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 -> 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.