Thermal stresses in a freezing sphere and its application to cryobiology

Thermal stresses in an inwardly solidifying sphere are studied analytically. A closed-form solution is given which accounts for thermal expansion associated with temperature gradients and volume changes associated with phase transition. Consistent with the target application of cryopreservation of biological solutions and tissues the material is modeled as elastic-perfectly plastic. Parametric studies using appropriate material properties and typical cryopreservation protocols suggest that strains associated with phase transition lead to far higher stresses than those associated with thermal expansion, with important implications for cryopreservation procedures.