Migration of a van der Waals bubble: Lattice Boltzmann formulation

A numerical study of the isothermal migration of a two-dimensional bubble in Poiseuille flow is reported here for vapor-liquid density and dynamic viscosity ratios of 1/8, Re-d=1, and Ca=2. A lattice Boltzmann model with a van der Waals equation of state is employed to simulate the diffuse interface for three interface thickness to bubble diameter ratios, 1/5, 1/10, and 1/20. Point-by-point comparisons with the sharp-interface incompressible counterpart (reported in the literature) reveal velocity discrepancies which are more evident on the vapor side. These differences are a manifestation of a finite mass flux through the interface, associated with driven finite-thickness interfaces. An analytical study of the one-dimensional analog of the traveling diffuse interface problem explains this phenomenon and shows that this flux vanishes as a result of viscous dissipation as the interface thickness tends to zero. This trend is corroborated by the two-dimensional lattice Boltzmann results. (C) 2001 American Institute of Physics.