Particle settling in a shear-thinning, viscoelastic fluid in the presence of wall effects

The settling of particles in fluids is a widespread phenomenon and commonly involves accounting for the effects of walls. Particle settling and wall effects are well understood for Newtonian fluids but the consequences of non-Newtonian fluid properties on particle settling are less well known. Here, we present the results from a set of experiments quantifying wall effects on particle settling within quiescent shear-thinning and viscoelastic (non-Newtonian) fluids for sphere-to-tube diameter ratios lambda <= 0.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda \le 0.3$$\end{document}. We find that wall effects on particle settling are reduced in non-Newtonian fluids and settling velocities are poorly predicted by conventional wall-corrected Stokes' equations. We show that deviations in settling velocity are due to both the shear-thinning and viscoelastic properties of the fluid. Supported by our experimental dataset, we are able to show that calculating the shear-rate based on the particle diameter length-scale corresponds to an apparent viscosity that appropriately accounts for shear-thinning effects. A further correction factor for viscoelastic behaviour based on lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document} and the Weissenberg number, Wi, is applied, and shows good agreement with all experimentally measured velocities. Together, we provide a quantitative method to accurately predict the terminal settling velocity of particles in shear-thinning, viscoelastic fluids up to sphere-to-tube diameter ratios of 0.3.