nam 22 uu 4500 dbt_mods_00055091 10.3390/cryst12111657 doi dbt_mods_00055091 ger DE-601 rda eng 530 sdnb Titova, Ekaterina A. Author aut Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, 620000 Ekaterinburg, Russia Mathematical Modeling of the Solid–Liquid Interface Propagation by the Boundary Integral Method with Nonlinear Liquidus Equation and Atomic Kinetics Titova, Ekaterina A.;Alexandrov, Dmitri V.;Toropova, Liubov V.;Angelov, Borislav 2022-11-17 12 Seiten text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Zweitveröffentlichung In this paper, we derive the boundary integral equation (BIE), a single integrodifferential equation governing the evolutionary behavior of the interface function, paying special attention to the nonlinear liquidus equation and atomic kinetics. As a result, the BIE is found for a thermodiffusion problem of binary melt crystallization with convection. Analyzing this equation coupled with the selection criterion for a stationary dendritic growth in the form of a parabolic cylinder, we show that nonlinear effects stemming from the liquidus equation and atomic kinetics play a decisive role. Namely, the dendrite tip velocity and diameter, respectively, become greater and lower with the increasing deviation of the liquidus equation from a linear form. In addition, the dendrite tip velocity can substantially change with variations in the power exponent of the atomic kinetics. In general, the theory under consideration describes the evolution of a curvilinear crystallization front, as well as the growth of solid phase perturbations and patterns in undercooled binary melts at local equilibrium conditions (for low and moderate Péclet numbers). In addition, our theory, combined with the unsteady selection criterion, determines the non-stationary growth rate of dendritic crystals and the diameter of their vertices. boundary integral equation phase transitions curved solid–liquid interface undercooled melt article Alexandrov, Dmitri V. Author aut Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, 620000 Ekaterinburg, Russia Toropova, Liubov V. Author aut Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, 620000 Ekaterinburg, Russia Otto-Schott-Institut für Materialforschung, Friedrich-Schiller-Universität-Jena (DE-588)1279003006 Angelov, Borislav Editor edt Friedrich-Schiller-Universität Jena Physikalisch-Astronomische Fakultät host institution his 12:11:1657 Technische Universität Ilmenau, Universitätsbibliothek Crystals 2073-4352 dbt_mods_00048162 https://www.db-thueringen.de/receive/dbt_mods_00055091 object in context https://www.db-thueringen.de/servlets/MCRFileNodeServlet/dbt_derivate_00058374/crystals-12-01657-v2.pdf raw object https://www.db-thueringen.de/rsc/thumbnail/dbt_mods_00055091.png preview https://www.db-thueringen.de/receive/dbt_mods_00055091 uri