Surface growth on a deformable spherical substrate

Abstract

Kinetics of surface growth with coupled diffusion is studied for the case of growth on a spherical substrate. The considered material system is composed of two species, a solid matrix and a permeating solvent, which can interact by a chemical reaction on the boundaries of the body. It is shown that, for arbitrary substrate curvature, a transient diffusion dominated response is rapidly exhausted before the system arrives at a universal path that is independent of initial conditions. Along this path, the system evolves up to arrival at a steady state, called treadmilling, in which addition and removal of mass are balanced. This result confirms that the universal path, recovered in previous work for growth on a flat rigid substrate, generalizes to additional geometrical settings and also to situations in which the substrate is deformable. The universal path thus facilitates the investigation of the coupling between growth, diffusion and substrate deformation that is induced by buildup of internal stress. This complex coupling is shown to result in a non-monotonic evolution, before arriving at the treadmilling state.