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Numerical solution of inward solidification of a dilute ternary solution towards a semi-permeable spherical cell



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


We study a free-boundary problem arising in the cryopreservation of a biological cell. In particular, we examine a spherically-symmetric model of a biological cell separated by a ternary fluid mixture from an encroaching solid-liquid interface. The cell and liquid regions have associated with them intracellular and extracellular salts, respectively, that do not cross the cell membrane. The liquid surrounding the cell contains another solute - the cryoprotective agent - (CPA) commonly used in cryopreservation protocols. The cell membrane is permeable to both water and the CPA. As cooling and solidification proceed the extracellular chemical environment evolves and leads to mass transport across the cell membrane. Consequently, both the solidification front and the cell membrane are free boundaries whose dynamics are coupled through transport processes in the solid, liquid and cell regions. We describe a numerical procedure to solve this coupled free-boundary problem based on a domain transformation and method of lines approach. We also investigate how the thermal and chemical states inside the cell are influenced by different cooling protocols at the external boundary.
Journal of Computational Physics
ISSN 0025-5564


Cryobiology, Transport Processes, Solid-Liquid Interface, Semi-permeable Cell Membrane, Free-Boundary Problem


Anderson, D. , Benson, J. and Kearsley, A. (2019), Numerical solution of inward solidification of a dilute ternary solution towards a semi-permeable spherical cell, Journal of Computational Physics, [online], (Accessed July 24, 2024)


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Created September 30, 2019, Updated October 12, 2021