scholarly journals Mathematical modeling of bulk and directional crystallization with the moving phase transition layer

2021 ◽  
Author(s):  
Liubov V. Toropova ◽  
Danil L. Aseev ◽  
Sergei I. Osipov ◽  
Alexander A. Ivanov
Keyword(s):  
Mathematical Modeling ◽  
Phase Transition ◽  
Transition Layer ◽  
Directional Crystallization

Mathematical modeling of binary compounds with the presence of a phase transition layer

2020 ◽  
Author(s):  
Irina G. Nizovtseva ◽  
Ilya O. Starodumov ◽  
Eugeny V. Pavlyuk ◽  
Alexander A. Ivanov
Keyword(s):  
Mathematical Modeling ◽  
Phase Transition ◽  
Transition Layer ◽  
Binary Compounds

scholarly journals Mathematical modeling of bulk and directional crystallization with the moving phase transition layer

2021 ◽  
Author(s):  
Liubov Toropova ◽  
Danil Aseev ◽  
Sergei Osipov ◽  
Alexander Ivanov
Keyword(s):  
Mathematical Modeling ◽  
Phase Transition ◽  
Transition Layer ◽  
Solid Phase ◽  
Phase Region ◽  
Mushy Region ◽  
Solidification Velocity ◽  
Mushy Layer ◽  
Two Phase ◽  
Phase Layer

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.

On the theory of bulk crystallization in the moving phase transition layer

2020 ◽  
Vol 532 ◽  
pp. 125420
Author(s):  
D.V. Alexandrov ◽  
A.A. Ivanov ◽  
I.V. Alexandrova
Keyword(s):  
Phase Transition ◽  
Transition Layer ◽  
Bulk Crystallization

scholarly journals Solutions with transition layer and spike in an inhomogeneous phase transition model

2009 ◽  
Vol 246 (9) ◽  
pp. 3642-3667 ◽  
Author(s):  
Juncheng Wei ◽  
Jun Yang
Keyword(s):  
Phase Transition ◽  
Transition Layer ◽  
Transition Model ◽  
Inhomogeneous Phase

Mathematical modeling phase transition in solids

2014 ◽  
Vol 2 (2) ◽  
Author(s):  
J. Pribiš
Keyword(s):  
Mathematical Modeling ◽  
Phase Transition

On reconstitutive phase transitions and the jump of the chemical potential

Analysis ◽  
2008 ◽  
Vol 28 (1) ◽  
Author(s):  
Thomas Blesgen
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Weak Solutions ◽  
Transition Layer ◽  
Chemical Potential ◽  
Sharp Interface ◽  
Free Energies ◽  
Diffusion In Solids ◽  
Existence Of Weak Solutions ◽  
Two Phases

This article studies diffusion in solids in the case of two phases under isothermal conditions where due to plastic effects the number of vacancies changes when crossing a transition layer, i.e. a reconstitutive phase transition. A segregation model is derived and the equations are studied in the limit of a sharp interface. A Gibbs–Thomson law is derived and it is shown that the vacancy component of the chemical potential jumps across the transition layer thereby explaining recent experimental observations. The thermodynamic correctness of the model is shown as well as the existence of weak solutions with logarithmic free energies.

scholarly journals Mathematical modeling of convection drying process of wood taking into account the boundary of phase transitions

2021 ◽  
Vol 8 (4) ◽  
pp. 830-841
Author(s):  
Ya. I. Sokolovskyy ◽  
◽  
I. B. Boretska ◽  
B. I. Gayvas ◽  
I. M. Kroshnyy ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Phase Transition ◽  
Phase Transitions ◽  
Transition Temperature ◽  
Moisture Transfer ◽  
Drying Process ◽  
Evaporation Zone ◽  
Boundary Change ◽  
Phase Transition Boundary

The article deals with constructing and implementing mathematical models of non-isothermal moisture transfer during drying of anisotropic capillary-porous materials, in particular wood, taking into account the movement of the evaporation zone for non-steady drying schedules, as well as to the development of effective analytical and numerical methods for their implementation. An analytical-numerical method for the determination of non-isothermal moisture transfer under non-steady schedules of the drying process has been developed, taking into account the dynamics of the phase transition boundary change. Calculation relationships are established for determining the phase transition temperature taking into account transport gradients and time for which the relative saturation reaches the boundaries of the phase transition.

scholarly journals Mathematical modeling of phase transition and separation in fluids: A unified approach

2014 ◽  
Vol 19 (7) ◽  
pp. 1889-1909 ◽  
Author(s):  
Alessia Berti ◽  
◽  
Claudio Giorgi ◽  
Angelo Morro ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Phase Transition ◽  
Unified Approach
Sign in / Sign up

Export Citation Format

Share Document