Particulate Suspensions and Dispersions

Fredrickson model. Only shear stresses have been considered. 

This simple model predicts that the structure factor will develop a butterfly pattern and grow along an axis that is at 45° with respect to the flow direction, which is parallel to the principal axis of strain in this flow. Since the structure factor is the Fourier transform of the pattern of concentration fluctuations causing the scattering, the model predicts an enhancement of fluctuations perpendicular to the principal axis of strain. 

In a complex, polymeric liquid, normal stresses as well as the shear stress can be present, and these contributions will influence the shape of the structure factor. The simplest rheological constitutive model that can account for normal stresses is the second-order fluid model [64], where the first and second normal stress differences are quadratic functions of the shear rate. Calculations using this model [92,93,94,90,60], indicate that the appearance of normal stresses can rotate the structure factor towards the direction of flow in the case of simple shear flow and can induce a four-fold symmetry in the case of exten-sional flow. 

Suspensions and dispersions of particles are characterized by distributions describing their orientation and spatial distribution. Knowledge of these distributions then allow the calculation of bulk mechanical and optical properties. In the following sections, theories are presented for both dilute and semidilute systems. 

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