Abstract

The influence of particle-polymer interactions on the ensemble average stress is derived as a function of the Deborah number for a dilute suspension of spheres in an Oldroyd-B fluid in the limit of small polymer concentrations. The slow rate of decay of the particle-induced polymer stress with separation from a particle presents a challenge to the derivation of the average stress, which can be overcome by removing the linearized polymer stress disturbance before computing the bulk average stress from the particle-induced disturbance. The linearized stress can be shown to have zero ensemble average. The polymer influence on the particle's stresslet is computed with the aid of a generalized reciprocal theorem based on a regular perturbation from Newtonian flow for small polymer concentration. The analysis shows that the particle-polymer contributions to the shear stress and first normal stress difference shear thicken as has been observed in the experiments of Scirocco et al. ( Shear thickening in filled Boger fluids, J. Rheol. 49 , 551 ( 2005 ) JORHD2 0148-6055 10.1122/1.1849185 ). The particle-polymer contribution to the second normal stress difference is positive at small Deborah numbers but changes sign at a Deborah number of about 2.3.