Simulations of charged droplet collisions in shear flow

Collisions of charged droplets in the shear flow of an electrolyte were simulated to investigate the effects of surface charges and double layers on the critical conditions for coalescence. A lattice Boltzmann method phase field flow solver was coupled with an iterative finite-difference solver for the linearized Poisson-Boltzmann equation describing electric double layers. The simulations resolve both the phase field diffuse interface and electric double layer. The critical capillary numbers for coalescence were determined under varying strengths of the electric interactions. Critical capillary numbers between 0.03 and 0.2 were found for droplet radii spanning 25 to 50 lattice nodes (12.5 to 25 times the characteristic interface thickness), with lower critical values for larger droplets. The droplet interfaces had a constant potential. Once electric repulsion becomes comparable to the viscous shear force on the drops, the critical capillary numbers decrease, and the decrease is smaller for longer Debye lengths. Though the ratio of droplet size and Debye length that can be achieved in the simulations is constrained by high computational demands, the simulations provide insight into the effects of surface charge on the interactions between interfaces in multiphase flows.