Lattice Boltzmann simulation of three-phase flows with moving contact lines on curved surfaces

TL;DR

This paper introduces a lattice Boltzmann method for simulating complex three-phase flows with moving contact lines on curved surfaces, enabling accurate modeling of interfacial dynamics and wettability effects.

Contribution

It develops a novel numerical approach combining a color-gradient model and a characteristic line boundary condition for complex geometries and contact angles.

Findings

Validated with Janus droplet and capillary intrusion simulations

Demonstrated impact of surface wettability on droplet behavior

Simulated compound droplet flow through multi-pillar structures

Abstract

A numerical method for simulating three-phase flows with moving contact lines on arbitrarily complex surfaces is developed in the framework of lattice Boltzmann method. In this method, the immiscible three-phase flow is modeled through a multiple-relaxation-time color-gradient model, which not only allows for a full range of interfacial tensions but also produces stable outcomes for a wide range of viscosity ratios. A characteristic line model is introduced to implement the wetting boundary condition, which is not only easy to implement but also able to handle arbitrarily complex boundaries with prescribed contact angles. The developed method is first validated by the simulation of a Janus droplet resting on a flat surface, a perfect Janus droplet deposited on a cylinder, and the capillary intrusion of ternary fluids for various viscosity ratios. It is then used to study a compound droplet subject to a uniform incoming flow passing through a multi-pillar structure, where three different values of surface wettability are considered. The simulated results show that the surface wettability has significant impact on the droplet dynamic behavior and final fluid distribution.