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

Abstract

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.

Chromodynamic Lattice Boltzmann Method for the Simulation of Drops, Erythrocytes, and Other Vesicles

“…Accordingly, the latter was taken as an accessible proxy for stability and physical veracity, for membrane area simply must be conserved in all interactions between vesicles, constraining even the most extreme deformation, whilst it can vary significantly when immiscible drops interact. Previous work has validated drop simulations [45]; accordingly we have emphasised vesicles here, but also provided data on equivalent drops tests, for context and to emphasise the ease with which a spectrum of fluid objects emerge from simple differential parameterisation of the method. We might conclude from our reported series of tests, that the cross-sectional area of a vesicle membrane is a practical constant of the motion (but see below), verifying the algorithmic and computational integrity of the enhanced method (questions of quantitative validation of course remain).…”

Continuum Scale Non Newtonian Particle Transport Model for Hæmorheology

“…Very recently, we have developed a single framework, three-dimensional methodology for capturing detailed, particle-scale interactions between neutrally buoyant suspended vesicles (i.e., erythrocytes), using our novel chromodynamics multi-component Lattice Boltzmann method variant [11]. We have previously shown that this same essential model is able to capture detailed hydrodynamic interactions, lubrication effects and ballistic collisions between transported particles, in two dimensional simulations containing O(1000) liquid drops at high volume faction [12]. Current work aims to scale these models up, to allow extraction, through statistical averaging and measuring mechanical dissipation, of relevant transport coefficients, e.g.,…”

“…To address the much greater scales of medical significance, it is, therefore, necessary to develop macro or continuum scale models, which encapsulate an integrated effect of these interactions, without explicitly resolving them. Crucially, these continuum models must be amenable to parametrisation, in the present context using meso-scale information such as that encapsulated in the data of Burgin [12].…”