Rheology of non-Brownian particle suspensions in viscoelastic solutions. Part II: Effect of a shear thinning suspending fluid

The shear rheology of particle suspensions in shear-thinning polymeric fluids is studied experimentally using parallel plate measurements and numerically using fully resolved, 3D finite volume simulations with the Giesekus fluid model. We show in our experiments that the steady shear viscosity and first normal stress difference coefficient of the suspension evolve from shear-thickening to substantially shear-thinning as the degree of shear-thinning of the suspending fluid increases. Moreover, in highly shear-thinning fluids, the suspension exhibits greater shear-thinning of the viscosity than the suspending fluid itself. Our dilute body-fitted simulations show that in the absence of hydrodynamic interactions, shear-thinning can arise from the particle-induced fluid stress (PIFS), which ceases to grow with increasing shear rate at low values of $β$ (solvent viscosity ratio) and finite values of $α$ (the Giesekus drag coefficient). In a Giesekus suspending fluid, the polymers surrounding the suspended particle are unable to stretch sufficiently at high Weissenberg numbers (Wi) and the reduced polymer stress results in a lower PIFS. When coupled with the shear-thinning stresslet, this effect creates an overall shear-thinning of the viscosity. We then explore the effects of particle-particle interactions on the suspension rheology using immersed boundary simulations. We show that multiparticle simulations are necessary to obtain the shear-thinning behavior of the per-particle viscosity of suspensions in shear-thinning fluids at moderate values of $β$⁠. Particle-particle interactions lead to a substantial decrease in the PIFS and an enhancement of the shear-thinning of the stresslet compared to the single particle simulations. This combination leads to the shear-thinning of the per-particle viscosity seen in experiments. We also find that very low values of $β$ and finite values of $α$ have opposing effects on the per-particle viscosity that can lead to a nonmonotonic per-particle viscosity versus shear rate in a highly shear-thinning fluid. Overall, the addition of rigid particles to highly shear-thinning fluids, such as joint synovial fluid, leads to increased viscosity and also increased shear-thinning at high shear rates.