Non-Newtonian suspension behavior due to flow disturbance inertial effects

A theoretical study of a dilute and neutrally buoyant suspension of rigid spheres within an incompressible Newtonian fluid is presented. It is shown that the kinetic energy of the flow disturbance, arising from the presence of the spheres, and the sphere's rotational motion are mechanisms for storing energy and causing memory effects which give rise to phenomena similar to those found in viscoelastic fluids. An analytical expression for the Weissenberg number is provided in terms of the dimensions of the inclusions and their volume fraction, the fluid characteristics, and the rate of the flow field. Such an expression is used to predict the size of the spherical inclusions for cases in which the normal stresses are comparable to the shear stress.