The Tip of Dendritic Crystal in an Inclined Viscous Flow

Starodumov, Ilya; Титова, Э. А.; Pavlyuk, Eugeny V.; Alexandrov, Dmitri V.

doi:10.3390/cryst12111590

Cited by 6 publications

(3 citation statements)

References 69 publications

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“…As a special note, the boundary integral equation under consideration has great potential applications for the further development of crystallization theory. For example, it can be used for simulating the pattern formation and crystal growth in undercooled liquids [12,29], studying the development of morphological instability [2,9,10,30], and deriving a selection criterion for a stable mode of dendritic growth [1,21,30]. An important task of crystallization theory is to derive the boundary integral while taking into account the nucleation and growth of particles in an undercooled liquid ahead of the phase transformation boundary.…”

Section: Discussionmentioning

confidence: 99%

Mathematical Modeling of the Solid–Liquid Interface Propagation by the Boundary Integral Method with Nonlinear Liquidus Equation and Atomic Kinetics

2022

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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.

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Section: Discussionmentioning

confidence: 99%

Mathematical Modeling of the Solid–Liquid Interface Propagation by the Boundary Integral Method with Nonlinear Liquidus Equation and Atomic Kinetics

2022

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“…The previous work has also confirmed that iron dendrites continue to grow with increasing electrolysis time. [32] The EDS mappings inserted in Fig. 7b-d reveal the uniform element distribution of iron.…”

Section: Influences Of Electrodeposition Conditions On the Electrodep...mentioning

confidence: 94%

Direct Electrodeposition of High-Purity Iron from Fe<sub>2</sub>O<sub>3</sub> in Molten Calcium Chloride

Pang,

Li,

Chen

et al. 2024

ISIJ Int.

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The low-cost production of high-purity metallic iron is of great practical importance. Herein, we report the direct production of high-purity metallic iron (99.92 %) via a one-step electrochemical strategy in molten CaCl 2 -CaO-Fe 2 O 3 system at 850 o C. The involved CaO-assisted dissolution of Fe 2 O 3 and electrodeposition mechanism were systematically studied, and the obtained iron products were characterized using scanning electron microscopy, inductively-coupled high-frequency plasma emission spectrometry, and glow discharge mass spectrometry. The results show that the crystalline iron products with tunable morphologies can be obtained in a controlled manner. The electrolysis parameters (voltage, current density, electrodeposition time and substrate material) have significant effects on the electrodeposition process and the characteristics of iron products. In particular, highpurity dense iron film can be directly electrodeposited at 15 mA•cm −2 , and its thickness increases considerably with increasing electrodeposition time. Furthermore, the as-deposited iron product can also be processed into bulk iron materials with high-purity of 99.995 wt.% by plasma melting for the potential applications. In general, this one-step electrodeposition process provides an acid-/alkalinefree strategy for the facile production of high-purity iron materials direct from Fe 2 O 3 .

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“…Thirdly, in the case of turbulent fluid flow, additional diffusion terms of turbulent heat and mass fluxes appear in the equations of heat and mass transfer [14][15][16]. The presence of such terms makes nonlinear the heat and mass transport in liquid due to the strong mixing of liquid and the occurrence of complex circulation currents near the interphase boundary [17]. Fourth, a nonlinearity of the problem arises due to the morphological instability of the phase transformation boundary and the formation of new periodic and/or irregular crystallization scenarios [18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Wavy Ice Patterns as a Result of Morphological Instability of an Ice–Water Interface with Allowance for the Convective–Conductive Heat Transfer Mechanism

Alexandrov,

Makoveeva,

Pashko

2024

Crystals

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In this research, the wavy ice patterns that form due to the evolution of morphological perturbations on the water–ice phase transition interface in the presence of a fluid flow are studied. The mathematical model of heat transport from a relatively warm fluid to a cold wall includes the mechanism of convective–conductive heat transfer in liquid and small sinusoidal perturbations of the water–ice interface. The analytical solutions describing the main state with a flat phase interface as well as its small morphological perturbations are derived. Namely, the migration velocity of perturbations and the dispersion relation are found. We show that the amplification rate of morphological perturbations changes its sign with variation of the wavenumber. This confirms the existence of two different crystallization regimes with (i) a stable (flat) interfacial boundary and (ii) a wavy interfacial boundary. The maximum of the amplification rate representing the most dangerous (quickly growing) perturbations is found. The theory is in agreement with experimental data.

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The Tip of Dendritic Crystal in an Inclined Viscous Flow

Cited by 6 publications

References 69 publications

Mathematical Modeling of the Solid–Liquid Interface Propagation by the Boundary Integral Method with Nonlinear Liquidus Equation and Atomic Kinetics

Mathematical Modeling of the Solid–Liquid Interface Propagation by the Boundary Integral Method with Nonlinear Liquidus Equation and Atomic Kinetics

Direct Electrodeposition of High-Purity Iron from Fe<sub>2</sub>O<sub>3</sub> in Molten Calcium Chloride

Wavy Ice Patterns as a Result of Morphological Instability of an Ice–Water Interface with Allowance for the Convective–Conductive Heat Transfer Mechanism

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