Quantitative phase field modeling of planar ice growth in sucrose solutions

We extend existing phase-field simulation methods to develop an accurate method for simulating ice growth in aqueous solutions. This method is then applied to model ice growth in sucrose-water solutions. Starting with a model for the free energy of the sucrose solution in coexistence with ice, we describe its equilibrium thermodynamics. This results in a phase diagram for solutions of sucrose in water that agrees well with experimental data. We show how this free energy function can be introduced into a phase-field model to dynamically generate the experimentally observed equilibrium state. We then connect the model's non-equilibrium dynamics to irreversible thermodynamics by defining an entropy functional that includes the gradients of the phase field and concentration variables. We verify the thermodynamic consistency of our phase-field model by showing that the non-equilibrium dynamics drive the system to the correct equilibrium state under both isothermal and non-isothermal conditions. We also perform a sensitivity analysis on the parameters of the model to better understand their importance in determining the rate of ice crystal growth. We then calculate the velocity of the ice crystallization front by fitting a power law to the time dependence of the ice fraction. The results are of the same order of magnitude as experimentally measured crystallization front velocities for systems that satisfy the requirements for planar crystal growth.