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Revisiting the 1954 Suspension Experiments of R. A.Bagnold

Hunt, M. L. and Zenit, R. and Campbell, C. S. and Brennen, C. E. (2002) Revisiting the 1954 Suspension Experiments of R. A.Bagnold. Journal of Fluid Mechanics, 452 . pp. 1-24. ISSN 0022-1120.

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In 1954 R. A. Bagnold published his seminal findings on the rheological properties of a liquid-solid suspension. Although this work has been cited extensively over the last fifty years, there has not been a critical review of the experiments. The purpose of this study is to examine the work and to suggest an alternative reason for the experimental findings. The concentric cylinder rheometer was designed to measure simultaneously the shear and normal forces for a wide range of solid concentrations, fluid viscosities and shear rates. As presented by Bagnold, the analysis and experiments demonstrated that the shear and normal forces depended linearly on the shear rate in the 'macroviscous' regime; as the grain-to-grain interactions increased in the 'grain-inertia' regime, the stresses depended on the square of the shear rate and were independent of the fluid viscosity. These results, however, appear to be dictated by the design of the experimental facility. In Bagnold's experiments, the height (h) of the rheometer was relatively short compared to the spacing (t) between the rotating outer and stationary inner cylinder (h/t=4.6). Since the top and bottom end plates rotated with the outer cylinder, the flow contained two axisymmetric counter-rotating cells in which flow moved outward along the end plates and inward through the central region of the annulus. At higher Reynolds numbers, these cells contributed significantly to the measured torque, as demonstrated by comparing Bagnold's pure-fluid measurements with studies on laminar-to-turbulent transitions that pre-date the 1954 study. By accounting for the torque along the end walls, Bagnold's shear stress measurements can be estimated by modelling the liquid-solid mixture as a Newtonian fluid with a corrected viscosity that depends on the solids concentration. An analysis of the normal stress measurements was problematic because the gross measurements were not reported and could not be obtained.

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Hunt, M. L.0000-0001-5592-2334
Additional Information:(Received 11 April 2001 and in revised form 1 August 2001) The authors thank Professors Ronald F. Scott, Rolf H. Sabersky and Norman H. Brooks for their interest and assistance in writing this paper, and to G. G. Joseph for the use of his library. M.L.H. also thanks Professor D. A. Kaminski for suggesting a review article on liquid-solid flows. We acknowledge the support of NASA through grant NAF3-2358, the National Science Foundation through grant CTS-9908430, and UNAM-PAPIIT grant IN-103900. "Reprinted with the permission of Cambridge University Press."
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ID Code:106
Deposited By: Christopher Brennen
Deposited On:08 Oct 2004
Last Modified:09 Mar 2020 13:18

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