Simulation of contact line dynamics in a two-dimensional capillary tube by the lattice Boltzmann model

During immiscible-fluid displacement, the contact angle between the interface and the wall of a tube, as well as the velocity V of the contact line where a fluid interface intersects the wall of a tube, depends on the applied capillary pressure $P_{\mathrm{cap}}.$ In this paper, the contact line dynamics of immiscible-fluid displacement is simulated by using the lattice Boltzmann model in a two-dimensional capillary channel with an ideally smooth wall. The V dependence of the contact angle is studied for two different wetting cases. Our simulational results are in good agreement with those based on theoretical computations and with molecular dynamics simulations. In particular, the power-law behavior $P_{\mathrm{cap}}\sim V^x$ is found with an exponent x very close to $1.$ The simulations suggest that the lattice Boltzmann model may serve as an alternative reliable quantitative approach to study the contact line dynamics, and also may be a promising tool for invesitgating some other immiscible displacement related subjects.