Capillary filling for multicomponent fluid using the pseudo-potential Lattice Boltzmann method

We present a systematic study of capillary filling for a binary fluid by using mesoscopic a lattice Boltzmann model describing a diffusive interface moving at a given contact angle with respect to the walls. We compare the numerical results at changing the ratio the typical size of the capillary, H, and the wettability of walls. Numerical results yield quantitative agreement with the theoretical Washburn law, provided that the channel height is sufficiently larger than the interface width and variations of the dynamic contact angle with the capillary number are taken into account.