The dynamics of two-layer system of immiscible liquids under the action of horizontal linear vibrations in the field of gravity was investigated. The numerical simulation was carried out by the lattice Boltzmann method (LBM) with model D2Q9. For the first time LBM was used to achieve the appearance of frozen wave (quasi-stationary relief) at the interface of two fluids. There are two types of boundary conditions for the sidewalls: a periodic condition for comparison with analytical results and no-slip condition for comparison with experiments. Various computational domains were considered. Both cases with the same viscosities of both phases and different viscosity ratios were studied. HCZ model was used to describe two-phase system and the interface of two liquids. The presence of a frozen wave on the interface of liquids was found. The dependence of liquids viscosity on the relief was studied. The obtained critical wave number coincides well with the theoretically predicted value for liquids with the equal viscosity and vanishing viscosity. The results of numerical calculations show a weak viscosity effect for a more viscous lower liquid. However, the destabilizing effect of viscosity is more significant for a more viscous upper liquid.
Solution of the equations for one-dimensional, two-phase filtration in porous medium with heat exchange by geometric methods
