Mathematical modeling of surface deformation during vitrification.

Mathematical modeling of surface deformation during cryopreservation by vitrification is presented in this study. The specific problem under consideration is of a cryoprotective agent (CPA) solution vitrifying in a vial, following previously obtained cryomacroscopy observations. A multiphysics solution is proposed in this study, combining coupled effects associated with heat transfer, fluid mechanics, and solid mechanics. Consistent with previous investigations, this study demonstrates that surface deformation is the result of material flow, which is the combined outcome of temperature gradients developed during the inward cooling process, the tendency of the material to change its volume with temperature, and the exponential increase in material viscosity with the decreasing temperature. During this process, the behavior of the CPA changes from liquid to a solid-like amorphous material, where the arrested flow in the vitrified state results in mechanical stresses. Results of this study show a good qualitative agreement of surface deformation with previously obtained experimental data, and support prior investigations to explain fracture tendencies propagating from the deformed surface. Results of this study also highlight the effect of heat convection in the CPA at the early stage of cooling.