Simulating phase inversion processes by coupled map lattice: Toward the theoretical design of food texture and quality in dairy processing from fresh cream to butter via whipped cream

Abstract

We present a theoretical model and simulation for the formation dynamics of diverse texture patterns that emerge spontaneously or self-organize during phase inversion processes of fresh cream by mechanical whipping. The results suggest that the model should be applied for theoretically designing the texture and quality of whipped cream and butter products. The modeling complexity in phase inversion processes, from fresh cream via whipped cream to butter, was overcome by using a well-established complex systems approach, the coupled map lattice (CML). The proposed CML consists of a minimal set of procedures (i.e., parameterized nonlinear maps), such as whipping, coalescence, and flocculation, acting on the appropriately coarse-grained field variables, surface energy, cohesive energy, and velocity (flow) of the emulsion defined on a two-dimensional square lattice. In the CML simulations, two well-known and different phase inversion processes are reproduced at high and low whipping temperatures. The overrun and viscosity changes simulated in these processes are at least qualitatively consistent with those observed in experiments. We characterize these processes exhibiting different texture patterns as the viscosity dominance at high whipping temperatures and as the overrun dominance at low whipping temperatures on the viscosity–overrun plane, which is one of the state diagrams.