Scaling of dynamic contact angles in a lattice-Boltzmann model

We study the origins of the dynamic contact angle in a two-dimensional lattice-Boltzmann model of immiscible fluids. We show that the dynamic contact angle changes as a function of capillary number as observed in laboratory experiments and explain how this dependence arises in the lattice-Boltzmann model. We also explain how the fluid-fluid interface can move while retaining its shape. The interface has an apparent slip length. The apparent slip follows the classical Navier slipping rule where the velocity of the fluid at the wall is proportional to the viscous stress at the wall. This apparent slip length is proportional to the viscous length scale associated with the spurious flow induced by uncompensated stress at the three-phase contact point.