The shape of dendritic tips: a test of theory with computations and experiments

Alexandrov, Dmitri V.; Toropova, Liubov V.; Титова, Э. А.; Kao, Anne; Demange, Gilles; Galenko, Peter; Rettenmayr, Markus

doi:10.1098/rsta.2020.0326

Cited by 25 publications

(17 citation statements)

References 40 publications

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“…The main conclusions following from this theory are the solvability and selection criteria, which are presented and discussed in detail for different solidification conditions, including forced convection and local non-equilibrium processes described by hyperbolic equations for dissolved impurities. This theory is continued in the next paper [18], where the influence of a nonlinear transport process on the shape of dendritic crystals forming in various growth conditions in undercooled melts is presented. The analytically obtained dendritic shapes [19] are compared with experiments and computations carried out via the enthalpy and phase-field methods.…”

Section: The General Content Of the Issuementioning

confidence: 95%

Transport phenomena in complex systems (part 1)

Alexandrov

Zubarev

2021

Phil. Trans. R. Soc. A.

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The issue, in two parts, is devoted to theoretical, computational and experimental studies of transport phenomena in various complex systems (in porous and composite media; systems with physical and chemical reactions and phase and structural transformations; in biological tissues and materials). Various types of these phenomena (heat and mass transfer; hydrodynamic and rheological effects; electromagnetic field propagation) are considered. Anomalous, relaxation and nonlinear transport, as well as transport induced by the impact of external fields and noise, is the focus of this issue. Modern methods of computational modelling, statistical physics and hydrodynamics, nonlinear dynamics and experimental methods are presented and discussed. Special attention is paid to transport phenomena in biological systems (such as haemodynamics in stenosed and thrombosed blood vessels magneto-induced heat generation and propagation in biological tissues, and anomalous transport in living cells) and to the development of a scientific background for progressive methods in cancer, heart attack and insult therapy (magnetic hyperthermia for cancer therapy, magnetically induced circulation flow in thrombosed blood vessels and non-contact determination of the local rate of blood flow in coronary arteries). The present issue includes works on the phenomenological study of transport processes, the derivation of a macroscopic governing equation on the basis of the analysis of a complicated internal reaction and the microscopic determination of macroscopic characteristics of the studied systems. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

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Section: The General Content Of the Issuementioning

confidence: 95%

Transport phenomena in complex systems (part 1)

Alexandrov

Zubarev

2021

Phil. Trans. R. Soc. A.

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“…So, for example, when describing dendritic tip shapes, the authors of Refs. [35,36] used the exponential sewing functions. On the other hand, when describing dynamics of intracellular clusters of nanoparticles, the authors of Ref.…”

Section: Sewing Together Undercooling Balancesmentioning

confidence: 99%

“…An important point is that these equations should describe both undercooling limits: low ∆θ (convective mechanism prevails) and moderate ∆θ (conductive mechanism prevails). Note that a behaviour of ρ(∆θ) and V(∆θ) will substantially depend on the sewing functions B cond (∆θ) and B conv (∆θ), which can be chosen in different ways [35][36][37]48,49]. The essential conditions are only those B cond (∆θ) → 0 for ∆θ → 0 and B conv (∆θ) → 0 for ∆θ ∆θ c .…”

Section: Sewing Together Selection Criteriamentioning

confidence: 99%

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

2022

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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 Al24Ge76 and Ti45Al55 undercooled melts.

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“…The fundamental understanding of dendrite growth relies on the pioneering works of Ivantsov [10] which latches the Péclet number to the thermodynamical driving force, and the microscopic solvablity theory [11,12,12] which provides a selection criterion for the charactertistic wavelength of the tip [13][14][15][16][17][18][19][20][21][22]. As for secondary branching, the conventional theory [23][24][25][26] postulates that side-branches stem from selective (thermal) noise amplification close to the tip.…”

Section: Introductionmentioning

confidence: 99%

Induced side-branching in smooth and faceted dendrites: theory and Phase-Field simulations

Demange,

Patte,

Zapolsky

2021

Preprint

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The present work is devoted to the phenomenon of induced side branching stemming from the disruption of free dendrite growth. Therein, we postulate that the secondary branching instability can be triggered by the departure of the morphology of the dendrite from its steady state shape. Thence, the instability results from the thermodynamic trade-off between non monotonic variations of interface temperature, surface energy, kinetic anisotropy and interface velocity within the Gibbs Thomson equation. For purposes of illustration, the toy model of capillary anisotropy modulation is prospected both analytically and numerically by means of phase field simulations. It is evidenced that side branching can befall both smooth and faceted dendrites, at a normal angle from the front tip which is specific to the nature of the capillary anisotropy shift applied.

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The shape of dendritic tips: a test of theory with computations and experiments

Cited by 25 publications

References 40 publications

Transport phenomena in complex systems (part 1)

Transport phenomena in complex systems (part 1)

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

Induced side-branching in smooth and faceted dendrites: theory and Phase-Field simulations

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