Kinetics of the intermediate stage of phase transition in batch crystallization

Buyevich, Yu.A.; Mansurov, V. V.

doi:10.1016/0022-0248(90)90112-x

Cited by 125 publications

(100 citation statements)

References 7 publications

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“…His approach only roughly describes the crystallization process because it does not take into account the ocean salinity. The account for the salt displacement by the growing ice and its diffusion in the liquid within Stefan's thermal problem slightly improves the situation (BUYEVICH et al, 2001). However, both the purely thermal and thermal diffusion model with a planar front poorly describe the data of different laboratory and field observations [see, among others, HUPPERT and WORSTER, (1985), WORSTER (1986), ALEXANDROV and MALYGIN (2006a)].…”

Section: Sea Ice Growth With a Mushy Layermentioning

confidence: 99%

“…3 and 4 to study the role of stochastic fluctuations of corresponding parameters on the nonlinear dynamics of crystallization processes). The phase transition zone represents a quasi-equilibrium mushy layer (HILLS et al, 1983;BUYEVICH et al, 2001). Since a relaxation time of the temperature field is far less than characteristic times of the process (a relaxation time of the salinity field or a characteristic time of the motion of the phase transition boundary), the temperature field in the mushy layer (false bottom) is considered as a linear function of the spatial coordinate.…”

Section: Sea Ice Growth With a Mushy Layermentioning

confidence: 99%

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Sea Ice Dynamics Induced by External Stochastic Fluctuations

Alexandrov

Bashkirtseva

Malygin

et al. 2013

Pure Appl. Geophys.

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Abstract-The influence of stochastic fluctuations in the atmosphere and in the ocean caused by different occasional phenomena (noises) on dynamic processes of sea ice growth with a mushy layer is studied. It is shown that atmospheric temperature variances substantially increase the sea ice thickness, whereas dispersion variations of turbulent flows in the ocean to a great extent decrease the ice content produced by false bottom evolution.

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Section: Sea Ice Growth With a Mushy Layermentioning

confidence: 99%

Section: Sea Ice Growth With a Mushy Layermentioning

confidence: 99%

Sea Ice Dynamics Induced by External Stochastic Fluctuations

Alexandrov

Bashkirtseva

Malygin

et al. 2013

Pure Appl. Geophys.

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“…For the sake of simplicity, equations and their approximate analytical solutions will be discussed further separately in each of the regions. The heat-conduction and diffusion equations in the primary mushy layer (ϕ B = ϕ C = 0) can be written in the form [1,10]:…”

Section: The Moving Boundary Problem and Its Analytical Solutionmentioning

confidence: 99%

“…Their rich nonlinear behavior has attracted substantial scientific interest and their ubiquity in fields ranging from metallurgy to geophysics stimulates developing new mathematical approaches (including phase-field models) (see, among others [1][2][3][4][5][6][7][8]). Solidification of single-component and binary solutions within the framework of the classical frontal approach as well as of the mushy layer scenario has intensively been studied by many authors for the last few years.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution for a Problem of Directional Solidification in a Ternary System

Alexandrov

Ivanov

2009

Acta Phys. Pol. A

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“…Recently a mathematical procedure using the steepest descents method of integration was developed for the problem of crystallization in an isolated, initially supercooled system [Buyevich and Mansurov, 1990] …”

Section: Influence Of Kinetics On Convectionmentioning

confidence: 99%

Kinetics of crystal growth in a terrestrial magma ocean

Solomatov¹,

Stevenson²

1993

J. Geophys. Res.

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The problem of crystal sizes is one of the central problems of differentiation of a terrestrial magma ocean and it has been an arbitrary parameter in previous models. The crystal sizes are controlled by kinetics of nucleation and crystal growth in a convective magma ocean. In contrast with crystallization in magma chambers, volcanic lavas, dikes, and other relatively well studied systems, nucleation and crystallization of solid phases occur due to the adiabatic compression in downward moving magma (adiabatic "cooling"). This problem is solved analytically for an arbitrary crystal growth law, using the following assumptions: convection is not influenced by the kinetics, interface kinetics is the rate controlling mechanism of crystal growth, and the adiabatic cooling is sufficiently slow for the asymptotic solution to be valid. The problems of nucleation and crystal growth at constant heat flux from the system and at constant temperature drop rate are shown to be described with similar equations. This allows comparison with numerical and experimental data available for these cases. A good agreement was found. When, during the cooling, the temperature drops below the temperature of the expected solid phase appearance, the subsequent evolution consists of three basic periods: cooling without any nucleation and crystallization, a short time interval of nucleation and initial crystallization (relaxation to equilibrium), and slow crystallization due to crystal growth controlled by quasi-equilibrium cooling. In contrast to previously discussed problems, nucleation is not as important as the crystal growth rate function and the rate of cooling. The physics of this unusual behavior is that both the characteristic nucleation rate and the time interval during which the nucleation takes place are now controlled by a competition between the cooling and crystallization rates. A probable size range for the magma ocean is found to be 10 -2 -1 cm, which is close to the upper bound for the critical crystal size dividing fractional and nonfractional crystallization discussed elsewhere in this issue. Both the volatile content and pressure are important and can influence the estimate by 1-2 orders of magnitude. Different kinds of Ostwald ripening take place in the final stage of the crystal growth. If the surface nucleation is the rate-controlling mechanism of crystal growth at small supercooling, then the Ostwald ripening is negligibly slow. In the case of other mechanisms of crystal gro•vth, the crystal radius can reach the critical value required to start the fractional crystallization. It can happen in the latest stages of the evolution when the crystals do not dissolve completely and the time for the ripenlug is large.

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Kinetics of the intermediate stage of phase transition in batch crystallization

Cited by 125 publications

References 7 publications

Sea Ice Dynamics Induced by External Stochastic Fluctuations

Sea Ice Dynamics Induced by External Stochastic Fluctuations

Analytical Solution for a Problem of Directional Solidification in a Ternary System

Kinetics of crystal growth in a terrestrial magma ocean

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