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.
Highlights
Capillarity and wetting phenomena, driven primarily by interfacial forces, are ubiquitous in a wide spectrum of natural phenomena and technological applications
We observe that the final configurations are different depending on whether or not an adaptive time step is used, which can be attributed to the high sensitivity of the solution to perturbations of the initial condition chosen for this test case; the areas where separation of the phases first occurs is influenced by numerical errors in the early stages of the simulation
We have proposed a new, fast and reliable numerical method to solve the CH equation with a wetting boundary condition
Summary
Capillarity and wetting phenomena, driven primarily by interfacial forces, are ubiquitous in a wide spectrum of natural phenomena and technological applications. We outline a numerical scheme that extends and appropriately generalises OD2 as follows: (a) it includes a non-linear wetting boundary condition; (b) it adopts an efficient energy-based time-step adaptation strategy. In contrast with the time-adaptation scheme introduced in [45], where the time step is adapted to limit numerical dissipation, here we base the time-step adaptation directly on the variation of free energy With this method we are able to solve the CH system efficiently and systematically to capture wetting phenomena in both two- and three-dimensional (2D and 3D, respectively) settings, and in a wide range of situations, including confinement with complex geometry, chemical and topographical heterogeneities, or both.
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