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

摘要

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 theological 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 Wi = 1 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.