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 nonNewtonian 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 strainγ , 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.

The drainage of non-Newtonian fluids in the quasi-steady motion of a sphere towards a plane

“…Under this condition, the behaviour of the fluid in this almost Poiseuille-type flow (viscometric one) can be modelled in first approximation by a powerlaw fluid, which takes account of a possible shear thinning behaviour. Furthermore, recent experimental results on particle-wall collision in polymeric liquids (Guala and Stocchino 2007;Ardekani et al 2009) confirmed that the viscoelasticity of the fluid was negligible relative to its shear thinning character at low Deborah numbers, supporting the choice of the power-law model in this particular flow. Moreover, as the drag is principally due to the pressure induced by the drainage flow, the shear velocity gradient is limited by its value reached near the axis of symmetry.…”

“…Moreover, the time needed for the contact of two spheres in Newtonian or non-Newtonian fluid plays an important role in the aggregation and the formation of the plug flow during the transport of suspensions. Another application concerns the particle-particle or particle-wall collision in non-Newtonian fluids, which takes place in particle-laden flows (Stocchino and Guala 2005;Guala and Stocchino 2007;Ardekani et al 2009;Marston et al 2010). Therefore, this study deals with the calculation of the Stokes-type law correction factor, for the hydrodynamic resistance of a sphere of radius a moving at steady velocity U, towards or away from a plane wall in powerlaw fluids.…”

Two shallow-water type models for viscoelastic flows from kinetic theory for polymers solutions

“…At intermediate values of De the elasticity of the fluid begins to affect the sedimentation of the particles and an important drag reduction occurs. When higher values of the Deborah number are found, the drag increases again and it exceeds the Newtonian value [16].…”

“…Many works have been devoted to the study of fluids at small De number [16,18,25] and it is put in evidence that the behavior of the flow in this case is equivalent to the case of a Newtonian fluid with a proper viscosity. Nevertheless it is also shown (in theoretical and experimental way) that there is a difference in their behaviour.…”

Cavitation structures formed during the collision of a sphere with an ultra-viscous wetted surface

“…More relevant to the work presented in this paper, Guala & Stocchino (2007) used particle image velocimetry to investigate large-scale flow structures formed during fully immersed particle-wall collisions in Newtonian (water, aqueous glycerol) and in non-Newtonian (1 % aqueous CMC, shear thinning, weakly viscoelastic, De 1) liquids. A similar velocity field and vortical structure evolution was obtained in both the glycerol and CMC solutions, which showed that the shear-thinning effect of the non-Newtonian CMC fluid was dominant over its viscoelastic nature for low Deborah numbers.…”