The sedimentation of a sphere through an elastic fluid. Part 1. Steady motion

Arigo, Mark T.; Rajagopalan, Dilip; Shapley, Nina C.; McKinley, Gareth H.

doi:10.1016/0377-0257(95)01379-6

Cited by 83 publications

(55 citation statements)

References 34 publications

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“…The flow is in the positive y-direction in the middle of the channel (see figure 7(b5)). In a Giesekus fluid, the flow shows a strong fore-aft asymmetry due to both inertia and the viscoelastic wake, similar to the flow field around a settling sphere (Arigo et al 1995;Fabris et al 1999;Abedijaberi & Khomami 2012). These secondary flows interact with the particle-induced flow, and further enhance the fluid mixing.…”

Section: Particle-induced Fluid Transportmentioning

confidence: 95%

Dynamics of particle migration in channel flow of viscoelastic fluids

2015

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The migration of a sphere in the pressure-driven channel flow of a viscoelastic fluid is studied numerically. The effects of inertia, elasticity, shear-thinning viscosity, secondary flows and the blockage ratio are considered by conducting fully resolved direct numerical simulations over a wide range of parameters. In a Newtonian fluid in the presence of inertial effects, the particle moves away from the channel centreline. The elastic effects, however, drive the particle towards the channel centreline. The equilibrium position depends on the interplay between the elastic and inertial effects. Particle focusing at the centreline occurs in flows with strong elasticity and weak inertia. Both shear-thinning effects and secondary flows tend to move the particle away from the channel centreline. The effect is more pronounced as inertia and elasticity effects increase. A scaling analysis is used to explain these different effects. Besides the particle migration, particle-induced fluid transport and particle migration during flow start-up are also considered. Inertia effects, shear-thinning behaviour, and secondary flows are all found to enhance the effective fluid transport normal to the flow direction. Due to the oscillation in fluid velocity and strong normal stress differences that develop during flow start-up, the particle has a larger transient migration velocity, which may be potentially used to accelerate the particle-focusing.

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Section: Particle-induced Fluid Transportmentioning

confidence: 95%

Dynamics of particle migration in channel flow of viscoelastic fluids

2015

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“…viscoelastic, inelastic, shear thinning), with the purpose of measuring basic quantities, such as the terminal velocity and the drag on the sphere, and of comparing the results with Newtonian experiments, see for example [14][15][16][17][18][19][20]. Recently Stocchino and Guala [13] measured experimentally the coefficient of restitution of a spherical particle impacting a rigid wall immersed in the same viscoelastic shear thinning fluid of the present investigation.…”

Section: Introductionmentioning

confidence: 66%

“…In the literature, most of the work published focused the attention on the pure settling under gravity of a spherical particle inside a cylindrical container [14][15][16][17][18][19][20]. In particular, Mena et al [14] performed a sequence of experiments of particle settling in different fluids (Newtonian, viscoelastic, inelastic and constant viscosity elastic) with the aim to study the influence of the rheological properties on the drag force.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…On the contrary, Jones et al [16] used a different fluid for the same problem; in fact, they employed two different constant-viscosity elastic fluid varying the Deborah number between 0.2 and 5. Argon et al [17] and Rajagopalan et al [18] addressed the problem of a sphere settling under gravity through a cylindrical tube filled with viscoelastic fluid, comparing numerical results obtained by means of finite elements simulations with detailed velocity measurements. Indeed, laser Doppler velocimetry was employed to measure the fluid velocity in the vicinity of the settling particle in order to validate the numerical simulations over a wide range of Deborah numbers.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

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

Guala

Stocchino

2007

European Journal of Mechanics - B/Fluids

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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.

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“…The sphere speed is continuously measured as it falls into a cylinder filled with oil. Arigo and McKinley [23] visualized the falling ball using a fixed camera. Lommatzsch [24] proposed the following measurement method : the camera is given a speed close to that of the ball.…”

Section: Measurement Of U ∝ ∝ ∝ ∝mentioning

confidence: 99%

Design of a high precision falling-ball viscometer

Brizard

Megharfi

Mahe

et al. 2005

Review of Scientific Instruments

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The increase in uncertainty throughout the viscosity scale being the principal disadvantage of capillary viscometry, the BNM-LNE decided to develop an absolute falling-ball viscometer making it possible to cover a wide range of viscosity while keeping a weak uncertainty. The measurement of viscosity then rests on the speed limit measurement of falling ball, corrected principal identified effects (edge effects, inertial effects, etc). An experimental bench was developed in order to reach a relative uncertainty of the order of 10 -3 to the measure of viscosity. This bench must allow to observe the trajectory of the ball inside a cylindrical tube filled with liquid for which the viscosity is to be measured, and to obtain the variations in speed throughout the fall in order to determine the area where the speed limit is reached.

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The sedimentation of a sphere through an elastic fluid. Part 1. Steady motion

Cited by 83 publications

References 34 publications

Dynamics of particle migration in channel flow of viscoelastic fluids

Dynamics of particle migration in channel flow of viscoelastic fluids

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

Design of a high precision falling-ball viscometer

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