Large surface deformation due to thermo-mechanical effects during cryopreservation by vitrification – mathematical model and experimental validation

Abstract

This study presents a simplified thermal-fluids (TF) mathematical model to analyze large surface deformations in cryoprotective agents (CPA) during cryopreservation by vitrification. The CPA deforms during vitrification due to material flow caused by the combined effects of thermal gradients within the domain, thermal contraction due to temperature, and exponential increase in the viscosity of the CPA as it is cooled towards glass transition. While it is well understood that vitrification is associated with thermo-mechanical stress, which might lead to structural damage, those large deformations can lead to stress concentration, further intensifying the probability to structural failure. The results of the TF model are experimentally validated by means of cryomacroscopy on a cuvette containing 7.05M dimethyl sulfoxide (DMSO) as a representative CPA. The TF model presented in this study is a simplified version of a previously presented thermo-mechanics (TM) model, where the TM model is set to solve the coupled heat transfer, fluid mechanics and solid mechanics problems, while the TF model omits further deformations in the solid state. It is demonstrated in this study that the TF model alone is sufficient to capture large-body deformations during vitrification. However, the TF model alone cannot be used to estimate mechanical stresses, which become significant only when the deformation rates become so small that the deformed body practically behaves as an amorphous solid. This study demonstrates the high sensitivity of deformation predictions to variation in material properties, chief among which are the variations of density and viscosity with temperature. Finally, this study includes a discussion on the possibility of turning on and off the TF and TM models in respective parts of the domain, in order to solve the multiphysics problem in a computationally cost-effective manner.