Kinetics of surface growth with coupled diffusion and the emergence of a universal growth path
2019
Surface growth by association or dissociation of material on the boundary of a body is ubiquitous in both natural and engineering systems. It is the fundamental mechanism by which biological materials grow, starting from the level of a single cell, and is increasingly applied in engineering processes for fabrication and self-assembly. A significant challenge in modelling such processes arises due to the inherent coupled interaction between the growth kinetics, the local stresses and the diffusing constituents needed to sustain the growth. Moreover, the volume of the body changes not only due to surface growth but also by variation in solvent concentration within the bulk. In this paper, we present a general theoretical framework that captures these phenomena and describes the kinetics of surface growth while accounting for coupled diffusion. Then, by the combination of analytical and numerical tools, applied to a simple growth geometry, we show that the evolution of such growth processes tends towards a u...
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