A general solution of the problem about local nonequilibrium heat transfer with a moving heat sou... more A general solution of the problem about local nonequilibrium heat transfer with a moving heat source at the planar solidification front is obtained. The steady-state and nonsteady-state regimes of rapid solidification are analyzed. The self-consistent regimes of solidification front motion are found.
Fluid flow decisively influences the heat and mass transport during solidification of melts and c... more Fluid flow decisively influences the heat and mass transport during solidification of melts and consequently the properties of the as-solidified materials. In this work we present investigations on the influence of convection on the non-equilibrium solidification of different undercooled Al-Ni alloy melts. The dendrite growth velocities in Al-Ni melts containerlessly processed by electromagnetic levitation have been measured on Earth and under the conditions of reduced gravity. While under terrestrial conditions strong electromagnetic fields are required for levitation against gravity, the fields necessary to compensate disturbing accelerations under reduced gravity conditions are smaller by orders of magnitude. Consequently, convective fluid flow induced by electromagnetic stirring effects is significantly decreased in experiments performed under reduced gravity. Comparative experiments on congruently melting Al50Ni50 alloys revealed that the dendrite growth velocities measured at ...
We consider the modifi ed Cahn-Hilliard equation for phase separation suggested to account for sp... more We consider the modifi ed Cahn-Hilliard equation for phase separation suggested to account for spinodal decomposition in deeply supercooled binary alloy systems or glasses. This equation contains, as additional term, the second-order time derivative of the concentration multiplied by a positive coefficient $\Tau_d$ (time for relaxation). We consider a numerical approximation scheme based on Fourier spectral method and perform numerical analysis of the scheme. We present results of numerical simulations for three spatial dimensions, and examine the stability and convergence of the scheme.
The European Physical Journal Special Topics, 2020
Hyperbolic-type equations of both phase field and concentration arising from a phase-field model ... more Hyperbolic-type equations of both phase field and concentration arising from a phase-field model for fast phase transformations in binary dilute systems yield in the one-dimension moving frame of reference to the concentration-and phase field governing equations, respectively. These equations have been solved numerically and applied to the case of Si-0.1 at.% As binary alloy [P.K. Galenko et al., Phys. Rev. E 84 , 041143 (2011)]. In this paper, the coupling of the hodograph equation for the interface with the solute diffusion equation leads to an exact analytical solution of the one-point Cauchy problem of an ordinary differential equation in a parametric form. Application of this solution to the case of Si-0.1 at.% As gives (i) the same tendency of concentration variation along dimensionless spatial coordinate (ii) the same values of interface velocity with a very slight difference in the value of concentration for a given undercooling at the interface. Based on the results obtained, the established hodograph-equation confirms again its usefulness to predict, for instance, certain aspects of rapid solidification processes for binary alloys.
The European Physical Journal Special Topics, 2020
In the present work we report results of the model experiments that allow us to study effect of d... more In the present work we report results of the model experiments that allow us to study effect of different cooling rates of samples on relationship for amorphous/crystalline phase in freezed Pd-based samples. For the model experiments Pd 40 Cu 30 Ni 10 P 20 alloy samples were used which are typical bulk metal glasses with a relatively small temperature interval of liquid to glass transition. The main focus of the study was on the effect of cooling rate and glass transition temperature on the microstructure of samples, cooled from the liquid to (semi)amorphous states of the alloy. Ground based experiments were conducted using the multi-zone vacuum furnace MEP-01 situated in the institute of launch complexes (NIISK, Moscow). Composition, structure and thermodynamic properties of the samples were determined by electron probe microanalysis, X-ray diffraction, transmission electron microscopy and differential scanning calorimetry.
We consider a thermo-solutal growth of an anisotropic dendrite in a binary liquid with allowance ... more We consider a thermo-solutal growth of an anisotropic dendrite in a binary liquid with allowance for the convective heat and mass transfer mechanism at the dendrite surface. We obtain a new stability criterion for stable mode of dendritic evolution. Also in this work, a stable relation for the dendrite tip velocity and its tip diameter via the selection theory and undercooling balance is discussed. The undercooling balance and selection criterion allow us to obtain two nonlinear equations determining the crystal tip velocity and its tip diameter as functions of undercooling.
Physica A: Statistical Mechanics and its Applications, 2017
A method based on boundary integral approach to the propagation of curved phase interface in a bi... more A method based on boundary integral approach to the propagation of curved phase interface in a binary non-isothermal mixture is developed. Previously known equations and solutions for thermally controlled growth and needle-like dendrites follow from the obtained boundary integral equations as limiting cases.
International Journal of Heat and Mass Transfer, 2016
Abstract We present an analysis of a free dendrite growing in a binary mixture under non-isotherm... more Abstract We present an analysis of a free dendrite growing in a binary mixture under non-isothermal conditions. The stable growth mode is analyzed through the solvability condition giving the stability criterion for the dendrite tip as a function of the thermal Peclet number, P T , and ratio, W = V / V D , of the dendrite velocity V and solute diffusion speed V D in bulk liquid. We extend previous studies limited to small values of the Peclet numbers, by considering the effect of the anisotropy of surface energy for the needle-like dendrite growing at arbitrary Peclet numbers and under local non-equilibrium solute diffusion described by a hyperbolic type of transport equation. Transitions in growth regimes, namely, from solute diffusion-limited to thermo-solutal regime and, finally, to pure thermally controlled regime of the anisotropic dendrite are derived and revealed. Limiting cases of known criteria for anisotropic dendrite growing at small and high growth Peclet numbers are provided. A comparison with the previously obtained criterion of marginal stability of rapidly growing dendrite is made.
A general solution of the problem about local nonequilibrium heat transfer with a moving heat sou... more A general solution of the problem about local nonequilibrium heat transfer with a moving heat source at the planar solidification front is obtained. The steady-state and nonsteady-state regimes of rapid solidification are analyzed. The self-consistent regimes of solidification front motion are found.
Fluid flow decisively influences the heat and mass transport during solidification of melts and c... more Fluid flow decisively influences the heat and mass transport during solidification of melts and consequently the properties of the as-solidified materials. In this work we present investigations on the influence of convection on the non-equilibrium solidification of different undercooled Al-Ni alloy melts. The dendrite growth velocities in Al-Ni melts containerlessly processed by electromagnetic levitation have been measured on Earth and under the conditions of reduced gravity. While under terrestrial conditions strong electromagnetic fields are required for levitation against gravity, the fields necessary to compensate disturbing accelerations under reduced gravity conditions are smaller by orders of magnitude. Consequently, convective fluid flow induced by electromagnetic stirring effects is significantly decreased in experiments performed under reduced gravity. Comparative experiments on congruently melting Al50Ni50 alloys revealed that the dendrite growth velocities measured at ...
We consider the modifi ed Cahn-Hilliard equation for phase separation suggested to account for sp... more We consider the modifi ed Cahn-Hilliard equation for phase separation suggested to account for spinodal decomposition in deeply supercooled binary alloy systems or glasses. This equation contains, as additional term, the second-order time derivative of the concentration multiplied by a positive coefficient $\Tau_d$ (time for relaxation). We consider a numerical approximation scheme based on Fourier spectral method and perform numerical analysis of the scheme. We present results of numerical simulations for three spatial dimensions, and examine the stability and convergence of the scheme.
The European Physical Journal Special Topics, 2020
Hyperbolic-type equations of both phase field and concentration arising from a phase-field model ... more Hyperbolic-type equations of both phase field and concentration arising from a phase-field model for fast phase transformations in binary dilute systems yield in the one-dimension moving frame of reference to the concentration-and phase field governing equations, respectively. These equations have been solved numerically and applied to the case of Si-0.1 at.% As binary alloy [P.K. Galenko et al., Phys. Rev. E 84 , 041143 (2011)]. In this paper, the coupling of the hodograph equation for the interface with the solute diffusion equation leads to an exact analytical solution of the one-point Cauchy problem of an ordinary differential equation in a parametric form. Application of this solution to the case of Si-0.1 at.% As gives (i) the same tendency of concentration variation along dimensionless spatial coordinate (ii) the same values of interface velocity with a very slight difference in the value of concentration for a given undercooling at the interface. Based on the results obtained, the established hodograph-equation confirms again its usefulness to predict, for instance, certain aspects of rapid solidification processes for binary alloys.
The European Physical Journal Special Topics, 2020
In the present work we report results of the model experiments that allow us to study effect of d... more In the present work we report results of the model experiments that allow us to study effect of different cooling rates of samples on relationship for amorphous/crystalline phase in freezed Pd-based samples. For the model experiments Pd 40 Cu 30 Ni 10 P 20 alloy samples were used which are typical bulk metal glasses with a relatively small temperature interval of liquid to glass transition. The main focus of the study was on the effect of cooling rate and glass transition temperature on the microstructure of samples, cooled from the liquid to (semi)amorphous states of the alloy. Ground based experiments were conducted using the multi-zone vacuum furnace MEP-01 situated in the institute of launch complexes (NIISK, Moscow). Composition, structure and thermodynamic properties of the samples were determined by electron probe microanalysis, X-ray diffraction, transmission electron microscopy and differential scanning calorimetry.
We consider a thermo-solutal growth of an anisotropic dendrite in a binary liquid with allowance ... more We consider a thermo-solutal growth of an anisotropic dendrite in a binary liquid with allowance for the convective heat and mass transfer mechanism at the dendrite surface. We obtain a new stability criterion for stable mode of dendritic evolution. Also in this work, a stable relation for the dendrite tip velocity and its tip diameter via the selection theory and undercooling balance is discussed. The undercooling balance and selection criterion allow us to obtain two nonlinear equations determining the crystal tip velocity and its tip diameter as functions of undercooling.
Physica A: Statistical Mechanics and its Applications, 2017
A method based on boundary integral approach to the propagation of curved phase interface in a bi... more A method based on boundary integral approach to the propagation of curved phase interface in a binary non-isothermal mixture is developed. Previously known equations and solutions for thermally controlled growth and needle-like dendrites follow from the obtained boundary integral equations as limiting cases.
International Journal of Heat and Mass Transfer, 2016
Abstract We present an analysis of a free dendrite growing in a binary mixture under non-isotherm... more Abstract We present an analysis of a free dendrite growing in a binary mixture under non-isothermal conditions. The stable growth mode is analyzed through the solvability condition giving the stability criterion for the dendrite tip as a function of the thermal Peclet number, P T , and ratio, W = V / V D , of the dendrite velocity V and solute diffusion speed V D in bulk liquid. We extend previous studies limited to small values of the Peclet numbers, by considering the effect of the anisotropy of surface energy for the needle-like dendrite growing at arbitrary Peclet numbers and under local non-equilibrium solute diffusion described by a hyperbolic type of transport equation. Transitions in growth regimes, namely, from solute diffusion-limited to thermo-solutal regime and, finally, to pure thermally controlled regime of the anisotropic dendrite are derived and revealed. Limiting cases of known criteria for anisotropic dendrite growing at small and high growth Peclet numbers are provided. A comparison with the previously obtained criterion of marginal stability of rapidly growing dendrite is made.
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