Analysis of the Moving Boundary Problem for Spinodal Transformations in Thin Films

The equations of Spinodal Decomposition as postulated by Cahn and Hilliard involve a fourth order pde which to date has not been solved analytically. In this article these equations are examined in their various versions, and solutions obtained for the steady state and transient forms using various methods.Then the moving boundary associated with transformation is examined using a heat transfer approach and a solution attempted using a series and a similarity transformation approach. The equation is postulated to have two contributions one from the usual Laplacian and Fickian contribution part for which Stefan solutions are known, and one with a Double Laplacian which has not been examined. The thin film approximation is applied to simplify some parts of the analysis and to try to get a numerical solution.