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To elucidate the key factor for the quantitative prediction of theshear-thickening in suspensions in viscoelastic fluids, direct numericalsimulations of many-particle suspensions in a multi-mode Oldroyd-B fluid areperformed using the smoothed profile method. Suspension flow under simple shearflow is solved under periodic boundary conditions by using Lees--Edwardsboundary conditions for particle dynamics and a time-dependent obliquecoordinate system that evolves with mean shear flow for fluid dynamics.Semi-dilute many-particle suspensions up to a particle volume fraction of 0.1are investigated. The presented numerical results regarding the bulkrheological properties of the shear-thickening behavior agree quantitativelywith recent experimental results of semi-dilute suspensions in a Boger fluid.The presented result clarifies that an accurate estimation of the first normalstress difference of the matrix in the shear-rate range where theshear-thickening starts to occur is crucial for the quantitative prediction ofthe suspension shear-thickening in a Boger fluid matrix at around theWeissenberg number $\rm{Wi}=1$ by an Oldroyd-B model. Additionally, the effectof suspension microstructures on the suspension viscosity is examined. Thepaper concludes with a discussion on how the flow pattern and the elasticstress development change with the volume fraction and Weissenberg number.

Prediction of shear-thickening of particle suspensions in viscoelastic fluids by direct numerical simulation