Work

A Cahn–Hilliard–Navier–Stokes system with degenerate mobilities: a finite difference solution

Year: 2026

Type: article

Abstract: The Cahn-Hilliard equation is increasingly popular in two-phase flow simulations due to its implicit capture of the interface and its easy extension to higher dimensions. However, it also has its drawbacks, for instance, the mass shrinkage of a small drop in a large computational domain. To that end, a Cahn–Hilliard equation with a degenerate mobility is proposed and coupled with the Navier–Stokes equation. To solve the system equations, a simple and efficient finite difference method is employed. The Laplacian of the chemical potential is discretized using a modified central difference scheme. It is this modification that lends the model to larger time steps. Moreover, the method is fully explicit. The model was tested on a number of cases and compared with the Cahn–Hilliard equation with a constant mobility. It was shown that the new model can conserve mass better, thus sustaining a small drop longer due to the eliminated bulk diffusion. The model was also compared with experimental and analytical outcomes, showing reasonable agreement.

Source: Engineering With Computers

DOI: 10.1007/s00366-025-02257-2

Authors: Mingguang Shen, Ben Q. Li, Huan Yang

Institutions: Yancheng Teachers University, University of Michigan–Dearborn, Xidian University, Guangzhou Institute of Technology

Language: English

Topic: Fluid Dynamics and Heat Transfer

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,190

Funder: Basic and Applied Basic Research Foundation of Guangdong Province