To elucidate the key factor for the quantitative prediction of the shear thickening in suspensions in viscoelastic fluids, direct numerical simulations of many-particle suspensions in a multi-mode Oldroyd-B fluid are performed using the smoothed profile method. Suspension flow under simple shear flow is solved under periodic boundary conditions by using Lees-Edwards boundary conditions for particle dynamics and a time-dependent oblique coordinate system that evolves with mean shear flow for fluid dynamics. Semidilute many-particle suspensions up to a particle volume fraction of 0.1 are investigated. The presented numerical results regarding the bulk rheological properties of the shear-thickening behaviour agree quantitatively with recent experimental results of semidilute suspensions in a Boger fluid. The presented result clarifies that an accurate estimation of the first normal stress difference of the matrix in the shear-rate range where the shear thickening starts to occur is crucial for the quantitative prediction of the suspension shear thickening in a Boger fluid matrix at around the Weissenberg number by an Oldroyd-B model. Additionally, the effect of suspension microstructures on the suspension viscosity is examined. The paper concludes with a discussion on how the flow pattern and the elastic stress development change with the volume fraction and Weissenberg number.
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