Fragmentation of two-dimensional mass fractals by surface-diffusion sintering

The sintering process by surface diffusion of computer-generated two-dimensional mass-fractal aggregates with tunable fractal dimension $D$ is numerically studied. The evolution of the contour is obtained by discretizing and numerically solving the relevant partial differential equation, taking care of possible fragmentation and/or coalescence events. It is shown that, when the cluster is sufficiently large, it splits into several pieces during the sintering process which all evolve towards circular shapes as time goes on. The final number of pieces is roughly proportional to the surface area of the initial cluster but the precise way it decreases when the fractal dimension increases turns out to be nontrivial. These general trends are explained using rough theoretical arguments.