Fresh dairy cream (O/W emulsion) is a naturally complex food consisting of multi-component, multi-phase, and multi-scale materials and interfaces that undergoes a phase inversion phenomenon of turning into butter (W/O emulsion) via whipped cream by mechanical whipping. Thus, there are high technical barriers to the modeling and simulation of the phase inversion, such as consistent approximation in macroscopic equations and massive computation in microscopic simulations. This modeling complexity inherent to food can be easily addressed by employing a complex systems approach, Coupled Map Lattice (CML), which flexibly describes elementary processes by parameterized nonlinear maps. CML has successfully reproduced various complex phenomena such as nucleate to film boiling, soft to hard turbulence, stratus to cumulonimbus cloud formation, and spiral arm to stellar and substellar companion formation [1, 2].

We have proposed a CML for understanding the formation and self-organization of diverse food texture patterns appearing in the phase inversion processes [3]. The proposed CML has three field variables, surface energy, cohesive energy, and velocity (flow) of the virtual emulsion defined on a two-dimensional square lattice, and is constructed by the three simple procedures (i.e., nonlinear maps with cooking parameters), whipping, coalescence, and flocculation, acting on the field variables. In the simulations, two different phase inversion processes are reproduced at high and low whipping temperatures. The overrun and viscosity changes in these processes are at least qualitatively 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, a macroscopic state diagram, as the viscosity dominance at high whipping temperatures and the overrun dominance at low whipping temperatures, while on the particle size-density plane, a microscopic state diagram, as the isodensity size dominance and the isosize density dominance, respectively.

The butters obtained at high whipping temperatures are large size and low density and thus low overrun and viscosity, so to say, have a soft and creamy texture, while those obtained at low whipping temperatures are small size and high density and thus high overrun and viscosity, so to say, have a hard and fluffy texture. In the presentation, we will explore the theoretical design of a new texture (fluffy and creamy with moderate firmness) by controlling the cooking parameters of the CML procedures based on this relationship between the macroscopic texture and microscopic structure.

[1] E. Nozawa, Physica D 405 (2020) 132377.

[2] E. Nozawa, Prog. Theor. Exp. Phys. 2023 (6) (2023) 063A02.

[3] E. Nozawa and T. Deguchi, J. Chem. Phys. 162 (6) (2025) 064902