Enhancing non-newtonian fluid modeling: A novel extension of the cross flow curve model

A number of viscosity and flow curve models can be used to numerically investigate the non-Newtonian behavior of fluids. Although particle size, grain size distribution and concentration play a crucial role in determining the viscosity and flow behavior of suspensions and colloidal systems, they are either ignored or considered indirectly in almost all models. We present a mathematical extension of the widely used Cross flow curve model to account for the effect of concentration and particle size in modeling viscosity and flow curves. In particular, this study takes into account a variable total number of individual particles in unit volume, which is assumed to be constant in other models. The proposed extension allows the flow curve to model suspensions that are typically shear-thinning but can also be Newtonian, or shear-thickening for at different shear rates and concentrations. These considerations provide insight into studying and designing suspensions, colloidal systems, and other complex fluid–solid interactions.