Capillary filling with pseudo-potential binary Lattice-Boltzmann model

TL;DR

This paper uses a lattice Boltzmann model to study capillary filling of binary fluids, analyzing contact angles, wetting behavior, and precursor films, with results aligning with theoretical laws.

Contribution

It introduces a mesoscopic lattice Boltzmann approach to simulate binary fluid capillary filling, including contact angle effects and precursor film dynamics.

Findings

Quantitative agreement with Washburn law when viscosity ratios are correct.

Complete wetting with zero contact angle is effectively modeled.

Precursor films advance with a square-root law but different prefactors.

Abstract

We present a systematic study of capillary filling for a binary fluid by using a mesoscopic lattice Boltzmann model for immiscible fluids describing a diffusive interface moving at a given contact angle with respect to the walls. The phenomenological way to impose a given contact angle is analysed. Particular attention is given to the case of complete wetting, that is contact angle equal to zero. Numerical results yield quantitative agreement with the theoretical Washburn law, provided that the correct ratio of the dynamic viscosities between the two fluids is used. Finally, the presence of precursor films is experienced and it is shown that these films advance in time with a square-root law but with a different prefactor with respect to the bulk interface.