The rheology of suspensions of solid particles

We present data for the rheology of suspensions of monodisperse particles of varying aspect ratio, from oblate to prolate, and covering particle volume fractions phi from dilute to highly concentrated. Rheology is characterized by. tting the experimental data to the model of Herschel & Bulkley (Herschel & Bulkley 1926 Kolloid Z. 39, 291-300 (doi: 10.1007/BF01432034)) yielding three rheometric parameters: consistency K (cognate with viscosity); flow index n (a measure of shear-thinning); yield stress tau(0). The consistency K of suspensions of particles of arbitrary aspect ratio can be accurately predicted by the model of Maron & Pierce (Maron & Pierce 1956 J. Colloid Sci. 11, 80-95 (doi: 10.1016/0095-8522(56)90023-X)) with the maximum packing fraction phi(m) as the only fitted parameter. We derive empirical relationships for phi(m) and n as a function of average particle aspect ratio r(p) and for tau(0) as a function of fm and a fitting parameter tau*. These relationships can be used to predict the rheology of suspensions of prolate particles from measured phi and r(p). By recasting our data in terms of the Einstein coefficient, we relate our rheological observations to the underlying particle motions via Jeffery's (Jeffery 1922 Proc. R. Soc. Lond. A 102, 161-179 (doi: 10.1098/rspa. 1922.0078)) theory. We extend Jeffery's work to calculate, numerically, the Einstein coefficient for a suspension of many, initially randomly oriented particles. This provides a physical, microstructural explanation of our observations, including transient oscillations seen during run start-up and changes of rheological regime as phi increases.