Lattice Boltzmann Simulation of Two-Phase Viscoelastic Fluid Flows

A lattice Boltzmann method (LBM) for two-phase viscoelastic fluid flows is proposed. The method is mainly an extension of the LBM for two-phase flows with large density differences proposed by Inamuro et al. [Journal of Computational Physics Vol. 198, No. 2 (2004), pp. 628-644]. The viscoelastic effects are introduced by the constitutive equation based on the Maxwell model, which has a spring and a dashpot connected with each other in series. The method is applied to simulations of a drop under shear flow in viscoelastic fluids and of a bubble rising in viscoelastic fluids. In the simulation of drop deformation under shear flows, the effects of viscoelasticity on the deformation and orientation angle are evaluated. In the simulation of bubble rising in viscoelastic fluids, a cusp configuration at the trailing edge is investigated and compared with the theoretical prediction and other numerical results.