Abstract
Fresh cream is a multi-component, multi-phase and multi-scale emulsion1). Thus, there are high technical barriers to modeling and simulating the phase inversion from fresh cream via whipped cream to butter, such as consistent approximation in macroscopic equations and massive computation in microscopic simulations. These barriers are overcome by using a well-established complex systems approach, coupled map lattice2) (CML). CML has successfully reproduced various complex phenomena such as nucleate to film boiling3), soft to hard turbulence4), stratus to cumulonimbus cloud formation5), and spiral arm to stellar gas clump formation6, 7). We shall present in detail the modeling and simulation of the CML for the phase inversion of fresh cream8). The modeling follows the general method of CML construction2): the introduction of a lattice, the assignment of field variables, and the formulation of procedures. (1) Consider a relatively flat container filled with an emulsion. Introduce a two-dimensional square lattice as we view the emulsion from above. (2) Consider the physical and chemical state of the emulsion. Assign to each lattice point the surface energy, cohesive energy, and velocity (flow) of the emulsion. (3) Consider only important elementary processes of physical and chemical changes of the emulsion in the phase inversion. Formulate the whipping, coalescence, and flocculation procedures. In the simulations, two well-known and different phase inversion processes are reproduced at high and low whipping temperatures (WTs). The overrun and viscosity changes in these processes are consistent with
those in experiments. The two processes give rise to distinctive spatial patterns of overrun (surface energy) and viscosity (cohesive energy), and are characterized on the viscosity-overrun plane which is one of the state diagrams, as the viscosity dominance at high WT and the overrun dominance at low WT, respectively. The butters in the two processes have different textures.
