A Discrete Particle Model of Diffusion-limited Dissolution

Yuexia Lin, Harvard University

Photo of Yuexia Lin

The diffusion-limited aggregation (DLA) model of Witten & Sander (1981) has been widely used to represent a variety of physical processes such as electrodeposition. In the model, a single fixed seed particle is introduced and additional particles undergo diffusive random walks that adhere to it upon contact, creating a growing particle cluster over time with a complex fractal shape. Here we consider the diffusion-limited dissolution (DLD) model by switching the sign of growth in DLA so diffusing particles annihilate part of an existing cluster on contact. This provides a simple model for dissolution, erosion or melting. We develop a new numerical approach for two-dimensional DLD that uses conformal mapping and first-passage problems to efficiently solve the dissolution process. By averaging over a large stochastic ensemble of DLD realizations, we numerically obtain the spatial distribution of the last surviving particle in a cluster, which we compare to predictions in the continuum limit. In addition, we examine the effect that the orientation of the dissolving surface has on the asymptotic variance of the interface height. We also create a hybrid model by mixing DLD and DLA, with probabilities of annihilation and aggregation as free parameters, and explore the resulting structures.

Abstract Author(s): Y.L. Lin, C.H. Rycroft