Non-Newtonian flow in parallel-disk viscometers in the presence of wall slip

Finite element computation is used to investigate the effects of wall slip on the slow viscous flow of non-Newtonian fluids in parallel-disk viscometers. A simplified Bird-Carreau constitutive equation is used to describe the general shear thinning behavior exhibited by non-Newtonian fluids. The linear relationship between wall shear stress and slip velocity proposed by Navier and two of its non-linear generalizations are investigated. The main objective here is to determine whether the kinematics of the flow field satisfies the key assumption implicit in the method of Yoshimura and Prud'homme for determining wall slip functions. The results of the finite element computation indicate that these assumptions are approximately met but the amplification of the non-linearity of the shear stress with respect to the radial coordinate means that the popular method of converting the measured torque into rim shear stress may incur significant error.