loading page

Mathematical modeling of bulk and directional crystallization with the moving phase transition layer
  • +1
  • Liubov Toropova,
  • Danil Aseev,
  • Sergei Osipov,
  • Alexander Ivanov
Liubov Toropova
Friedrich-Schiller-Universit├Ąt Jena

Corresponding Author:[email protected]

Author Profile
Danil Aseev
UrFU Institute of Natural Sciences and Mathematics
Author Profile
Sergei Osipov
Ural Federal University named after the first President of Russia B N Yeltsin
Author Profile
Alexander Ivanov
Ural Federal University named after the first President of Russia B N Yeltsin
Author Profile


This paper is devoted to the mathematical modeling of a combined effect of directional and bulk crystallization in a phase transition layer with allowance for nucleation and evolution of newly born particles. We consider two models with and without fluctuations in crystal growth velocities, which are analytically solved using the saddle-point technique. The particle-size distribution function, solid-phase fraction in a supercooled two-phase layer, its thickness and permeability, solidification velocity, and desupercooling kinetics are defined. This solution enables us to characterize the mushy layer composition. We show that the region adjacent to the liquid phase is almost free of crystals and has a constant temperature gradient. Crystals undergo intense growth leading to fast mushy layer desupercooling in the middle of a two-phase region. The mushy region adjacent to the solid material is filled with the growing solid phase structures and is almost desupercooled.
08 Aug 2021Submitted to Mathematical Methods in the Applied Sciences
09 Aug 2021Assigned to Editor
09 Aug 2021Submission Checks Completed
15 Aug 2021Reviewer(s) Assigned
13 Sep 2021Review(s) Completed, Editorial Evaluation Pending
13 Sep 2021Editorial Decision: Accept
15 Sep 2022Published in Mathematical Methods in the Applied Sciences volume 45 issue 13 on pages 8011-8021. 10.1002/mma.7864