A NEW CONSTITUTIVE MODEL FOR FIBER SUSPENSIONS - FLOW PAST A SPHERE

A new phenomenological constitutive equation for homogeneous suspensions of macrosized fibres is proposed. In the model, the local averaged orientation of the fibres is represented by a director field, which evolves in time in a manner similar to the rotation of a prolate spheroid. The stress is linear in the strain rate, but the viscosity is a fourth-order tensor that is directly related to the director field. In the limit of low-volume fractions of fibres, the model reduces properly to the leading terms of the constitutive equation for dilute suspensions of spheroids. The model has three parameters: the aspect ratio R of the fibres, the volume fraction PHI, and ALPHA, which plays the role of the maximum-volume fraction of the fibres. Experimental shear data are used to estimate the parameter ALPHA, and the resulting model is used in a boundary-element program to study the flow past a sphere placed at the centre line of a cylinder for the whole range of volume fractions from 0.01 to near maximum volume fraction. The agreement with experimental data from Milliken et al. [1] is good.