Rheology of a suspension of particles in viscoelastic fluids

In this paper we study the bulk stress of a suspension of rigid particles i n viscoelastic fluids. We first apply the theoretical framework provided by Batchelor [J. Fluid Mech. 41 (1970) 545] to derive an analytical expressio n for the bulk stress of a suspension of rigid particles in a second-order fluid under the limit of dilute and creeping flow conditions. The applicati on of the suspension balance model using this analytical expression leads t o the prediction of the migration of particles towards the centerline of th e channel in pressure-driven flows. This is in agreement with experimental observations. We next examine the effects of inertia (or flow Reynolds numb er) on the rheology of dilute suspensions in Oldroyd-B fluids by two-dimens ional direct numerical simulations. Simulation results are verified by comp aring them with the analytical expression in the creeping flow limit. It is seen that the particle contribution to the first normal stress difference is positive and increases with the elasticity of the fluid and the Reynolds number. The ratio of the first normal stress coefficient of the suspension and the suspending fluid decreases as the Reynolds number is increased. Th e effective viscosity of the suspension shows a shear-thinning behavior tin spite of a non-shear-thinning suspending fluid) which becomes more pronoun ced as the fluid elasticity increases. (C) 2001 Published by Elsevier Scien ce B.V.