Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published April 15, 2009 | Published
Journal Article Open

Interface Growth Driven by Surface Kinetics and Convection

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.

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

Attached Files

Published - Fok2009p5497Siam_J_Appl_Math.pdf

Files

Fok2009p5497Siam_J_Appl_Math.pdf
Files (345.4 kB)
Name Size Download all
md5:65f97c3dce82aef301d689d8e41b573b
345.4 kB Preview Download

Additional details

Created:
August 21, 2023
Modified:
October 18, 2023