An experimental investigation of negative wakes behind spheres settling in a shear-thinning viscoelastic fluid |
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Authors: | Mark T Arigo G H McKinley |
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Institution: | (1) Division of Engineering and Applied Sciences Harvard University Cambridge, Massachusetts 02138, USA, US;(2) Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge, Massachusetts 02139, USA, US |
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Abstract: | We present detailed experimental results examining “negative wakes” behind spheres settling along the centerline of a tube
containing a viscoelastic aqueous polyacrylamide solution. Negative wakes are found for all Deborah numbers (2.43≤De(˙γ)≤8.75) and sphere-to-tube aspect ratios (0.060≤a/R≤0.396) examined. The wake structures are investigated using laser-Doppler velocimetry (LDV) to examine the centerline fluid
velocity around the sphere and digital particle image velocimetry (DPIV) for full-field velocity profiles. For a fixed aspect
ratio, the magnitude of the most negative velocity, U
min
, in the wake is seen to increase with increasing De. Additionally, as the Deborah number becomes larger, the location of this minimum velocity shifts farther downstream. When
normalized with the sphere radius and the steady state velocity of the sphere, the axial velocity profiles become self-similar
to the point of the minimum velocity. Beyond this point, the wake structure varies weakly with aspect ratio and De, and it extends more than 20 radii downstream. Inertial effects at high Reynolds numbers are observed to shift the entire
negative wake farther downstream. Using DPIV to investigate the transient kinematic response of the fluid to the initial acceleration
of the sphere from rest, it is seen that the wake develops from the nonlinear fluid response at large strains. Measurements
of the transient uniaxial extensional viscosity of this weakly strain-hardening fluid using a filament stretching rheometer
show that the existence of a negative wake is consistent with theoretical arguments based on the opposing roles of extensional
stresses and shearing stresses in the wake of the sphere.
Received: 10 November 1997 Accepted: 1 May 1998 |
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Keywords: | Sphere negative wake viscoelastic shear-thinning strain-hardening |
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