Finite Reynolds number effect on the rheology of a dilute suspension of neutrally buoyant circular particles in a Newtonian fluid

Knowledge of suspension rheology can help in the prediction of its behavior under various flow conditions. Considerable theoretical effort has been made to model the macroscopic properties of suspensions of rigid particles in a Newtonian fluid, but for the most part it has been limited to zero particle Reynolds number. In this paper we investigate the effect of finite particle Reynolds number on the macroscopic properties of suspensions of rigid circular particles in a Newtonian fluid in the dilute limit (no interaction between particles). Two-dimensional numerical simulations are performed. Navier–Stokes equations are solved for the fluid without neglecting any terms. It is seen that the viscosity of the suspension shear thickens. The first normal stress difference is negative and increases in magnitude as the Reynolds number is increased.