Random-walk simulations of flow in Hele Shaw cells

Abstract

An algorithm related to diffusion-limited aggregation is used to generate patterns of interface motion in the Hele Shaw geometry. With increasing surface tension, the objects generated change from fractal structures to smooth boundary ‘‘fingers.’’ The fingers’ profiles agree with experiments and numerical solutions. The fingers’ width as the function of the surface tension is consistent with the results obtained through other simulational methods. As the surface tension is decreased, apparently unstable patterns of flow develop. For very small values of the surface tension, a kind of dendritic growth is produced.