Apparent Wall Slip in Capillary Rheometry of Viscoplastic Liquids

Abstract

We employ a recently proposed viscosity function (Souza Mendes and Dutra, 2004) to analyze the fully developed flow of yield-stress liquids through tubes. We first show that its dimensionless form gives rise to the so-called jump number, a novel material property that measures the shear rate jump that the material undergoes as the yield stress is reached. We integrate numerically the momentum conservation equation that governs this flow together with the generalized Newtonian Liquid model and the above mentioned viscosity function. We obtain velocity and viscosity profiles for the entire range of the jump number. We show that the friction factor f.Re curves display sharp peaks as the shear stress value at the tube wall approaches the yield stress. Finally, we demonstrate the existence of sharp flow rate increases (or apparent slip) as the wall shear stress is increased in the vicinity of the yield stress.