Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T09:05:44.422Z Has data issue: false hasContentIssue false
  • English
  • Français

On the sedimentation of a sphere in a centrifuge

Published online by Cambridge University Press:  29 March 2006

Isom H. Herron ,
Stephen H. Davis  and
Francis P. Bretherton
Isom H. Herron
Affiliation:
Department of Mechanics and Materials Science, The Johns Hopkins University, Baltimore, Maryland 21218 Present address: Department of Mathematics, Howard University, Washington, D.C. 20059.
Stephen H. Davis
Affiliation:
Department of Mechanics and Materials Science, The Johns Hopkins University, Baltimore, Maryland 21218
Francis P. Bretherton
Affiliation:
Department of Mechanics and Materials Science, The Johns Hopkins University, Baltimore, Maryland 21218 Present address: National Center for Atmospheric Research, Boulder, Colorado 80302.
Get access Rights & Permissions [Opens in a new window]

Abstract

The flow field about a small, slowly sedimenting particle in a centrifuge is examined using matched asymptotic expansions. The near field is dominated by Stokes flow while in the far field a non-axisymmetric cubical conical structure (a viscously modified Taylor column) is found. This far field induces a Coriolis modification in the near field leading to Coriolis corrections to the Stokes drag law. The Coriolis modification of the predicted molecular weight (if the particle were a molecule) of a small particle is calculated. The analysis is applied to an unbounded fluid as well as to a fluid bounded between parallel plates oriented normal to the rotation vector. In the latter case the governing equations for the rotating fluid are posed as a self-adjoint system of partial differential equations and solved using (symmetric) Green's matrices.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 68 , Issue 2 , 25 March 1975 , pp. 209 - 234
Copyright
© 1975 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

Berman, A. S. 1966 J. Nat. Cancer Inst. Monograph, 21, 41.
Blake, J.R. 1971 Proc. Camb. Phil. Soc. 70, 303.
Bowen, T. J. 1970 An Introduction to Ultracentrifugation. Interscience.
Bretherton, F. P. 1967 J. Fluid Mech. 28, 545.
Ckeng, P. Y. & Schachman, H. K. 1955 J. Polymer Sci. 16, 19.
Childress, S. 1964 J. Fluid Mech. 20, 305.
COX, R. G. & Brenner, H. 1967 J. Fluid Mech. 28, 391.
Faxén, H. 1922 Ann. Phys. 68, 89.
Friedman, B. 1956 Principles and Techniques of Applied Mathematics. Wiley.
Fujita, H. 1962 The Mathematical Theory of Sedimentation Analysis. Academic.
Gel'fand, I. M. & Shilov, G. E. 1964 Generalized Functions, vol. 1. Academic.
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Hooyman, G. J., Holtan, H., Mazur, P. & DE Groot, S. R. 1953 Physica, 19, 1095.
Ince, E. L. 1926 Ordinary Differential Equations. Longmans.
Kaplun, S. & Lagerstrom, P. A. 1957 J. Math. Mech. 6, 585.
Langford, D. 1968 J. Appl. Mech. 35, 683.
Moore, D. W. & Saffman, P. G. 1969 J. Fluid Mech. 39, 831.
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. McGraw-Hill.
Saffman, P. G. 1965 J. Fluid Mech. 22, 385.
Scrachman, H. K. 1959 Ultracentrifugation in Biochemistry. Academic.
Sharp, D. G. & Beard, J. W. 1950 J. Biol. Chem. 185, 247.
Stewartson, K. 1957 J. Fluid Mech. 3, 17.
Taylor, G. I. 1923 Proc. Roy. Soc. A 104, 213.