Rheology of non-Brownian particle suspensions in viscoelastic solutions. Part 1: Effect of the polymer concentration

We study the effect of varying polymer concentration, measured by the dimensionless polymer viscosity partition function $β$⁠, on the steady shear rheology of rigid particle suspensions using direct numerical simulation of the Oldroyd-B model. We compare the bulk rheology using immersed boundary simulations at $Φ=2.5%$ and $5%$ to body-fitted single-particle simulations and find that the per-particle viscosity and first normal stress difference coefficient are always shear-thickening at all values of $β$ considered. However, as $β$ decreases, the polymer stress transforms the flow field near each particle from closed concentric streamlines to helical streamlines that advect stretched polymers away from the particle surface. At low $β$⁠, the polymer stress is diffuse, where the distribution of the particle induced fluid stress (PIFS) caused by the stretched polymers is spread out in the simulation domain rather than concentrated near the particle surface. Therefore in multiparticle simulations, the polymer stress can be significantly affected by particle-particle interactions. The stress generated by a given particle is disrupted by the presence of particles in its vicinity, leading to a significantly lower PIFS than that of the single-particle simulation. In addition, at increased volume fractions and low values of $β$⁠, the polymer stress distribution on the particle surface shifts so as to increase the magnitude of the polymer stress moments, resulting in a shear-thickening stresslet contribution to the viscosity that is not seen in single particle or high $β$ simulations. This result indicates that for suspensions in highly viscoelastic suspending fluids that are characterized by a low $β$ parameter, hydrodynamic interactions are significant even at modest particle concentrations and fully resolved multiparticle simulations are necessary to understand the rheological behavior.