Eur. Phys. J. Special Topics 171, 63-71 (2009)
https://doi.org/10.1140/epjst/e2009-01012-0

Modelling capillary filling dynamics using lattice Boltzmann simulations

The Rudolf Peierls Centre for Theoretical Physics, Oxford University, 1 Keble Road, Oxford, OX1 3NP, UK

Corresponding author: j.yeomans1@physics.ox.ac.uk

Abstract

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.