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Interface Growth Driven by Surface Kinetics and Convection

Fok, Pak-Wing and Chou, Tom (2009) Interface Growth Driven by Surface Kinetics and Convection. SIAM Journal on Applied Mathematics, 70 (1). pp. 24-39. ISSN 0036-1399. http://resolver.caltech.edu/CaltechAUTHORS:20090820-105237857

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Abstract

A moving, solidifying interface that grows by the instantaneous adsorption of a diffusing solute can be described by equations analogous to those of the classical one-sided Stefan problem for solidification. However, the behavior of precipitate growth by material deposition can depend on both surface kinetics and bulk drift of the depositing species. We generalize the Stefan problem and its interface boundary condition to explicitly account for both surface kinetics and particle convection. A surface layer, within which the surface adsorption and desorption kinetics occurs, is introduced. We find that surface kinetics regularizes the divergent interface velocity at short times, while a finite surface layer thickness further regularizes an otherwise divergent initial acceleration. At long times, we find the behavior of the interface position to be governed by the particle drift. The different asymptotic regimes and the cross-over among them are found from numerical solutions of the partial differential equations, as well as from analysis of a nonlinear integro-differential equation.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1137/070710354DOIArticle
http://www.siam.org/journals/siap/70-1/71035.htmlPublisherArticle
ORCID:
AuthorORCID
Fok, Pak-Wing0000-0001-9655-614X
Additional Information:© 2009 SIAM. Received December 7, 2007; accepted January 12, 2009; published April 15, 2009. This work was supported by National Science Foundation grant DMS-0349195 and National Institutes of Health grant K25AI41935. AMS subject classifications: 74H10, 80A30, 74N20
Funders:
Funding AgencyGrant Number
NSFDMS-0349195
NIHK25AI41935
Subject Keywords:Stefan problem; kinetics; moving boundary; asymptotics
Issue or Number:1
Record Number:CaltechAUTHORS:20090820-105237857
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20090820-105237857
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15187
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:20 Aug 2009 19:53
Last Modified:15 Apr 2017 04:11

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