Force imbalance in lattice Boltzmann equation for two-phase flows.

The capability of modeling and simulating complex interfacial dynamics of multiphase flows has been recognized as one of the main advantages of the lattice Boltzmann equation (LBE). A basic feature of two-phase LBE models, i.e., the force balance condition at the discrete lattice level of LBE, is investigated in this work. An explicit force-balance formulation is derived for a flat interface by analyzing the two-dimensional nine-velocity (D2Q9) two-phase LBE model without invoking the Chapman-Enskog expansion. The result suggests that generally the balance between the interaction force and the pressure does not hold exactly on the discrete lattice due to numerical errors. It is also shown that such force imbalance can lead to some artificial velocities in the vicinity of phase interface.