Thin Film Solution of the Cahn Hilliard Equations

EasyChair Preprint 13924

Abstract

The Cahn-Hilliard equation describes phase separation and coarsening in binary MGA’s. Perturbation solutions of the one-dimensional Cahn-Hilliard equation for small distances and times are examined. Using a small perturbation a the first-order perturbation expansion, series and Fourier transforms solve the linearized form of the Cahn-Hilliard equation to obtain a general solution. The dispersion relation reveals the growth rates of the perturbation modes, providing insight into the early-time dynamics of phase separation. This analytical approach lays the groundwork for revealing the evolution of small disturbances and their impact on phase separation in binary systems. This work has potential applications in materials science, particularly in the microstructural development of alloys, MGA’s and polymer blends.

Keyphrases: Alloy development, Cahn-Hilliard, Cahn-Hilliard equation, MGA, Perturbation solutions, Spinodal, boundary conditions, d cahn hilliard equation, describes phase separation, diffusion, materials science, microstructural development of alloys, thin films, zeroth order solution

@booklet{EasyChair:13924,
  author    = {Rahul Basu},
  title     = {Thin Film Solution of the Cahn Hilliard Equations},
  howpublished = {EasyChair Preprint 13924},
  year      = {EasyChair, 2024}}