Numerical Simulation of Three-Dimensional Motion of Droplets by Using Lattice Boltzmann Method

This study describes the numerical simulation of three-dimensional droplet formation and the following motion in a cross-junction microchannel by using the Lattice Boltzmann Method (LBM). Our aim is to develop the three-dimensional binary fluids model, consisting of two sets of distribution functions to represent the total fluid density and the density difference, which introduces the repulsive interaction consistent with a free-energy function between two fluids. We validated the LBM code with the velocity profile in a 3-dimensional rectangular channel. Then, we applied our code to the numerical simulation of a binary fluid flow in a cross-junction channel focusing on the investigation of the droplet formulation. Due to the pressure and interfacial-tension effect, one component of the fluids which is injected from one inlet is cut off into many droplets periodically by the other component which is injected from the other inlets. We considered the effect of the boundary conditions for density difference (order parameter) on the wetting of the droplet to the side walls.