Mullins' Self-Similar Grooving Solution Revisited

Vadim Derkach; Amy Novick-Cohen

doi:10.4028/www.scientific.net/DDF.383.112

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HomeDefect and Diffusion ForumDefect and Diffusion Forum Vol. 383Mullins' Self-Similar Grooving Solution Revisited

Mullins' Self-Similar Grooving Solution Revisited

Abstract:

In W.W. Mullins' classical 1957 paper on thermal grooving, motion by surface diffusion was proposed to describe the development of a thermal groove separating two grains in a simple semi-infinite planar geometry. After making a small slope approximation which is often realistic, Mullins' sought self-similar solutions, and obtained an explicit time series solution for the groove depth. In the years since, Mullins' grooving solution has become a standard tool; however it has yet to be rigorously demonstrated that self-similar solutions exist when the small slope approximation is not applicable. Here we demonstrate that reformulation of Mullins' nonlinear problem in arc-length variables yields a particularly simple fully nonlinear formulation, which is useful for verifying large slope grooving properties and which should aid in proving existence.

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Periodical:

Defect and Diffusion Forum (Volume 383)

Pages:

112-117

DOI:

https://doi.org/10.4028/www.scientific.net/DDF.383.112

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Online since:

February 2018

Authors:

Vadim Derkach, Amy Novick-Cohen*

Keywords:

Arc-Length Variables, Self-Similar Solutions, Surface Diffusion, Thermal Grooving

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