The rheology of soft bodies suspended in the simple shear flow of a viscoelastic fluid

Many industrial applications involve soft suspended bodies in viscoelastic fluids. Moreover, many biological fluids contain high molecular weight macromolecules which impart viscoelasticity to the fluid, and any cells which are suspended in such fluids again form a suspension of elastic bodies in a viscoelastic fluid. For control purposes, microfluidic platforms are beginning to utilizing viscoelastic solvents to perform tasks such as cell focusing [34]. However, despite numerical studies into the kinematics of such deformable bodies in viscoelastic fluids, no studies currently consider the rheology of such systems. Due to the competing effects of the viscoelasticity of the fluid and the elasticity of the solids it is clear that there exists a non-trivial rheological behavior exhibited by such suspensions. In this study, we present simulations of dilute systems of deformable particles with viscoelastic suspending fluids. We compute the effective viscosity and the first/second normal stresses for a suspension of neoHookean particles sheared in a Giesekus suspending fluid up to modest deformations characterized by a capillary number, Ca, up to Ca = 0.3. The results indicate that the per particle extra stress that originates from the suspending fluid (the particle induced fluid stress) remains relatively constant regardless of deformation. In contrast, the component of the extra stress that arises from the stress inside the particle (the stresslet) is a strong function of both the capillary number and the Weissenberg number for the parameter space investigated. Note that we find the suspensions "thicken" and/or "thin" with increasing shear depending on the range of parameter space examined.