Solution of an Integral Equation Associated with the Nucleation and Growth of Precipitates
Dr. James Baird
Department of Chemistry
University of Alabama in Huntsville
April 12, 2002
A liquid solution that contains more solute than is thermodynamically allowed is said to be supersaturated. In most cases, this supersaturated state relaxes by nucleation and growth of a crystalline precipitate. The rates of nucleation and growth of the precipitate grains combine to determine the time course of the relaxation. The principle of conservation of mass can be expressed in the form of an integral equation, which determines the time dependence of the supersaturation. By direct differentiation, this integral equation can be converted into a differential equation that can be solved by elementary methods. Precipitation experiments suggest that certain special cases of the general solution to this equation are preferred in Nature.
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