Shear Flows of Dilatant Fluids with Limited Shear Rates: Analytical Results and Linear Stability Analysis

Abstract

In this paper, we study the simple shear flows of a class of dilatant fluids with a limited shear rate. This class of fluids is characterized by shear thickening behavior in which the apparent viscosity tends to infinity as the modulus of the stress approaches a finite threshold. The apparent viscosity function is a logarithmic type with two material parameters. We considered this specific form because it fits very well with the flow curves of some granular suspensions for specific values of the material parameters. Despite the nonlinearity of the constitutive law, it is possible to determine explicit steady-state solutions for a simple shear flow, namely (i) the channel flow; (ii) the flow between coaxial cylinders, and (iii) the flow down an inclined plane. We performed a two-dimensional linear stability analysis to investigate the onset of possible instabilities of the steady basic flow, putting into evidence the dependency of the critical Reynolds number on the material parameters.