and can be solved readily, with c p as the heat capacity of the solution. The missing constraint to determine the evolution of the freezing process in the presence of ice lies at the micro-scale, where one may characterize freezing as the process of nucleation and growth of ice crystals. The kinetics of nucleation and of growth, expressed by the corresponding rates of nucleation J, and of crystal growth, govern the rate of change of the ice mass. As discussed earlier, one commonly expresses these rates as a power law of the thermodynamic driving force (T eq -T ), which is the difference between the temperature of the formulation inside the vial and the equilibrium freezing temperature, T eq . The equilibrium freezing temperature is governed purely by thermodynamics and depends on the composition of the formulation. It may be expressed using a constitutive equation, e.g., the widely applied law derived by Blagden: 42