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We consider the growth of a spherical crystal in a supersaturatedsolution. In the first part, existence and uniqueness resultsfor radially symmetric growth are obtained, provided that thesupersaturation is not too large; conversely, when the far-fieldsupersaturation exceeds a critical value, it is shown that theradially symmetric solution ceases to exist in finite time.In the second part, we examine the linear stability of a radiallysymmetric similarity solution (in which the radius grows ast?) to shape perturbations. The results are compared with previousquasi-static analyses, and, in particular, the critical radiusat which the crystal becomes unstable is found to be largerfor small supersaturations, but smaller for large supersaturations,than those predicted by the quasi-static analysis 相似文献
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Reactive Infiltration Instabilities 总被引:3,自引:0,他引:3
CHADAM J.; HOFF D.; MERINO E.; ORTOLEVA P.; SEN A. 《IMA Journal of Applied Mathematics》1986,36(3):207-221
When a fluid flow is imposed on a porous medium, the infiltrationflow may interact with the reaction-induced porosity variationswithin the medium and may lead to fingering instabilities. Anonlinear model of such interaction is developed and morphologicalinstability of a planar dissolution front is demonstrated usinga linear stability analysis of a moving-free-boundary problem.The fully nonlinear model is also examined numerically usingfinite-difference methods. The numerical simulations confirmthe predictions of linear stability theory and, more importantly,reveal the growth of dissolution fingers that emerge as a resultof these instabilities 相似文献
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A generalized Stefan problem which includes surface tensionis presented as a mathematical model for the growth and meltingof a solid. It is shown that planar melting is linearly morphologicallystable with or without surface tension, while planar solidificationis unstable without surface tension and is stabilized with itsinclusion. The technique used is an adaptation to this situationof Rubinstein's recent work on the one-dimensional, two-phaseproblem without surface tension. 相似文献
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