Dissipation in a dilute suspension of spheres in a second-order fluid

We examine the effective medium properties of a dilute suspension of spheres in a second-order fluid under linear shear. Since the second-order fluid is the first step toward the general viscoelastic fluid, the results obtained may provide a qualitative feel for the problem in which the suspending fluid obeys a more complicated (and realistic) constitutive relation.The dissipation in the medium is calculated by determining the rate of working by surface forces; this is compared to the dissipation in a homogeneous fluid to give the effective properties. The results show that the term linear in volume fraction increases the corresponding rheological coefficient, just as in the Newtonian case. It is to be noted that the second-order dissipation is zero for simple shear and other weak flows, whereas for strong flows the small correction may increase or decrease the overall dissipation.