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A complete analytical solution to the integro-differential model describing the nucleation and evolution of ellipsoidal particles
  • Margarita Nikishina,
  • Dmitri Alexandrov
Margarita Nikishina
Ural Federal University named after the first President of Russia B N Yeltsin
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Dmitri Alexandrov
Ural Federal University named after the first President of Russia B N Yeltsin
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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.

Peer review status:UNDER REVIEW

29 Jul 2021Submitted to Mathematical Methods in the Applied Sciences
29 Jul 2021Assigned to Editor
29 Jul 2021Submission Checks Completed
31 Jul 2021Reviewer(s) Assigned
03 Sep 2021Review(s) Completed, Editorial Evaluation Pending