)) yielding three rheometric parameters: consistency K (cognate with viscosity); flow index n (a measure of shear-thinning); yield stress τ 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:10.101690023-X)) with the maximum packing fraction φ m as the only fitted parameter. We derive empirical relationships for φ m and n as a function of average particle aspect ratio r p and for τ 0 as a function of φ m and a fitting parameter τ * . These relationships can be used to predict the rheology of suspensions of prolate particles from measured φ 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 φ increases.

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