Numerical methods for the implementation of the Cahn-Hilliard equation in one dimension and dynamic boundary condition in two dimensions

TL;DRAbstract

This project can be divided into two parts. The goal of the first part is to numerically implement the Cahn-Hilliard equation in one dimension both explicitly and implicitly. This will be done using Matlab. The goal of the second part is to validate the coupled Cahn-Hilliard-Navier-Stokes equation and the dynamic boundary condition for moving contact lines of (Carlson et al, 2011, p.9) by considering a two-dimensional spreading droplet case. This will be done using the CFD software OpenFOAM. In Chapter 1, the theory of positive and negative diffusion, including the normal diffusion equation and the Cahn-Hilliard equation, are discussed. Some background is given regarding the thermodynamics of the Cahn-Hilliard equation and its steady-state solution. After that, the theory of the coupled Cahn-Hilliard-Navier-Stokes equation, the dynamic boundary condition for moving contact lines and the case which is implemented in OpenFOAM, are discussed. In Chapters 2 and 3, the diffusion equation an

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