Hostname: page-component-84b7d79bbc-rnpqb Total loading time: 0 Render date: 2024-07-25T19:47:22.188Z Has data issue: false hasContentIssue false
  • English
  • Français

Experiments on the pressure drop created by a sphere settling in a viscous liquid. Part 2. Reynolds numbers from 0·2 to 21,000

Published online by Cambridge University Press:  28 March 2006

Guili A. Feldman  and
Howard Brenner
Guili A. Feldman
Affiliation:
Department of Chemical Engineering, New York University
Howard Brenner
Affiliation:
Department of Chemical Engineering, New York University
Get access Rights & Permissions [Opens in a new window]

Abstract

The pressure drop ΔP created by the motion of a ‘small’ spherical particle settling along the axis of a large-diameter circular cylinder filled with a quiescent liquid was measured in the particle Reynolds number range (based on diameter) from Re = 0·2 to 21,000. For Re < 125 it was found that ΔPA/D = 2·0 (A = cylinder cross-sectional area; D = particle drag), in agreement with existing theory in the Stokes and Oseen regimes. Beyond Re = 125 a fairly abrupt transition occurs, the ΔPA/D ratio decreasing asymptotically towards 1·0, the limiting value predicted by elementary momentum principles for an ‘unbounded’ fluid, with increasing Re. At Re ≈ 6000 the transition is essentially complete.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 32 , Issue 4 , 18 June 1968 , pp. 705 - 720
Copyright
© 1968 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brenner, H. 1962 Dynamics of a particle in a viscous fluid Chem. Engng Sci. 17, 435.Google Scholar
Brenner, H. 1966 Hydrodynamic resistance of particles at small Reynolds numbers. Chapter 5 in Advances in Chemical Engineering, Volume 6 (T. B. Drew, J. W. Hoopes and T. Vermeulen, eds.), pp. 340, 396. New York: Academic Press.
Cox, R. G. & Brenner, H. 1968 The lateral migration of solid particles in Poiseuille flow: Part 1. Theory. Chem. Engng Sci. (in the Press).Google Scholar
Feldman, G. A. 1967 Experiments on the pressure drop created by a sphere settling in a liquid at Reynolds numbers up to 20,000. Ph.D. dissertation, New York University, Bronx, New York.
Fidleris, V. & Whitmore, R. L. 1961 Experimental determination of the wall effect for spheres falling axially in cylindrical vessels Br. J. Appl. Phys. 12, 490.Google Scholar
Haberman, W. L. & Sayre, R. M. 1958 Motion of rigid and fluid spheres in stationary and moving liquids inside cylindrical tubes. David Taylor Model Basin Rept no. 1143, U.S. Navy Dept., Washington, D.C.Google Scholar
Karnis, A., Goldsmith, H. L. & Mason, S. G. 1966 The flow of suspensions through tubes: V. Inertial effects. Canad. J. Chem. Engng. 44, 181.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics, p. 86. Reading, Massachusetts: Addison-Wesley.
Lapple, C. E. & Shepherd, C. B. 1940 Calculation of particle trajectories Industr. Engng Chem. 32, 605.Google Scholar
Maxworthy, T. 1965 Accurate measurements of sphere drag at low Reynolds numbers J. Fluid Mech. 23, 369.Google Scholar
Mcnown, J. S., Lee, H. M., Mcpherson, M. B. & Engez, S. M. 1948 Influence of boundary proximity on the drag of spheres. Proc. 7th Intern. Congr. Appl. Mech., London 1948, Vol. 2, Part I, p. 17. (Reprinted as State University of Iowa Reprints in Engineering, Reprint 81, Iowa City, Iowa.)Google Scholar
Perry, J. H. 1963 (editor) Chemical Engineers' Handbook, 4th edition, pp. 3–70 and 3–201. New York: McGraw-Hill.
Pliskin, I. & Brenner, H. 1963 Experiments on the pressure drop created by a sphere settling in a viscous liquid J. Fluid Mech. 17, 89.Google Scholar
Taneda, S. 1956 Experimental investigation of the wake behind a sphere at low Reynolds numbers J. Phys. Soc. Japan, 11, 1104.Google Scholar
Torobin, L. B. & Gauvin, W. H. 1959 Fundamental aspects of solids-gas flow. Part II. The sphere wake in steady laminar fluids Canad. J. Chem. Engng. 37, 167.Google Scholar