Deterministic model for ice cream solidification

This work presents a deterministic model that simulates unaerated ice cream solidification. Some initial ice seeds are introduced at random into a known volume. All the volume, including the initial ice seeds, is discretized into voxels (cubic volume elements). A concentration of sugar is introduced homogeneously into the matrix, i.e. the continuous liquid phase. Voxels on the ice surface are determined using a gaussian-smoothing algorithm. Solidification of the surface voxels is determined by the ice–water–sugar phase diagram; when a voxel solidifies, the sugar is expelled to its neighbours. Once a layer of one voxel in thickness grows over all the microstructure, a diffusion algorithm is applied to rearrange the sugar. The solidification process is repeated until no more voxels solidify. Simulations made using experimental data for initial conditions result in very realistic final microstructures. Different microstructures are obtained when different sugar diffusion rates or initial sugar concentration are used. The proposed model is focused on unaerated ice cream microstructures, but it could also be useful to simulate the solidification of other two-phases systems, such as binary metal alloys.