Journal of Statistical Physics, Vol. 121, Nos. 1/2, October 2005, p. 197-207.
The dynamics of capillary flow has several practical applications in the industry and has been extensively investigated. The main focuses in these studies are the motion of the interface, especially near the three-phase contact line, and the change of contact angle during the invasion process. In this work we present several simulations results of capillary invasion in two- and three-dimensions, using the Lattice-Boltzmann model based on field mediators. We investigate the velocity field near the solid surface, the changes in the contact angle as a consequence of the flow, and the boundary conditions that can be used in the inlet and outlet of the capillary tube. In all simulations the diameter of tube is made large enough to enable the evaluation of the contact angle directly from the density field and the results of capillary rise are compared with a theoretical model based on the Bosanquet equation, which includes capillary, viscous, inertial and gravitational effects.