An Estimation of Thermal Stress Induced by the Freezing Process for Biological Cell Preservation
Thermal stresses in a frozen solution, induced by the freezing process, are related to the cryoinjury of biological cells which are suspended inside a physiological medium for the purpose of preservation. Experimental and analytical results indicate that the circumferential compressive stresses inside the frozen solution are much higher than the radial and axial stresses. The maximum circumferential compressive stress is located at the interface position between the frozen and the unfrozen solution.
In this paper, an estimation of the maximum circumferential compressive stress is presented and is based on the one-dimensional experimental freezing model for simulation of cell freezing preservation taking place in a long cylindrical test tube. The result of the analysis indicates that a decrease of the temperature at the outside surface of the tube results in an increase of the maximum thermal stress in the frozen solution. For freezing preservation, a slow freezing process having a relatively high surface temperature has the benefit of reducing the cryoinjury of biological cells caused by the thermal stress.
KeywordsThermal Stress Dimensionless Time Biological Cell Freezing Process Freeze Solution
- C, C1, C2
latent heat of water freezing
dimensionless parameter defined in Eq. (8)
- K1, K2
constants defined in Eqs. (20) and (21), respectively
length of the tube
heat transfer rate
outside radius of the tube
inside radius of the tube
dimensionless interface position between the ice and water, defined in Eq. (6)
outside surface temperature of the tube
freezing temperature of water
temperature difference (T-Tf)
interface position between the ice and water
linear thermal expansion coefficient
initial strain of the ice
dimensionless time defined in Eq. (7)
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