(423e) Numerical Study of the Shear Rheology of Suspensions in Viscoelastic Fluids at Low Volume Fraction

The rheology of viscoelastic fluids with particulate fillers is of both industrial and academic interest due to the wide use of such materials in manufacturing, such as injection molding and 3D printing, and technologies such as oil recovery. However, existing models to describe the steady shear rheology of viscoelastic suspensions fail to adequately predict experimental results even at low volume fractions. This reflects an insufficient fundamental understanding of the mechanism by which particles alter the bulk stress of viscoelastic fluids. Furthermore, the nonlinearities of the suspending fluid present a challenge for deriving analytical results. As such, fully 3-D simulations that can resolve particle-scale hydrodynamics can provide useful insights into such systems and inform more predictive models. We present steady shear simulations of freely suspended rigid spheres at low volume fractions in a viscoelastic fluid described by the Giesekus model. We use a fully parallel code based on an unstructured finite volume formulation for incompressible flow. The Giesekus model is implemented using a log-conformation formulation, which allows us to probe the high Weissenberg number regime (large deformation rate and high elasticity). The code can accommodate boundary-fitted meshes, which allow high resolution of particle boundaries, as well as an immersed-boundary formulation that can efficiently handle multi-body dynamic simulations. Using these tools we study both dilute and semi-dilute suspensions, making comparisons to theoretical results and experimental measurements. Single particle results are used to validate the theories in the dilute limit and explore the effect of high shear rates. We show that the competing effect between the particle extra stress and polymer stresses induced in the fluid by particle disturbances determines the particle contribution to the bulk rheology. At high shear rates, the particle-induced polymer stress dominates. We also present multi-particle simulations at low volume fractions to show how hydrodynamic interactions between particles affect the microstructure and resulting bulk stresses.