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Mueller, S, Llewellin, EW & Mader, HM (2010). The rheology of suspensions of solid particles. Proceedings Of The Royal Society A-mathematical Physical And Engineering Sciences 466(2116): 1201-1228.

Author(s) from Durham


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.