Static contact angle in lattice Boltzmann models of immiscible fluids

We study numerically the capillary rise between two horizontal plates and in a rectangular tube, using a lattice Boltzmann (LB) method. We derive an equation for the static fluid-solid contact angle as a function of the wetting tendency of the walls and test its validity. We show that the generalized Laplace law with two independent radii of curvature is followed in capillary rise in rectangular tubes. Our method removes the history dependence of the fluid-solid contact angle that had been present in earlier LB schemes.