We consider the flow of a dilute suspension of equisized solid spheres in a viscous fluid. The viscosity of such a suspension is dependent on the volume fraction, c, of solid particles. If the particles are perfectly smooth, then solid spheres will not come into contact, because lubrication forces resist their approach. In this paper, however, we consider particles with microscopic surface asperities such that they are able to make contact. For straining motions we calculate the O(c 2 ) coefficient of the resultant viscosity, due to pairwise interactions. For shearing motions (for which the viscosity is undetermined because of closed orbits on which the probability distribution is unknown) we calculate the c 2 contribution to the normal stresses N 1 and N 2 . The viscosity in strain is shown to be slightly lower than that for perfectly smooth spheres, though the increase in the O(c) term caused by the increased effective radius due to surface asperities will counteract this decrease. The viscosity increases with increasing contact friction coefficient. The normal stresses N 1 and N 2 are zero if the surface roughness height is less than a critical value of 2.11 × 10 −4 times the particle radius, and then become negative as the roughness height is increased above this value. N 1 is larger in magnitude than N 2 .This file is not a faithful reproduction of the paper printed in JFM; rather, errors which were discovered after publication have been corrected here in red.

We develop a tensorial constitutive model for dense, shear-thickening particle suspensions subjected to time-dependent flow. Our model combines a recently proposed evolution equation for the suspension microstructure in rate-independent materials with ideas developed previously to explain the steady flow of shear-thickening ones, whereby friction proliferates among compressive contacts at large particle stresses. We apply our model to shear reversal, and find good qualitative agreement with particle-level, discreteelement simulations whose results we also present.

We develop a model for the microstructure and the stress, in dense suspensions of non-Brownian, perfectly smooth spheres at vanishing particle Reynolds number. These quantities are defined in terms of the second-order moment a of the distribution function of the orientation unit vector between hydro-dynamically interacting particles. We show, from first principles, that the evolution equation of a contains a source term, that accounts for the association and the dissociation of interacting particle pairs. This term provides a microscopic explanation for typical non-Newtonian behaviour, observed in experiments in the literature, including normal stress differences in steady shear flow, as well as time-dependent stress after abruptly reversed shear flow and during oscillating shear flow.

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Shear thinning is fundamental to a broad range of particle suspensions, both in nature and in industrial applications. Yet the mechanisms governing it remain unclear. In particular, the distinct, and often competing, roles of the interparticle, particle-fluid interactions and the particle surface morphology need clarity. By using non-Brownian silica particles with different morphology, surface functional groups and suspending media, here we reveal two different shear thinning mechanisms, controlled either by frictional or adhesion forces between particles. Smooth glass sphere suspensions in a polar medium (glycerol), where particles interact strongly with the solvent, showed no shear thinning even at high volume fractions (φ≥0.5), while rough silica particles, with similar size distribution, induced shear thinning behaviour at φ values of 0.25 and above. The latter is attributed to the increased frictional contacts in rough and irregular particles. Considering surface irregularity as elastically deformable asperities enabled us to estimate the critical load above which two neighbouring rough particles experience frictional contacts giving rise to shear thinning. In contrast, in a non-polar (mineral oil) solvent, with which the particles do not interact strongly, both glass spheres and the rough silicas showed a pronounced shear thinning response and yield stress behaviour at volume fractions as low as 2% v/v. The rheology of these suspensions is dictated by the adhesion forces between the particles that lead to the formation of large agglomerates, which breakdown under increasing shear. The evolution of the sheared suspensions microstructure was captured using an optical shearing cell, which also enabled us to quantify the particle agglomeration characteristics using an aggregation index. To demonstrate the generality of our approach, we modified the surface chemistry of the glass spheres by introducing hydrophobic groups (e.g. a fluorosilane or palmitic acid) to inhibit inter-particle interactions and improve the dispersion of the otherwise inherently hydrophilic glass spheres in mineral oil; as expected, this suppressed the shear thinning behaviour of the suspensions. The present results clearly elucidate alternative design routes to controlling suspension rheology, whether to promote or suppress shear thinning, offering new insights for the manufacturing and manipulation of complex particle suspensions.