Parameter Estimation for Rheology Models in Emulsions

Abstract

Emulsions, which are oil-water mixtures, are ubiquitous in the food industry, and precise control of their flow and deformation (rheological properties like the storage modulus G'(ω) and the loss modulus G''(ω)) is critical. However, establishing a connection between the microscopic droplet characteristics of emulsions and their macroscopic viscoelastic behavior remains a major challenge. In this thesis, we propose a framework for estimating rheological model parameters of emulsions to address this issue. Our method combines comprehensive rheological testing of mayonnaise-type emulsions with two types of theoretical models: (1) frequency sweep viscoelastic models, including the classical Palierne model, Maxwell model, Kelvin-Voigt model, and combined models; (2) a energy minimization elasticity model (EEI), which accounts for entropic, electrostatic, and interfacial interactions between droplets. Model parameters were optimized via numerical algorithms to ensure that simulated storage and loss modulus spectra closely match experimental measurements. Results indicate that classical frequency sweep models alone cannot achieve optimal fitting, while a combined approach using Kelvin-Voigt and multi-mode Maxwell models achieves consistency with measured data. Additionally, the two adjustable parameters in the EEI model successfully capture droplet rearrangement and interfacial tension effects, accurately reproducing the low frequency elastic plateau. Notably, each emulsion formulation produces a distinct parameter set, highlighting how variations in droplet size, volume fraction, or surfactant chemistry translate into different rheological profiles. By quantitatively correlating microstructure with macroscopic rheology, this study provides insights into emulsion science and offers a theoretical foundation for designing emulsions with customized texture and stability.