Large-scale flow structures in particle–wall collision at low Deborah numbers

Abstract

PIV measurements of two dimensional velocity fields during the rebound of a steel spherical particle colliding a wall are provided in Newtonian fluids (distilled water and aqueous solution of Glycerol) and in a viscoelastic shear thinning fluid (aqueous solution of carboxymethyl cellulose). The experiments are designed in order to reproduce the same conditions in which the coefficient of restitution was observed to be significantly affected by viscoelasticity at the typical scales of the lubrication layer [A. Stocchino, M. Guala, Particle–wall collision in shear thinning fluids, Exp. Fluids 65 (2005) 17–46]. In such conditions, the Deborah number, which is a measure of the relevance of the viscoelastic effects compared to the inertial effects, is however relatively low. The aim of the present study is to investigate the relative influence of the elasticity and of the shear thinning character of the non-Newtonian fluid on the large scale flow structures triggered by the particle impact. Special attention is dedicated to the definition of a proper viscosity when the non-Newtonian fluid is involved. In this respect, a scaling argument is suggested to derive the value of the viscosity for an assigned rate of strain γ ˙ , given a constitutive law of the kind τ = τ ( γ ˙ ) , where τ is the shear stress. The scaling analysis is supported by previous works on particle settling in non-Newtonian fluids and by recent studies on the flow structures that form as a consequence of a particle–wall collision in Newtonian fluids. The experimental validation of the proposed scaling is provided by first choosing a Newtonian fluid with viscosity equal to the non-Newtonian viscosity and, then, carrying out a comparative analysis of the large-scale vortical structure formed during the collision-rebound process. The statistical analysis suggests that the large scale flow structures observed during the Glycerol experiment and the CMC solution experiment behaves similarly in term of spatial and temporal scales. Therefore, at least for the values of the dimensionless parameters investigated, the shear thinning character of the non-Newtonian fluid employed is dominant with respect of its viscoelasticity.