A theoretical model describing the thermodynamics of intracellular ice nucleation is developed for red blood cells as a model biomaterial. Analytical expressions based on current theories of ice nucleation by both homogeneous and heterogeneous nucleation processes are coupled with a thermodynamic model for the loss of intracellular water during freezing. Numerical solutions for both modes of nucleation identify two cooling regions—high cooling rates and low cooling rates—separated by a sharp demarcation zone. The nucleation temperature for high cooling rates is approximately 20° K higher than the nucleation temperature for low cooling rates and is essentially independent of cooling rate in each region. The nucleation temperatures for heterogeneous nucleation are approximately 30° K higher than the nucleation temperatures for homogeneous nucleation in the two regions. For the case of heterogeneous nucleation, it is possible to increase the nucleation temperature by packing of catalysts via the concentration polarization effect. If the cell suspension is allowed to supercool before nucleation occurs in the extracellular medium, the sharp transition from low cooling rates to high cooling rates for heterogeneous nucleation shifts to much lower cooling rates. The dependence of the transition cooling rate on the degree of supercooling has been established for a typical freezing situation.
The Thermodynamics of Intracellular Ice Nucleation in the Freezing of Erythrocytes
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Toscano, W. M., Cravalho, E. G., Silvares, O. M., and Huggins, C. E. (August 1, 1975). "The Thermodynamics of Intracellular Ice Nucleation in the Freezing of Erythrocytes." ASME. J. Heat Transfer. August 1975; 97(3): 326–332. https://doi.org/10.1115/1.3450374
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