Orientation and rheology of rodlike particles with strong Brownian diffusion in a second-order fluid under simple shear flow

Abstract

An analysis of orientation in a dilute suspension of rodlike macromolecules in a second-order fluid is presented and the effect of the elasticity of the fluid on the orientation of the suspended particles is examined. Distributions of particle orientation under a simple shear flow have been obtained for small β where β is the ratio of the intrinsic relaxation time of the fluid to the rotational relaxation time of the particle, the latter being inversely proportional to the Brownian rotation diffusion coefficient D r of the particle. The parameter β represents also the ratio of the Weissenberg number of the fluid to the non-dimensional shear rate, g/ D r. An expression of the stress tensor of the suspension is derived and used in conjuntion with the orientation distribution to obtain the rheological properties of the mixture subjected to a simple shear.