Rotations of elongate rigid particles in slow non-Newtonian flows

In Jeffery's well-known theoretical model each end of the symmetry axis of an isolated rigid prolate ellipsoid embedded in a Newtonian matrix undergoing simple shear flow describes one of an infinite family of accurately closed periodic orbits. The usefulness of this model in relating particle orientation distributions to bulk finite strain is reassessed in the light of recent theoretical and experimental work. This work shows that Jeffery's analysis is readily extended to include any axisymmetric particle shape (with a centre of symmetry), and that small surface irregularities may be neglected. In nonNewtonian media (both power-law and elasticoviscous) particle motions, although still periodic, show a progressive drift through the family of Jeffery orbits. In a secondorder Rivlin—Ericksen fluid the orbital drift estimated for the strain magnitudes and particle axis ratios likely in most tectonites is slight, and leads to negligibly small departures from the predictions of Jeffery's model. More orbital drift is anticipated in powerlaw fluids although Jeffery's model is still likely to yield an acceptable approximation except for very high strains.