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 - β = η_p/(η_s + η_p) which measures the coupling between the polymer stress and flow: η_p and η_s are the polymer and solvent viscosity, respectively. As 1 - β increases, while the stresslet does not change significantly compared to that in the β → 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 β reveals that at large 1 - β, polymer stress modulates flow, leading to suppression of polymer stretch. This effect of β 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.