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

Abstract

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 coupled map lattice (CML) 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 change" 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.

Figures (8)

• Figure 1: (a) Residual fuctor $f(h)$ and (b) surface tension $\kappa(h)$ of the emulsion at emulsion energy $h$. The red lines represent each plot at high whipping temperature and the blue lines at low whipping temperature. The red dotted lines are drawn at $h=\theta_{H}$, the blue dotted lines at $h=\theta_{L}$, and the green dash-dotted line at $\kappa(h)=\kappa$.
• Figure 2: Curvature change of the emulsion interface during phase inversion. (a) Schematic illustration of an emulsion molecular complex in whipped cream and (b) its interface. (c) Schematic illustration of an emulsion molecular complex in butter and (b) its interface. A&W denotes the air and water phase, and O denotes the oil phase. For ease of illustration, the details of the complex were omitted here, although the oil phase (i.e., MFGs) contains fat droplets and lipid crystals, and MFG membranes exist at the interface.
• Figure 3: (a) Time series of average air bubble size $l_{a}$ at high whipping temperatures, and (b) at low whipping temperatures. The green dash-dotted lines are drawn at the time $t$ when $l_{a}=l_{b}$.
• Figure 4: (a) Semi-log plot of average air bubble size $l_{a}$ versus $t$ at high whipping temperatures, and (b) log-log plot of $l_{a}$ versus $t$ at low whipping temperatures.
• Figure 5: (a) Time series of average butter grain size $l_{b}$ at high whipping temperatures, and (b) at low whipping temperatures.