Surface tension models with different viscosities

Surface tension in ILB models for fluids with different viscosities and different numbers of rest populations is derived, starting from the so-called mechanical definition. It is shown that the standard perturbation, inserted into these models in order to create surface tension, should be slightly modified for models with different viscosities in order to avoid the dependence of surface tension upon the actual phase distribution. The analytical results are numerically confirmed by mechanical and bubble tests. It is demonstrated also that the perturbation of the lattice Boltzmann equation gives rise to the appearance of anisotropic terms in population solutions related to anomalous currents and density fluctuations. When particular values of the eigenvalues of the collision operators are used, these spurious currents are annihilated in the time-independent solutions of the mechanical tests in arbitrarily inclined channels when bounce-back conditions are imposed at the solid boundaries.