Kinetics of surface growth and coupled diffusion in a continuum framework

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2019 ; Cataloged from PDF version of thesis. ; Includes bibliographical references (pages 163-173). ; 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 modeling 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 of the body. In this thesis we present a general theoretical framework that captures these phenomena and describes the kinetics of surface growth while accounting for coupled diffusion.We then use a combination of analytical and numerical tools to study growth in simple geometries. ; In the particular problems of growth on flat and on spherical surfaces, we show that the growth process typically involves two stages. Initially, the body deforms, primarily due to diffusion with minimal growth. This is followed by a second stage during which surface growth and diffusion act harmoniously. It is shown that during this latter stage the body evolves along a 'universal path' that is independent of initial conditions. We make use of this path to analytically describe the evolution of a body from inception up to treadmilling, the latter being a steady state in which the addition and removal of material are balanced. Among the wide spectrum of possible applications for our general continuum framework, we chose to examine in this thesis a specific problem of high interest in microbiology. In this context, we explore the kinetics of degradation of biomatter in the ...