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A viscosity function for highly-shear-thinning or yield-stress liquids such as pastes and slurries is proposed. This function is continuous and presents a low shear-rate viscosity plateau, followed by a sharp viscosity drop at a threshold shear stress value (yield stress), and a subsequent power-law region. The equation was fitted to data for Carbopol aqueous solutions at two different concentrations, a drilling fluid, an water/oil emulsion, a commercial mayonnaise, and a paper coating formulation. The quality of the fittings was generally good.

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Circular Couette flow of inelastic shear-thinning materials in annuli is examined. The curved streamlines of the circular Couette flow can cause a centrifugal instability leading to toroidal vortices, well known as Taylor vortices. The presence of these vortices changes the hydrodynamic and heat transfer characteristics of the processes at which this type of flow occurs. Therefore, it is quite important to be able to predict the onset of instability. Most of the available theoretical and experimental analyses are for Newtonian and viscoelastic (dilute polymeric solutions) liquids. In this work, the effect of the shear-thinning behavior of high concentration suspensions on the onset of the Taylor vortices is determined theoretically by solving the conservation equations, constructing the solution path as the inner cylinder speed rises and searching for the critical conditions. This procedure avoids the need for a stability analysis of the flow and the solution of an eigenproblem. The differential equations were solved by the Galerkin/finite-element method and the resulting set of nonlinear algebraic equations, by Newton’s method.

We analyze the liquid-liquid displacement in capillary tubes. The goal is to determine the amount of displaced liquid that remains attached to the tube wall and the configuration of the liquid-liquid interface at different operating parameters. The study encompasses both numerical and experimental approaches. The finite element method is used to solve the governing equations and, in order to validate the predictions, visualization experiments are performed to capture images of the interface. The numerical results were obtained for the assumption of negligible inertia, and the effects of viscosity ratio and capillary number are investigated. The predictions and experimental observations are in good agreement.