Lattice Boltzmann simulation of binary three-dimensional droplet coalescence in a confined shear flow

Abstract

Small-scale microscopic phenomena determine the behavior of large-scale droplets, which brings great challenges to accurately simulate the droplet coalescence process. In this paper, the mesoscopic lattice Boltzmann method based on the phase field theory is used to simulate the collision and coalescence of binary three-dimensional droplets in a confined shear flow. The numerical prediction of droplet coalescence behavior was first compared with the experimental result, and good agreement was reported. Then, we investigated the influences of a comprehensive range of capillary numbers ([Formula: see text]) and Reynolds numbers ([Formula: see text]) on the shearing dynamics of binary droplets and also provided a quantitative description of droplet behavior in terms of the droplet deformation parameter and relative trajectory. A shearing regime diagram is further constructed based on the coupling effect of Ca and Re, which reveals three distinct types of droplet behaviors, including coalescence, breakup after the coalescence, and non-coalescence. Concretely, three different patterns of droplets can be completely captured with the variation of Ca at low Re; only two types of coalescence and non-coalescence can be observed for a medium Re, and two droplets just slide over each other without the occurrence of the coalescence when Re is sufficiently large. Also, we identified two critical capillary numbers in the lower Re region and one critical capillary number in the middle Re region, respectively, characterizing flow type transitions from the coalescence to breakup, from the breakup to the non-coalescence, and from the coalescence to the non-coalescence. It is found that all the capillary numbers decrease with Re.