Capillary filling using Lattice Boltzmann Equations: the case of multi-component fluids

TL;DR

This paper uses a lattice Boltzmann model to study capillary filling of binary fluids, demonstrating quantitative agreement with Washburn's law and analyzing transient inertial effects and flow profiles.

Contribution

It introduces a systematic lattice Boltzmann approach for simulating multi-component fluid capillary filling, highlighting inertial effects and flow evolution.

Findings

Quantitative agreement with Washburn law for various channel sizes and wettability.

Transient inertial effects are well-controlled and match phenomenological expectations.

Velocity and pressure profiles evolve solely under capillary forces during filling.

Abstract

We present a systematic study of capillary filling for a binary fluid by using mesoscopic a lattice Boltzmann model describing a diffusive interface moving at a given contact angle with respect to the walls. We compare the numerical results at changing the ratio the typical size of the capillary, H, and the wettability of walls. Numerical results yield quantitative agreement with the Washburn law in all cases, provided the channel lenght is sufficiently larger then the interface width. We also show that in the initial stage of the filling process, transient behaviour induced by inertial effects are under control in our lattice Boltzmann equation and in good agreement with the phenomenology of capillary filling. Finally, at variance with multiphase LB simulations, velocity and pressure profiles evolve under the sole effect of capillary drive all along the channel.