An Alternative Method to Implement Contact Angle Boundary Condition on Immersed Surfaces for Phase-Field Simulations

TL;DR

This paper introduces a simple, geometric-based method for implementing contact angle boundary conditions on immersed surfaces in phase-field simulations, improving ease of implementation and accuracy for complex geometries.

Contribution

The paper presents a novel approach leveraging the hyperbolic tangent profile to determine boundary conditions from a single point, simplifying implementation on curved immersed surfaces.

Findings

Accurately models contact angles on complex immersed surfaces.

Demonstrates effectiveness through drop shape and spreading simulations.

Simplifies boundary condition implementation in phase-field methods.

Abstract

In this paper, we propose an alternative approach to implement the contact angle boundary condition on immersed surfaces for phase-field simulations of two-phase flows using the Cahn-Hilliard equation on a Cartesian mesh. This simple and effective method was inspired by previous works on the geometric formulation of the wetting boundary condition. In two dimensions, by making full use of the hyperbolic tangent profile of the order parameter, we were able to obtain its unknown value at a ghost point from the information at only one point in the fluid. This is in contrast with previous approaches using interpolations involving several points. The special feature allows this method to be easily implemented on immersed surfaces (including curved ones) that cut through the grid lines. It is verified through the study of two examples: (1) the shape of a drop on a circular cylinder with different contact angles; (2) the spreading of a drop on an embedded inclined wall with a given contact angle.