Average stress in a dilute suspension of rigid spheroids in a second-order fluid in a linear flow

The stress response of a suspension of nonspherical particles in polymeric fluids is important in many practical applications. This study examines the flow around a single spheroid in a polymeric fluid in the limit of small viscoelasticity, and performs an ensemble average of the stress tensor over all particle configurations to determine the effective long-time viscosity and normal stress coefficients of the suspension in linear flow fields. There are two contributions to the extra stress: one from the force dipole on the particles (stresslet) and another from the fluctuations in the velocity in the bulk fluid (fluid-induced particle stress), both of which are quantified in the paper.