Kinetics of Chemical Precipitation: General Evolutionary Patterns in Different Models

Abstract—The trends, general patterns, and stages of evolutionary processes, in particular, the evolution of solid matter in crystallization processes, have been considered. The role of the logistic (sigmoid) function in the description of the kinetics of evolutionary processes has been shown. Mathematical modeling of the chemical precipitation of slightly soluble salts has been performed taking into account the rates of crystal growth and nucleation. It has been found that different models lead to the S-shaped dependence of the same form, which adequately describes the formation of crystalline precipitates of slightly soluble calcium salts from supersaturated aqueous solutions.