Scaling laws for the flow of generalized Newtonian suspensions

It has been observed that flow curves (viscosity vs shear rate) of spherical solid inclusions suspended in a generalized Newtonian fluid medium can be rescaled so as to collapse onto the flow curve of the fluid medium. This result is surprising given the range of values and the spatial heterogeneity of local shear rates and viscosity in such systems. We consider such scaling for the cases of shear thinning, Newtonian, and shear-thickening fluid media. Results from experiment and computational modeling are presented that examine the microscopic origins of this scaling behavior. Over a wide range of volume fractions (5–50%), it is shown that the distribution of local shear rates can be collapsed onto a single universal curve. The parameters for rescaling the shear rate distributions can be analytically related to the macroscopic rescaling parameters for the viscosity. As a result of this rescaling capability, one may measure the properties of the fluid medium and predict the macroscopic behavior of the suspension.