Enhanced Numerical Modeling of Non-Newtonian Particle-Laden Flows: Insights from the Carreau–Yasuda Model in Circular Tubes

Particle-laden flows in non-Newtonian fluids are encountered in a variety of industrial applications, such as concrete pumping and battery electrode slurry processing, where accurate prediction of particle migration is essential for performance and product quality. This work investigates fully developed suspension flows in circular tubes, combining the shear-induced diffusion framework of Phillips et al. with the Krieger–Dougherty relative viscosity and the Carreau–Yasuda constitutive model. Unlike previous studies that generally rely on Newtonian or simple non-Newtonian rheology models, we employ the Carreau–Yasuda model, a more sophisticated constitutive relation that captures both shear-thinning behavior and Newtonian plateau regimes. By applying nondimensionalization and variable transformations, we reduce the governing coupled differential equations to a system of nonlinear algebraic equations, which allows for efficient computation of both particle concentration and velocity profiles. A systematic parametric study was conducted to evaluate the influence of several factors, including the pressure gradient, average particle concentration, and the five parameters of the Carreau–Yasuda model. Additionally, the migration parameter α=Kc/Kη was considered. The results reveal how the increased rheological complexity of the Carreau–Yasuda model significantly alters the migration dynamics when compared to simpler models. These novel findings have direct implications for optimizing industrial processes involving highly loaded suspensions, offering more accurate predictions of particle behavior under varying flow conditions. For the validation of our findings, experimental data in the literature was used.