Ice cream is a four phase system comprising ice, fat, air and an aqueous phase. We would like to determine under what conditions ice cream will flow at low temperatures, approximately -5°C to -25°C.
For a given ice cream formulation and temperature we can establish the viscosity of the continuous phase and the phase volume of solid dispersed phase. (Note that for a given formulation, changes in temperature will change the concentration of the continuous phase and the phase volume of ice.) From the above, we wish to calculate the bulk ice cream viscosity, which may contain a given phase volume or air. This system is then held in some sort of container for a given time. A pressure is applied (possible by only gravity and the weight of the system) and the ice cream is extruded through an orifice. We want to know what the flow rate is through the orifice.
In other words, we would like to model the flow rate of the material from the orifice as a function of viscosity of continuous phase, phase volume of solid phase, ratio of these two, phase volume of air, applied pressure and orifice size. Due to the complexity of this problem, achieving a full mathematical description may not be realistic. An understanding of the relative importance of the factors would be a useful first step.