A LATTICE BOLTZMANN APPROACH FOR IMMISCIBLE FLUIDS WITH VERY DIFFERENT VISCOSITIES

Abstract

In this article, a lattice Boltzmann model for two immiscible fluids with same density but a large viscosity difference is developed. The effect of surface tension is included. An indicator function is used to model the interface motion and is updated by a lattice Boltzmann scheme. The macroscopic equation for this function is derived using multi-scale analysis. Numerical results are compared with theoretical and experimental ones for the problem of drop deformation under steady linear flows. A qualitative comparison with results given by a level contour reconstruction method for drop collision in three dimensions is also shown. Other numerical applications, such as flow past obstacles and a falling drop, are presented.