  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 $l \propto t^{1/2}$. 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.
