Flow of viscoplastic fluids on an inclined plane: evaluation of yield stress

Abstract

Within the general category of so called generalized Newtonian fluids, there exists a class of materials which do not deform until the applied shear stress exceeds a critical value called yield stress. Conversely, such a material behaves like a solid as long as the shear stress is less than the yield stress. This class of materials is called viscoplastic fluids. The question whether the true yield stress exists or not is indeed far from settled (1), but the notion of a yield stress has proved to be quite useful in practice in describing the steady shear rheological behaviour of a range of materials especially of particulate suspensions. Consequently, yield stress appears as a parameter in all constitutive relations (which purport to describe the steady shear behaviour of viscoplastic materials), and its evaluation is important before an engineering flow problem can be solved. Conversely, there are some simple hydrodynamic situations which allow the value of the yield stress to be extracted from macroscopic quantities such as flow rate-pressure drop data. In this paper, we examine this possibility using gravity driven flow of a viscoplastic material on an inclined plane.