Theoretical relationship between the macro-texture and micro-structure in dairy processing revealed by the multi-scale simulation of coupled map lattice

The theoretical relationship between the macroscopic textural quality and microscopic structural quality appearing in the phase inversion processes from fresh cream via whipped cream to butter is revealed by the multi-scale simulation of a coupled map lattice based on the mesoscopic elementary processes of the emulsion interfaces. Using the Young-Laplace equation, we derive the microscopic particle quantities of the size and density of air bubbles and butter grains in an emulsion from the macroscopic rheological quantities of the overrun and viscosity of the emulsion. In doing so, we focus on the size determined by the "tug-of-war" between air bubbles and butter grains via their cohesion pressures and on the density determined by the "costume transformation" of the emulsion molecular complexes (clad particles, e.g., butter grain-clad air bubbles) to their suitable size. Using the obtained microscopic particle quantities, we now propose a microscopic state diagram, the size-density plane, in addition to the previously proposed macroscopic state diagram, the viscosity-overrun plane. These state diagrams reveal that while the two well-known different phase inversion processes at high and low whipping temperatures appear as the two parallel processes of viscosity dominance and overrun dominance in the viscosity-overrun plane, they appear as the two orthogonal processes of isodensity/size dominance and isosize/density dominance in the size-density plane. This theoretical simulation result is significant for the quality design of butter because it demonstrates that differences in macroscopic textural quality can be easily controlled by differences in microscopic structural quality.