Capillary filling using Lattice Boltzmann Equations: the case of multi-phase flows

TL;DR

This paper uses lattice Boltzmann models to study multi-phase capillary filling, demonstrating quantitative agreement with the Washburn law in the hydrodynamic limit and analyzing transient effects like inertia and vena contracta.

Contribution

It systematically investigates capillary filling with mesoscopic lattice Boltzmann models, highlighting the conditions for agreement with classical laws and transient phenomena.

Findings

Quantitative agreement with Washburn law at large density and size ratios.

Transient inertial effects cause deviations from Washburn law initially.

Lattice Boltzmann models effectively capture capillary filling phenomenology.

Abstract

We present a systematic study of capillary filling for multi-phase flows by using mesoscopic lattice Boltzmann models describing a diffusive interface moving at a given contact angle with respect to the walls. We compare the numerical results at changing the density ratio between liquid and gas phases and the ratio between the typical size of the capillary and the interface width. It is shown that numerical results yield quantitative agreement with the Washburn law when both ratios are large, i.e. as the hydrodynamic limit of a infinitely thin interface is approached. We also show that in the initial stage of the filling process, transient behaviour induced by inertial effects and ``vena contracta'' mechanisms, may induce significant departure from the Washburn law. Both effects are under control in our lattice Boltzmann equation and in good agreement with the phenomenology of capillary filling.