Modelling capillary filling dynamics using lattice Boltzmann simulations

We investigate the dynamics of capillary filling using two lattice Boltzmann schemes: a liquid-gas model and a binary model. The simulation results are compared to the well-known Washburn's law, which predicts that the filled length of the capillary scales with time as l ∝ t 1/2 . We find that the liquid-gas model does not reproduce Washburn's law due to condensation of the gas phase at the interface, which causes the asymptotic behaviour of the capillary penetration to be faster than t 1/2 . The binary model, on the other hand, captures the correct scaling behaviour when the viscosity ratio between the two phases is sufficiently high.