Effects of viscoelasticity on shear-thickening in dilute suspensions in a viscoelastic fluid

We investigate previously unclarified effects of fluid elasticity on shear-thickening in dilute suspensions in an Oldroyd-B viscoelastic fluid using a novel direct numerical simulation based on the smoothed profile method. Fluid elasticity is determined by the Weissenberg number Wi and by viscosity ratio $1-\beta=\eta_p/(\eta_s+\eta_p)$ which measures the coupling between the polymer stress and flow: $\eta_p$ and $\eta_s$ are the polymer and solvent viscosity, respectively.As $1-\beta$ increases, while the stresslet does not change significantly compared to that in the $\beta\to 1$ limit, the growth rate of the normalized polymer stress with Wi was suppressed.Analysis of flow and conformation dynamics around a particle for different $\beta$ reveals that at large $1-\beta$, polymer stress modulates flow, leading to suppression of polymer stretch.This effect of $\beta$ on polymer stress development indicates complex coupling between fluid elasticity and flow, and is essential to understand the rheology and hydrodynamic interactions in suspensions in viscoelastic media.