Modelling capillary filling dynamics using lattice Boltzmann simulations

TL;DR

This paper uses lattice Boltzmann simulations to study capillary filling dynamics, comparing two models and analyzing their ability to reproduce Washburn's law, revealing the effects of phase condensation and viscosity ratios.

Contribution

It introduces and compares two lattice Boltzmann models for capillary filling, highlighting the conditions under which each accurately reproduces Washburn's law.

Findings

Liquid-gas model does not follow Washburn's law due to gas condensation.

Binary model captures correct scaling with high viscosity ratio.

Capillary filling dynamics depend on phase interactions and viscosity ratios.

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