Theoretical analysis and simulation of obstructed breakup of micro-droplet in T-junction under an asymmetric pressure difference

Abstract

Asymmetric droplet breakup under a pressure difference at two outlets of a T-junction is investigated theoretically and numerically in this study. An accurate analysis of the evolution of droplet dynamics during the obstructed breakup process has been conducted. Meanwhile, the lattice Boltzmann method based on color gradient model is employed to simulate the system with the verification of the theoretical results. It is demonstrated that the Zou-He boundary setting at each outlet is advantageous for modifying the pressure drop of the two branches of T-junction. The results reveal that asymmetric breakup of the unequally sized droplets follows two steps, namely, the filling stage and the breakup stage. Then a universal parameter is proposed to describe the asymmetric condition of droplet breakup in T-junction, which plays a key role to characterize the temporal evolution of volume ratio and the droplet length of formed smaller droplets.