A complete analytical solution to the integro-differential model describing the nucleation and evolution of ellipsoidal particles

Abstract

In this paper, a complete analytical solution to the integro-differential model describing the nucleation and growth of ellipsoidal crystals in a supersaturated solution is obtained. The asymptotic solution of the model equations is constructed using the saddle-point method to evaluate the Laplace-type integral. Numerical simulations carried out for physical parameters of real solutions show that the first four terms of the asymptotic series give a convergent solution. The developed theory was compared with the experimental data on desupersaturation kinetics in proteins. It is shown that the theory and experiments are in good agreement. © 2021 John Wiley & Sons, Ltd.Ministry of Education and Science of the Russian Federation, Minobrnauka: FEUZ-2020-0057; Russian Science Foundation, RSF: 18-19-00008This work was supported by the Russian Science Foundation (grant no. 18-19-00008).This article contains two parts: (i) a new theory of the growth of an ensemble of ellipsoidal crystals in a metastable liquid and (ii) a computational simulation of crystal growth based on the developed theory. Part (i) was supported by the Russian Science Foundation (grant no. 18-19-00008), whereas part (ii) was made possible due to the financial support from the Ministry of Science and Higher Education of the Russian Federation (project no. FEUZ-2020-0057)