Development of explicit and constitutive lattice-Boltzmann models for food product rheology

Emulsions are found throughout various industries including oil extraction, biological materials, and food products such as milk, condiments, and spreads. The study of their rheology is therefore important due to its impact on manufacturing efficiency and end product desirability. A key rheological measure is the emulsion viscosity, the fluid’s resistance to flow, which affects the power required in production as well as the taste and texture. An emulsion’s viscosity displays complex behaviour due to the droplet interfaces and interactions. Similarly, the sheared self-diffusion coefficient measures the amount of movement the droplets exhibit, due to the interactions between droplets. The presented mesoscopic lattice-Boltzmann models allow for these macroscopic properties to emerge from the simulations due to the explicit modelling of the droplets. A continuous surface force is applied to the lattice fluids to model droplet interfaces. The model is implemented in such a way as to allow the simulation of hundreds of droplets with limited computing power. The model is initially applied to a pipe flow, with the development of a pressure boundary condition. Boundary effects from the solid walls require their removal, using Lees-Edwards boundary conditions to represent bulk flow in a sheared system. The boundary conditions are extended to the multi-component flow, which allowed simulations to provide results for various emulsion systems with varying droplet concentrations, surface tensions, viscosity ratios, and shear rates. Trends and results from experimental and theoretical literature are recovered and constitutive models of emulsion viscosity have been evaluated. The agreement of these two dimensional lattice-Boltzmann models with three dimensional experimental results shows the usefulness of the method. The structure of the droplets and clustering behaviour they exhibit are examined and compared to solid particle suspension literature. Finally, the model is used in exploratory simulations to examine the effect of droplet bidispersity on the macroscopic properties; the witnessed effect agrees well with solid suspension literature. This mesoscopic model will allow for phenomenon on this scale to be more easily studied and may provide more accurate information for multi-scale analysis.