Building phase field simulations to investigate cryoprotectant properties

The purpose of this research was to develop a method for simulating the effectiveness of cryoprotectants. To do this we built upon an existing phase field simulation from the literature. We first performed an analysis of the equilibrium thermodynamics described by the model’s free energy function. This was done by constructing state diagrams for both sucrose and trehalose in water solutions. We then showed how this free energy function can be introduced into the phase field model to preserve the correct equilibrium state. We then connect the model’s non-equilibrium dynamics to irreversible thermodynamics. To do this we use the definition of the entropy functional that only includes gradient terms in the phase field variable and concentration not in the temperature. This ensures the model is consistent with the second law of thermodynamics. The results of the phase field simulation are presented in two parts. The first verifies the model by showing that the non-equilibrium dynamics drives the system to the correct equilibrium state. The geometry of the ice crystals and the effects of varying the number of grid points used to resolve the system are also discussed. We also performed a sensitivity analysis on parameters important to the rate of ice crystal growth, to better understand what combination of parameters we would expect from a good cryoprotectant. We then compared the effectiveness of sucrose and trehalose at inhibiting ice crystal growth. This was done by measuring the amount of ice crystal grown with each solute under the same conditions and by comparing the velocities of the ice crystallization front. The velocities were calculated by fitting a power law to the ice fraction of the system over time. We observed that in the trehalose solution the ice grew more slowly than in the sucrose solution. This has been observed experimentally in the literature.