Thermo-solutal and kinetic modes of stable dendritic growth with different symmetries of crystalline anisotropy in the presence of convection

Motivated by important applications in materials science and geophysics, we consider the steady-state growth of anisotropic needle-like dendrites in undercooled binary mixtures with a forced convective flow. We analyse the stable mode of dendritic evolution in the case of small anisotropies of growth kinetics and surface energy for arbitrary Péclet numbers and n-fold symmetry of dendritic crystals. On the basis of solvability and stability theories, we formulate a selection criterion giving a stable combination between dendrite tip diameter and tip velocity. A set of nonlinear equations consisting of the solvability criterion and undercooling balance is solved analytically for the tip velocity V and tip diameter ? of dendrites with n-fold symmetry in the absence of convective flow. The case of convective heat and mass transfer mechanisms in a binary mixture occurring as a result of intensive flows in the liquid phase is detailed. A selection criterion that describes such solidification conditions is derived. The theory under consideration comprises previously considered theoretical approaches and results as limiting cases. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’. © 2018 The Author(s) Published by the Royal Society. All rights reserved.Russian Science Foundation, RSF: 16-11-1009550WM1541Data accessibility. This article has no additional data. Authors’ contributions. All authors contributed equally to the present review paper. Competing interests. The authors declare that they have no competing interests. Funding. This work was supported by the Russian Science Foundation (grant number 16-11-10095) and the German Space Center Space Management (under contract number 50WM1541)

Selection Criterion of Stable Dendritic Growth for a Ternary (Multicomponent) Melt with a Forced Convective Flow

A stable growth mode of a single dendritic crystal solidifying in an undercooled ternary (multicomponent) melt is studied with allowance for a forced convective flow. The steady-state temperature, solute concentrations and fluid velocity components are found for two- and three-dimensional problems. The stability criterion and the total undercooling balance are derived accounting for surface tension anisotropy at the solid-melt interface. The theory under consideration is compared with experimental data and phase-field modeling for Ni 98 Zr 1 Al 1 alloy

A Stable Mode of Dendritic Growth in Cases of Conductive and Convective Heat and Mass Transfer

In this paper, we develop a theory of stable dendritic growth in undercooled melts in the presence of conductive and convective heat and mass transfer boundary conditions at the solid/liquid interface of a dendrite. To simplify the matter and construct the analytical theory, conductive and convective mechanisms are considered separately. Namely, the laws for total undercooling and selection criterion defining the stable growth mode (dendrite tip velocity and diameter) are derived for conductive and convective boundary conditions. To describe the case of simultaneous occurrence of these heat and mass transfer mechanisms, we sew together conductive and convective laws using power stitching functions. The generalised selection theory is compared with experimental data for Al (Formula presented.) Ge (Formula presented.) and Ti (Formula presented.) Al (Formula presented.) undercooled melts. © 2022 by the authors.Russian Science Foundation, RSF: 21-19-00279This study was supported by the Russian Science Foundation (project No. 21-19-00279)

Medication errors

The article presents the descri ption of the causes, detection methodsand approaches to the prevention of medication error

On the theory of stable mode of dendritic growth in the case of convective heat and mass transport at the solid-liquid interface

In this work, a stable relation for the dendrite tip velocity V and its tip diameter via the selection theory and undercooling balance is discussed. The undercooling balance and selection criterion allow us to obtain a pair of most important parameters of primary solidification, V and , at a given undercooling T

Mathematical modeling of dendrite growth in an Al–Ge alloy with convective flow

A theory of stable dendrite growth in an undercooled binary melt is developed for the case of intense convection. Conductive heat and mass transfer boundary conditions are replaced by convective conditions, where the flux of heat (or solute) is proportional to the temperature or concentration difference between the surface of the dendrite and far from it. The marginal mode of perturbation wavelengths is calculated using the linear morphological stability analysis. Combining this analysis with the solvability theory, we have derived a selection criterion that represents the first condition to define a combination of dendrite tip velocity and tip diameter. The second condition—the undercooling balance—is derived for intense convection. The theory under consideration determines the dendrite tip velocity and tip diameter for low undercooling. This convective theory is combined with the classical theory of dendritic growth (conductive boundary conditions), which is valid for moderate and high undercooling. Thus, the entire range of melt undercooling is covered. Our results are in good agreement with experiments on Al–Ge crystallization. © 2021 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd.Ministry of Education and Science of the Russian Federation, Minobrnauka: 075-02-2021-1387; Russian Science Foundation, RSF: 21-19-00279; Foundation for the Advancement of Theoretical Physics and Mathematics: 21-1-3-11-1L.V.T. acknowledges financial support from the Ministry of Science and Higher Education of the Russian Federation (project 075-02-2021-1387 for the development of the regional scientific and educational mathematical center “Ural Mathematical Center”) for the linear stability analysis. Moreover, she is grateful to the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” (project No. 21-1-3-11-1) for the development of solvability theory. P.K.G. and D.V.A. acknowledge the Russian Science Foundation (Project No. 21-19-00279) for the stitching of selection criteria, computer simulations, and comparison with experimental data. Open Access funding enabled and organized by Projekt DEAL

Studying of the anti-ischemic action of <I>Rhaponticum uniflorum</I> and <I>Serratula centauroides</I> dry extracts on a model of bilateral occlusion of the carotid arteries

The aim of the study to evaluate the anti-ischemic effect of Serratula centauroides and Rhaponticum uniflorum dry extracts for bilateral carotid artery occlusion.Materials and methods. The studies were carried out on 77 Wistar rats. Rh. uniflorum and S. centauroides dry extracts at doses 50, 100, 200 mg/kg were administered intragastrically for 14 days prior to bilateral occlusion of the carotid arteries. To assess the anti-ischemic effect of the investigated agents, the total mortality, the dynamics of survival, the survival time, the animals’ neurological status were determined using a modified McGraw scale and the brain hydration degree.Results. S. centauroides at a dose 200 mg/kg reduced the percentage of animals’ death by 2.8 times (p ≤ 0.05) compared with the control. Life expectancy in animals treated with S. centauroides at doses 100 and 200 mg/kg and Rh. uniflorum at dose 100  mg/kg increased by 46, 52 and 64  %, respectively, compared to the control. The neurological deficit lowest severity was observed in animals treated with S. centauroides at dose 200 mg/kg. The most pronounced statistically significant decrease in the brain hydration level was observed in animals treated with Rh.  uniflorum at doses 100 and 200 mg/kg and S. centauroides at dose 100 mg/kg.Conclusion. S. centauroides and Rh. uniflorum dry extracts have an anti-ischemic effect in cerebral ischemia

Modeling of dendrite growth from undercooled nickel melt: sharp interface model versus enthalpy method

The dendritic growth of pure materials in undercooled melts is critical to understanding the fundamentals of solidification. This work investigates two new insights, the first is an advanced definition for the two-dimensional stability criterion of dendritic growth and the second is the viability of the enthalpy method as a numerical model. In both cases, the aim is to accurately predict dendritic growth behavior over a wide range of undercooling. An adaptive cell size method is introduced into the enthalpy method to mitigate against `narrow-band features' that can introduce significant error. By using this technique an excellent agreement is found between the enthalpy method and the analytic theory for solidification of pure nickel

A stable dendritic growth with forced convection: A test of theory using enthalpy-based modeling methods

The theory of stable dendritic growth within a forced convective flow field is tested against the enthalpy method for a single-component nickel melt. The growth rate of dendritic tips and their tip diameter are plotted as functions of the melt undercooling using the theoretical model (stability criterion and undercooling balance condition) and computer simulations. The theory and computations are in good agreement for a broad range of fluid velocities. In addition, the dendrite tip diameter decreases, and its tip velocity increases with increasing fluid velocity