Kinetics of surface growth with coupled diffusion and the emergence of a universal growth path
Name
1803.08399.pdf
Description
Submitted version
Size
998.73 KB
Format
Adobe PDF
Checksum (MD5)
7cbfbd98a72519f097ada1f117d329aa
Author(s)
Abi Akl, Rami
Abeyaratne, Rohan
Cohen, Tal
Date Issued
January 2019
Journal
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Publisher
The Royal Society
Citation
Rami Abi-Akl, Rohan Abeyaratne and Tal Cohen. "Kinetics of surface growth with coupled diffusion and the emergence of a universal growth path." Proceedings of the Royal Society A 2019 475: 20180465.
Version
Original manuscript
Abstract
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 universal path that is independent of initial conditions. This path, on which surface growth and diffusion act harmoniously, can be extended to analytically portray the evolution of a body from inception up to a treadmilling state, in which addition and removal of material are balanced.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1098/RSPA.2018.0465
