Existence and Stability for Spherical Crystals Growing in a Supersaturated Solution |
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Authors: | CHADAM, J. HOWISON, S. D. ORTOLEVA, P. |
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Affiliation: | Indiana University Bloomington, Indiana, USA and McMaster University Hamilton, Ontario, Canada Mathematical Institute 2429 St Giles, Oxford OX1 3LB Indiana University Bloomington, Indiana, USA |
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Abstract: | 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 |
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