Surface growth on a deformable spherical substrate
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Description
Accepted version
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303.56 KB
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Checksum (MD5)
1c0b814f6d00016238fe482de7ea72f1
Author(s)
Abi Akl, Rami
Cohen, Tal
Date Issued
November 2019
Journal
Mechanics Research Communications
Publisher
Elsevier BV
Citation
Abi-Akl, Rami and Tal Cohen. "Surface growth on a deformable spherical substrate." Mechanics Research Communications 103 (January 2020): 103457 © 2019 Elsevier Ltd
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/j.mechrescom.2019.103457
