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This work is focused on the modelling of the shear and normal stresses in fibre suspensions that are subjected to a simple shear flow in the presence of short-range lubrication forces, van der Waals and electrostatic forces, as well as solid friction forces between fibres. All of these forces are weighed by the contact probability. The theory is developed for attractive fibres with van der Waals interaction dominating over electrostatic repulsion. The model predicts a simple Bingham law for both the shear stress and the first normal stress difference, with the apparent shear and normal yield stresses proportional to the second and the third power of the particle volume fraction respectively. The model is applied to the experimental data of Rakatekar et al. (Adv. Mater., vol. 21, 2009, pp. 874-878) and Natale et al. (AIChE J., vol. 60, 2014, pp. 1476-1487) on suspensions of carbon nanotubes dispersed in a Newtonian epoxy resin. It reproduces well the quadratic dependence of the apparent yield stress on the particle volume fraction(πyασ2 for average particle aspect ratios of and 1200, while it underpredicts the power-law exponent for (always predicting σ2 behaviour instead of σ3.2). © 2016 Cambridge University Press.

The motion of an ellipsoidal particle immersed in a flow of a Newtonian fluid was obtained in the pioneering work of Jeffery in 1922. Suspensions of industrial interest usually involve particles with a variety of shapes. Moreover, suspensions composed of rods (a limit case of an ellipsoid) aggregate, leading to clusters with particular shapes that exhibit, when immersed in a flow, an almost rigid motion. In this work, we propose a framework for describing dilute suspensions of rigid particles and derive an expression for calculating the motion of rigid clusters of general shape immersed in a flow of a Newtonian fluid. We show that the cluster’s rotary velocity only depends on a symmetric tensor c with unit trace that can be considered as the appropriate conformation tensor for describing cluster kinematics.

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