REVIEW: Fractal-based rheological models: A review focused on waxy oil suspensions and gels

Waxy oil gels exhibit complex rheological behavior, sharing characteristics with colloidal, polymeric, and fat gels. The phenomena of viscoplasticity, viscoelasticity, and thixotropy are manifested due to the dynamics of the fractal microstructure under cooling and shear conditions. Previous studies have developed models to probe these properties, including viscosity, storage modulus, yield stress, critical elastic strain and stress, and structure parameters. The models incorporate fractal characteristics within the theoretical framework. However, a unified approach to fractal rheological models for waxy oils is still lacking. This work aims to comprehensively review three types of fractal models for cluster suspensions and gels: viscosity models, elastoplastic models, and structure parameter models. The essential features of waxy oil rheology and the determination of yield stress are first outlined. Subsequently, models that describe the elastoplastic properties, such as storage modulus and yield stress, are described. Then, the viscosity models for fractal cluster suspensions are revisited, highlighting the occurrence of high correlation and multiple local minima in the regression procedure. Finally, the fractal-based structure parameters that connect the elastoplastic and viscosity models are examined. The review offers a comprehensive understanding of the complex rheological behavior of waxy oils, laying a foundation for future research in this field.