A Simple Procedure for Determining Spatial and Transient Variations of Cooling Rate within a Specimen during Cryopreservation: Part 1: Analysis

Abstract

The cryopreservation of biological materials may involve cooling continuously in the liquid state (as in vitrification) or nucleation of ice, followed by thermal equilibration at a selected sub-zero temperature and subsequent cooling in the solid phase. Both of these processes may be approximated by a single-phase heat transport analysis, the most critical parameter of which, for biological survival, is the cooling rate. The Fourier series solution for the cooling rate in a specimen is presented for single-phase heat transfer in cartesian, cylindrical and spherical coordinates: extensive tables of the series constants and of the roots of the transcendental equations have been computed that include the cases of most relevance to cryopreservation. In particular, data are provided to calculate the cooling rate at process states close to the initial conditions, that is at small Fourier numbers. Graphical results of the analysis are given in Part 2.

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