A lattice Boltzmann method for incompressible two-phase flows with large density differences

A lattice Boltzmann method for two-phase immiscible fluids with large density differences is proposed. The difficulty in the treatment of large density difference is resolved by using the projection method. The method can be applied to simulate two-phase fluid flows with the density ratio up to 1000. To show the validity of the method, we apply the method to the simulations of capillary waves, binary droplet collisions, and bubble flows. In capillary waves, the angular frequencies of the oscillation of an ellipsoidal droplet are obtained in good agreement with theoretical ones. In the simulations of binary droplet collisions, coalescence collision and two different types of separating collisions, namely reflexive and stretching separations, can be simulated, and the boundaries of the three types of collisions are in good agreement with an available theoretical prediction. In the bubble flows, the effect of mobility on the coalescence of two rising bubbles is investigated. The behavior of many bubbles in a square duct is also simulated.