A constitutive approach for studying concentrated suspensions of rigid fibers in a non ‐ Newtonian Ellis fluid

Abstract

A constitutive model for a semi-concentrated suspension of rigid fibers in a non-Newtonian fluid is derived in the present study. This work is extended from a previous work by Dinh and Armstrong which counted rigid fibers suspended in a Newtonian fluid. To investigate the effect of the sheardependent suspending fluid on the shear viscosity of suspension, the Ellis fluid is assumed to model such a non-linear matrix. It is shown that the present derivation, via a cell model, gives an analytic form to calculate the drag coefficient of fibers and to illustrate the influence of material parameters of matrix fluid. The resulting equation gives the bulk stress in terms of an integral over a fourth-order orientation vector, e, similar to the expression of Doi and Edwards for dense macromolecular fluid. For the purpose of evaluation, the present model attempts to predict the rheological behavior in the inception of flow, steady simple shear flow and stress-growth experiments.

The effect of shear-thinning behaviour on rod orientation in filled fluids

“…Dinh & Armstrong (1984) also used the Batchelor approach to develop a rheological equation of state to describe non-dilute suspensions of fibres in Newtonian solvents undergoing homogeneous extensional and shear flows. This work was then extended by Wang & Cheau (1991) who proposed a constitutive model for semi-concentrated suspensions of rigid fibres in an Ellis fluid. However, in their model derivation, it was assumed that the outer boundary condition for the axial velocity isγ D/2 (γ and D/2 being respectively the shear rate and particle radius), which appears to be unphysical.…”

“…However, in their model derivation, it was assumed that the outer boundary condition for the axial velocity isγ D/2 (γ and D/2 being respectively the shear rate and particle radius), which appears to be unphysical. In addition, Wang & Cheau (1991) did not take into account the dependency of particle orientation on the axial velocity. Souloumiac & Vincent (1998) improved the original work of Batchelor (1971) and Goddard (1976a) by considering rod orientation and their result is applicable to homogeneous flow, especially to shear flow.…”