The shape of dendritic tips

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This article is devoted to the study of the tip shape of dendritic crystals grown from a supercooled liquid. The recently developed theory (Alexandrov & Galenko 2020 Phil. Trans. R. Soc. A 378 , 20190243. ( doi:10.1098/rsta.2019.0243 )), which defines the shape function of dendrites, was tested against computational simulations and experimental data. For a detailed comparison, we performed calculations using two computational methods (phase-field and enthalpy-based methods), and also made a comparison with experimental data from various research groups. As a result, it is shown that the recently found shape function describes the tip region of dendritic crystals (at the crystal vertex and some distance from it) well. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

Section: The Shape Of Dendritic Tips: Theorymentioning

confidence: 99%

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

Alexandrov

Toropova

Титова

et al. 2021

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“…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. The study of interface motion in fast phase transitions is continued in [20], where a new hodograph equation describing the motion by mean interface curvature, the relationship 'velocity-Gibbs free energy', the Klein-Gordon and Born-Infeld equations related to the anisotropic propagation of various interfaces are derived.…”

Section: The General Content Of the Issuementioning

confidence: 99%

Transport phenomena in complex systems (part 1)

Alexandrov

Zubarev

2021

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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)’.

“…A comparison of the theory given by equation (3.3) with simulation results obtained for the two coupling schemes (namely, variable viscosity model and the drag force model) is shown in figure 4. Because the shape of the dendrite deviates from parabola near the dendrite tip due to anisotropic effects [16,28,29], the dendrite radius R is obtained by a fit in a region roughly one radius away from the tip and from the bottom (for the details of deviations of the dendrite surface from the parabolic law behind the dendrite tip see the work [30]).…”

Section: Numerical Simulationsmentioning

confidence: 99%

Thin interface limit of the double-sided phase-field model with convection

Subhedar

Galenko

Varnik

2020

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The thin interface limit of the phase-field model is extended to include transport via melt convection. A double-sided model (equal diffusivity in liquid and solid phases) is considered for the present analysis. For the coupling between phase-field and Navier–Stokes equations, two commonly used schemes are investigated using a matched asymptotic analysis: (i) variable viscosity and (ii) drag force model. While for the variable viscosity model, the existence of a thin interface limit can be shown up to the second order in the expansion parameter, difficulties arise in satisfying no-slip boundary condition at this order for the drag force model. Nevertheless, detailed numerical simulations in two dimensions show practically no difference in dendritic growth profiles in the presence of forced melt flow obtained for the two coupling schemes. This suggests that both approaches can be used for the purpose of numerical simulations. Simulation results are also compared to analytic theory, showing excellent agreement for weak flow. Deviations at higher fluid velocities are discussed in terms of the underlying theoretical assumptions. This article is part of the theme issue ‘Patterns in soft and biological matters’.