Steady and unsteady shear flows of a viscoplastic fluid in a cylindrical Couette cell

Abstract

Yield stress fluid flows in Couette cells have been widely studied in the last decades for their intriguingly exhibiting phenomena. In this paper, we use a PIV technique to investigate the axisymmetric flow and rheological properties of a Carbopol gel in a relatively wide cylindrical Couette device. Carbopol gel is known to exhibit viscoplastic behavior and is often described using a Herschel–Bulkley law, which is characterized by a plastic yield stress τy and a shear-dependent nonlinear viscosity. In some cases, the elasticity of the material has to be accounted for to understand the whole dynamics of the system, in particular for unsteady flows as observed in the present study. Two set of experiments are conducted here in order to highlight these different rheological behaviors and the resulting dynamics: (i) a steady shear configuration and (ii) an unsteady shear configuration, in which the angular velocity of the inner cylinder is either constant or time dependent (sin profile), respectively. In the steady configuration, a simple optimization model, based on the Herschel–Bulkley law, is developed to extract the rheological parameters of the viscoplastic contribution of the gel from the steady velocity fields. Results are shown to be in good agreements with rheological parameters obtained from a standard rheometer. On the other hand, the elastic contribution of the material is highlighted in the unsteady shear configuration, for which a spatio-temporal transition between solid-elastic and fluid behaviors is observed. Different models are proposed to describe the dynamics of the unsteady flow. First, quasi-steady state models allow to predict both the fluid shear zone close to the inner cylinder and the elastic deformation of the material as long as their contributions can be decoupled in space and in time. For more complex dynamics, i.e. when the flow becomes strongly unsteady, an elasto-viscoplastic model is developed to describe the flow dynamics. It is shown to quantitatively reproduce the experimental measurements. Finally, an elastic wave model is derived to describe an elastic front propagating from the inner cylinder to the outer one, and observed at every half forcing period. The front velocity is thus shown to scale on the phase velocity of an elastic wave in a deformable solid.