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

Alexandrov, Dmitri V.; Galenko, Peter; Toropova, Liubov V.

doi:10.1098/rsta.2017.0215

Cited by 62 publications

(91 citation statements)

References 92 publications

(254 reference statements)

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“…Consider the steady-state growth of a two-dimensional thermal dendritic crystal along the spatial axis z in the presence of a forced convective flow coming from the opposite direction 14 (Fig. 1).…”

Section: Governing Equationsmentioning

confidence: 99%

A Stable Dendritic Growth with Forced Convection: A Test of Theory Using Enthalpy-Based Modeling Methods

Kao

Toropova

Krastiņš

et al. 2020

JOM

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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.

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Section: Governing Equationsmentioning

confidence: 99%

A Stable Dendritic Growth with Forced Convection: A Test of Theory Using Enthalpy-Based Modeling Methods

Kao

Toropova

Krastiņš

et al. 2020

JOM

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“…The selection criterion determining a stable combination between the dendrite tip velocity V and its tip diameter ρ is given by [32]…”

Section: Stability Criterion For Convective Heat and Mass Transportmentioning

confidence: 99%

“…The dendrite tip diameter ρ as a function of ∆T can be found from the modified undercooling balance (6). In the case of conductive heat and mass transfer boundary conditions the selection criterion takes the form [7,32,33] , P 0 = P g + P f ,…”

Section: Undercooling Balancementioning

confidence: 99%

“…U is the fluid velocity at infinity, P f = ρU/(2D T ), b is the stability constant, = ρU/ν is the Reynolds number, ν is the kinematic viscosity, and I C (∞) is determined in [32]. Criterion (8) should be supplemented with the corresponding undercooling balance condition, which coincides with expression (2) with contributions ∆T T , ∆T C , ∆T R , and ∆T K found in [32] for two-and three-dimensional geometries.…”

Section: Undercooling Balancementioning

confidence: 99%

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On the Theory of Stable Mode of Dendritic Growth in the Presence of Convective Heat and Mass Transfer Boundary Conditions

2020

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The dendritic form is one of the most common forms of crystals growing from supercooled melts and supersaturated solutions. In recent decades, an analytical theory has been developed that describes a stable dendrite growth mode under the conditions of a conductive heat and mass transfer process. However, in experiments, the growth of dendritic crystals is often observed under the conditions of convective fluid flow. In the present work, the theory of the growth of dendritic crystals is developed taking into account the convective mechanism of heat and mass transfer at the crystal-melt interface. A stable mode of dendritic growth in the case of intense convective flows near the steady-state growing dendritic tip is analyzed. The selection theory determining a stable growth mode in the vicinity of parabolic solutions as well as the undercooling balance condition are used to find the dendrite tip velocity and its tip diameter as functions of the melt undercooling. It is shown that the theoretical predictions in the case of convective boundary conditions are in agreement with experimental data for small undercoolings. In addition, the convective and conductive heat and mass transfer mechanisms near the growing dendritic surfaces are compared. Our calculations show that the convective boundary conditions essentially influence the stable mode of dendritic growth.

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“…In the review article written by the editors of this theme issue [45], the kinetics of thermosolutal dendrites via theoretical modelling is analysed. An inclusion of the flow and physically relevant n-fold symmetry of the surface energy makes their analysis flexible enough to estimate the experimental data for various crystal growth conditions and different chemical compositions of solidified samples.…”

Section: (B) Experimental Study and Mesoscopic Modelling Of Dendritesmentioning

confidence: 99%

From atomistic interfaces to dendritic patterns

Galenko

Alexandrov

2018

Phil. Trans. R. Soc. A.

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One contribution of 16 to a theme issue 'From atomistic interfaces to dendritic patterns' . Transport processes around phase interfaces, together with thermodynamic properties and kinetic phenomena, control the formation of dendritic patterns. Using the thermodynamic and kinetic data of phase interfaces obtained on the atomic scale, one can analyse the formation of a single dendrite and the growth of a dendritic ensemble. This is the result of recent progress in theoretical methods and computational algorithms calculated using powerful computer clusters. Great benefits can be attained from the development of micro-, meso-and macrolevels of analysis when investigating the dynamics of interfaces, interpreting experimental data and designing the macrostructure of samples. The review and research articles in this theme issue cover the spectrum of scales (from nano-to macro-length scales) in order to exhibit recently developing trends in the theoretical analysis and computational modelling of dendrite pattern formation. Atomistic modelling, the flow effect on interface dynamics, the transition from diffusion-limited to thermally controlled growth existing at a considerable driving force, two-phase (mushy) layer formation, the growth of eutectic dendrites, the formation of a secondary dendritic network due to coalescence, computational methods, including boundary integral and phase-field methods, and experimental tests for theoretical models-all these themes are highlighted in the present issue.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.

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

Cited by 62 publications

References 92 publications

A Stable Dendritic Growth with Forced Convection: A Test of Theory Using Enthalpy-Based Modeling Methods

A Stable Dendritic Growth with Forced Convection: A Test of Theory Using Enthalpy-Based Modeling Methods

On the Theory of Stable Mode of Dendritic Growth in the Presence of Convective Heat and Mass Transfer Boundary Conditions

From atomistic interfaces to dendritic patterns

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