We report results of extensive two-phase lattice-Boltzmann simulations of capillary rise dynamics. We demonstrate that the method can be used to model the hydrodynamic behaviour inside a capillary tube provided that the diameter of the tube is large enough, typically at least 30 lattice units. We also present results for the dependence of the cosine of the dynamic contact angle on the capillary number Ca. Its deviation from the static advancing contact angle has a power-law form, with the value of the exponent very close to 3/2 for capillary rise at zero gravity, while behaviour is more complex in the presence of gravity.
Raiskinmäki, P., Shakib-Manesh, A., Jäsberg, A., Koponen, A., Merikoski, J., & Timonen, J. (2002). Lattice-Boltzmann simulation of capillary rise dynamics. Journal of Statistical Physics, 107(1-2), 143-158. https://doi.org/10.1023/A:1014506503793