Higher order potential in the modified convective-viscous Cahn-Hilliard equation

TL;DR

This paper introduces a modified Cahn-Hilliard equation with a higher order potential and variable gradient coefficient to better model highly heterogeneous systems, providing exact solutions and conditions for their existence.

Contribution

It proposes a novel modification of the Cahn-Hilliard equation using a sixth-degree potential and quadratic gradient coefficient, advancing modeling of complex heterogeneous systems.

Findings

Exact solutions in the form of moving static waves are derived.

Conditions for the existence of these solutions depend on potential symmetry.

The modified equation better captures heterogeneity in systems.

Abstract

To describe highly heterogeneous systems using the Cahn-Hilliard equation, the standard form of the thermodynamic potential with a constant coefficient in the gradient term and a polynomial of the fourth degree may not be sufficient. The modification of the form of the thermodynamic potential with a polynomial of the sixth degree and the quadratic dependence of the coefficient at the gradient term is considered. Exact solutions in the form of a moving static wave and the conditions of their existence depending on the symmetry of the potential are obtained.