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The effect of nonlinear growth rates of crystals on the evolution of particulate ensembles in binary liquids

Motivated by an important role of growth kinetics of particulate ensembles in metastable liquids, we develop the theory of nucleation and growth of spherical crystals in a binary supercooled melt at the intermediate stage of a phase transition process. An integro-differential set of governing equations consisting of the Fokker-Planck and balance equations with allowance for the nonlinear growth and nucleation kinetics is formulated and analyzed. The particle population density distribution function and the degree of system metastability are found analytically with allowance for fluctuations of newly born crystals in a metastable binary liquid. We demonstrate that the nonlinear kinetics of crystal growth plays a decisive role in the nonlinear dynamics of particulate ensembles.