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Ostwald ripening with size-dependent rates: Similarity and power-law solutions

Madras, Giridhar and McCoy, Benjamin J (2002) Ostwald ripening with size-dependent rates: Similarity and power-law solutions. In: Journal of Chemical Physics, 117 (17). pp. 8042-8049.

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Abstract

The dynamics of Ostwald ripening is treated by cluster distribution kinetics represented by a population balance equation that also describes growth or dissolution. Unlike simple crystal growth driven by supersaturation, the smaller, more soluble clusters in the distribution dissolve during ripening near equilibrium and vanish when they reach the critical nucleus size. Larger clusters accordingly grow as the supersaturation decreases. The long-time asymptotic result of the numerical solution of the scaled population balance equation is power-law decrease of cluster number and growth of average cluster mass, Cavg(theta). The cluster distribution approximates an exponential self-similar solution, and eventually narrows until but one large cluster remains, satisfying the mass balance. A previous theory is here extended to include mass-dependent rate coefficients for growth and dissolution that satisfy microscopic reversibility. The asymptotic power-law growth, Cavg~theta 1/(4/3-lambda), is determined by the power lambda on the mass for rate coefficients. The power is lambda=1/3 for diffusion-controlled and lambda=2/3 for surface-controlled processes. Experimentally observed ripening behavior is realized by an apt choice of lambda for a given time range.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to American Institute of Physics (AIP).
Department/Centre: Division of Mechanical Sciences > Chemical Engineering
Date Deposited: 22 Nov 2004
Last Modified: 19 Sep 2010 04:17
URI: http://eprints.iisc.ernet.in/id/eprint/2345

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