# A linear, second-order, energy stable, fully adaptive finite-element method for phase-field modeling of wetting phenomena

## TL;DR

This paper introduces a new finite-element numerical method for phase-field modeling of wetting phenomena that is energy stable, adaptive, and preserves mass, demonstrated through various realistic tests.

## Contribution

It presents a novel, fully adaptive, second-order finite-element method for the Cahn-Hilliard equation with wetting boundary conditions, ensuring energy stability and mass conservation.

## Key findings

- Method is mass-conservative and energy-stable
- Accurately models wetting on heterogeneous substrates
- Effective in complex 2D and 3D scenarios

## Abstract

We propose a new numerical method to solve the Cahn-Hilliard equation coupled with non-linear wetting boundary conditions. We show that the method is mass-conservative and that the discrete solution satisfies a discrete energy law similar to the one satisfied by the exact solution. We perform several tests inspired by realistic situations to verify the accuracy and performance of the method: wetting of a chemically heterogeneous substrate in three dimensions, wetting-driven nucleation in a complex two-dimensional domain and three-dimensional diffusion through a porous medium.