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Foundations of modeling in cryobiology|III: Inward solidification of a ternary solution towards a permeable spherical cell in the dilute limit

Published

Author(s)

Daniel M. Anderson, James Benson, Anthony J. Kearsley

Abstract

In the previous two manuscripts we outlined the general theory of heat and mass transport in a cell-liquid-ice system with general boundaries and nonideal and nondilute assumptions. Here we simplify the models considerably by presenting a reduction to a spherically symmetric system|a spherical cell with an encroaching spherical ice front. We also reduce to linear approximations of the nonideal nondilute models, essentially assuming dilute and ideal conditions. We derive the resulting nondimensional combined heat and mass transport model for a ternary solution and present numerical solutions. We include an analysis of the effects of varying some nondimensional parameters on rates of ice growth with comments on the necessity of models that account for spatially varying quantities in cryobiology.
Citation
Cryobiology

Keywords

Gibbs Free Energy, partition coeffcient, density, diffusion, chemical potential gradient

Citation

Anderson, D. , Benson, J. and Kearsley, A. (2019), Foundations of modeling in cryobiology|III: Inward solidification of a ternary solution towards a permeable spherical cell in the dilute limit, Cryobiology, [online], https://doi.org/10.1016/j.cryobiol.2019.09.013 (Accessed June 18, 2024)

Issues

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Created October 8, 2019, Updated May 17, 2020