Color-Gradient Lattice Boltzmann Modeling of Wetting Boundary Condition on Curved Solid Boundaries

We introduce a wetting boundary condition for curved solid boundaries within a diffuse interface framework for lattice Boltzmann method. The boundary condition relies on updating the order parameter (color-field) values at ghost nodes inside the solid phase. The ghost node color modification rule, in turn, extends the equilibrium color profile into the solid phase. For a fixed fluid density ratio of 1000 and a dynamic viscosity ratio of 100, numerical simulations demonstrate that the wetting scheme produces relatively small spurious currents of the order ofO(10−6)in lattice units. The present scheme agrees well with analytical solutions for static contact lines on curved solid boundaries. In particular, for the range of contact angles investigated, the error in static contact angles remains below 2° for flat solid surfaces, even at coarse grid resolutions. For the dynamic contact line benchmark studied here, however, the numerical results deviate from analytical solutions by roughly 9% at coarse spatial resolution. This difference has been shown to decrease with increasing spatial resolution.