Exact results with the J-integral applied to free-boundary flows

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Exact results with the J-integral applied to free-boundary flows

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Title: Exact results with the J-integral applied to free-boundary flows
Author: Ben Amar, Martine; Rice, James R.

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Citation: Amar, Ben Martine, and James R. Rice. 2002. Exact results with the J-integral applied to free-boundary flows. Journal of Fluid Mechanics 461: 321-341.
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Abstract: We apply the J-integral to free-boundary flows in a channel geometry such as viscous fingering or blob injection in Hele-Shaw cells, void propagation in electromigration, and injection of air bubbles into inviscid liquids. The theory of that and related conservation integrals, developed in elasticity, is outlined in a way that is applicable to fluid mechanics problems. Depending on the boundary conditions, for infinite bubbles in Laplacian fields we are able to use the J-integral to predict finger width if such solutions exist or to predict that there are no solutions. For finite sized bubbles, bounds can sometimes be derived. In the case of Hele-Shaw flows, in which solutions appear as a continuum, finger width cannot be constrained, but we do obtain a new derivation and generalization of Richardson moment conservation. Applications to vortex motion are also outlined briefly.
Published Version: http://dx.doi.org/10.1017/S0022112002008418
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:2640594
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