Fracture patterns generated by diffusion controlled volume changing reactions

A simple two-dimensional model was developed for the growth of fractures in a chemically decomposing solid. Simulations were carried out under rapid chemical decomposition conditions for which the kinetics of fracture growth is controlled by diffusion of the volatile reaction product or the kinetics of evaporation. The growth of the fracture pattern is self-sustaining due to the volume reduction associated with the decomposition process. Consistent with the theoretical analysis of Yakobson [Phys. Rev. Lett. 67, 1590 (1991)], the fracture front propagates with a constant velocity v similar or equal to k(2/3)(Dl(0))(1/3) under evaporation controlled conditions and v similar or equal to D/l(0) under diffusion controlled conditions, where k is the evaporation rate constant, D is the diffusion constant for the volatile reaction product in the solid, and l(0) is the critical stable crack length. Under diffusion controlled conditions, the front width w scales as w similar or equal to(kl(0)/)D.