A mass-conserving contact line treatment for second-order conservative phase field methods based on the generalized Navier boundary condition

TL;DR

This paper introduces a mass-conserving contact line treatment for second-order conservative phase field methods, utilizing the generalized Navier boundary condition to improve accuracy and reduce spurious slip in simulations.

Contribution

It presents a novel boundary treatment based on GNBC for second-order phase field models, addressing the challenge of boundary conditions and slip velocity reduction.

Findings

Effective in equilibrium drop simulations

Reduces spurious slip velocity at contact lines

Validated with two-phase flow tests

Abstract

A mass-conserving contact line treatment for second-order conservative phase field methods is presented and applied to the conservative diffuse interface (CDI) model. The treatment centers on a no-flux boundary condition for the phase field along with a slip boundary condition for the velocity that is based on the generalized Navier boundary condition (GNBC). Since the CDI model is a second-order partial differential equation, it does not permit a second (contact angle) boundary condition, in contrast to the popular fourth-order Cahn-Hilliard model. As such, we use one-sided stencils and extrapolations from the interior of the domain to compute phase-field-related quantities on and near the wall. Additionally, we propose novel modifications to the GNBC on the continuous and discrete levels that reduce spurious slip velocity when the contact angle achieves its equilibrium value. The proposed treatment is validated with the equilibrium drop and two-phase Couette flow test cases.