplet breakup in symmetric T-junctions is one of the important phenomena in droplet microfluidics. Many studies have been done about the droplet breakup but none of them has provided a general analytical solution for the droplet breakup. In this study, we present an analytical solution to investigate the effect of important parameters such as the capillary number, droplet length, and channel widths ratio. The analytical solution is validated using the numerical simulation. Using the analytical equation and numerical results, we propose a generalized relationship. This general equation can be used as a rule of thumb for droplet breakup predictions with high accuracy. The results indicate that increasing the capillary number decreases the critical droplet length in which the breakup occurs. The results also reveal that increasing the width ratio increases the critical droplet length because increasing the channel width ratio reduces the extension and deformation of the droplet. The effect of width ratio is more important in lower capillary numbers rather than the higher capillary numbers. Numerical results also show that fluid properties such as the viscosity ratio, density ratio, and the power-law index have no significant effect on the phase diagram of droplet breakup.