Cellular Automaton Simulations of Surface Mass Transport Due to Curvature Gradients: Simulations of Sintering in 3-D.

Abstract

ABSTRACTA cellular automaton algorithm is described that simulates the evolution of a surface driven by the reduction of chemical potential differences on the surface. When the surface tension is isotropic, the chemical potential is proportional to the curvature at the surface. This process is important in the development of microstructure during the sintering of powders. The algorithm is implemented in two and three dimensions in a digital image mode, using discrete pixels to represent continuum objects. The heart of the algorithm is a pixel-counting-based method for computing the potential at a pixel located in a digital surface. This method gives an approximate measure of the curvature at the given surface pixel. The continuum version of this method is analytically shown to give the true curvature at a point on a continuum surface. The digital version of the curvature computation method is shown to obey the scaling laws derived for the continuum version. The evolution of the surface of a three dimensional loosely packed powder, along with the percolation characteristics of its pore space, are computed as an example of the algorithm.