A novel method for precise determination of maximum particle loading fraction in highly concentrated suspensions

Hypothesis: Accurately predicting the maximum particle loading fraction (phi max) of a suspension remains a significant challenge in both theoretical modeling and industrial applications. Experiments: We present a novel method that surpasses existing approaches by precisely determining phi max through predicting the general suspension viscosity at a constant shear rate as a function of particle volume fraction. Our approach leverages boundary and initial conditions to pinpoint phi max with precision. Findings: The proposed model flawlessly captures viscosity behavior across the entire range of volume fractions without pre-assumptions or limitations, showcasing its remarkable versatility. We validate the efficacy of our method by comparing its predictions with established theoretical models and diverse experimental data for various suspensions, including nanofluids and yield stress fluids, as reported in the literature. This extends to the evaluation of crucial parameters related to phi max within existing suspension viscosity models. Beyond its immediate applications, this approach opens avenues for exploring relationships between phi max and other suspension properties, potentially leading to broader advancements in understanding or manipulating suspension rheological behavior in material science.