DOI: 10.1017/s0022112071002854. A new technique for treating multiparticle slow viscous flow: axisymmetric flow past spheres and spheroids

A new technique for treating multiparticle slow viscous flow: axisymmetric flow past spheres and spheroids

10.1017/s0022112071002854

Crossref journal-article

Cambridge University Press (CUP)

Journal of Fluid Mechanics (56)

Abstract

This paper is the first in a series of investigations having the overall objective of developing a new technique for treating the slow viscous motion past finite assemblages of particles of arbitrary shape. The new method, termed the multi-pole representation technique, is based on the theory that any object conforming to a natural co-ordinate system in a particle assemblage can be approximated by a truncated series of multi-lobular disturbances in which the accuracy of the representation is systematically improved by the addition of higher order multipoles. The essential elements of this theory are illustrated by examining the flows past finite line arrays of axisymmetric bodies such as spheres and spheroids which conform to special natural co-ordinate systems. It is demonstrated that this new procedure converges more rapidly and is simpler to use than the method of reflexions and represents the desired boundaries more precisely than the point-force approximation even when the objects are touching one another. Comparison of these solutions with the exact solutions of Stimson & Jeffery (1926) for the two sphere problem demonstrates the rapidity of convergence of this multipole procedure even when the spheres are touching. Drag results are also presented for flows past chains containing up to 101 spheres as well as for chains containing up to 15 prolate or oblate spheroids. The potential value of the technique is suggested by the rapidity with which the drag calculations were made, the 101 sphere problem requiring about 10 seconds on an IBM 360–65 computer to determine both the fluid flow and the drag coefficient.

Bibliography

Gluckman, M. J., Pfeffer, R., & Weinbaum, S. (1971). A new technique for treating multiparticle slow viscous flow: axisymmetric flow past spheres and spheroids. Journal of Fluid Mechanics, 50(4), 705â740.

Authors 3

Michael J. Gluckman (first)
Robert Pfeffer (additional)
Sheldon Weinbaum (additional)

References 29 Referenced 145

Wakiya, S. 1965 J. Phys. Soc. Japan,20 (8),1502.
O'Brien, V. 1968 A.I.Ch.E. J. 14 (6), 870.
Slack, G. W. & Matthews, H. W. 1961 Porton Tech. Paper, Chemical Defence Exptl. Establishment, Porton, no. 797.
Burgers, J. M. 1940 Proc. Konigl. Akad. Wetenschap. (Amsterdam), 43,425,646.
Gluckman, M. J. , Weinbaum, S. & Pfeffer, R. 1971a A new technique for treating slow viscous flows: axisymmetric flow past arbitrary bodies of revolution. To be published. (10.1017/S0022112071002854)
Stimson, M. & Jeffery, O. B. 1926 Proc. Roy. Soc. A 111,110.
Broersma, S. 1960 J. Chem. Phys. 32,1632.
Davis, M. H. 1969 Chem. Engng. Sci. 24,1769.
Mcnown, J. S. & Lin, P. N. 1952 Proc. Second Midwestern Conf. Fluid Mech. Iowa State University. Reprint in Eng. 109.
Faxen, H. 1927 Z. angew. Math. Mech. 7,79.
Chen, T. C. & Skalak, R. 1970 Appl. Sci. Res. 22,403.
Goldman, A. J. , Cox, R. G. & Brenner, H. 1966 Chem. Engng. Sci. 21,1151.
Gluckman, M. J. , Pfeffer, R. & Weinbaum, S. 1971b A theoretical analysis of three spheres falling along their line of centres in an infinite viscous fluid. To be published.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics .Prentice-Hall.
Dean, W. R. & O'Neill, M. E. 1963 Mathematika,10,13.
Wang, H. & Skalak, R. 1969 J. Fluid Mech. 38,75.
Faxen, H. (with appendix by Dahl)1925 Ark. Mat. Astr. Fys. 19A, no. 13.
Burgers, J. M. 1942 Proc. Konigl. Akad. Wetenschap. (Amsterdam),45,9.
Burgers, J. M. 1938 Second Report on Viscosity and Plasticity. Amsterdam:North Holland Publishing Co.
Kynch, G. J. 1959 J. Fluid Mech. 5,193.
Sampson, R. A. 1891 Phil. Trans. Roy. Soc. A 182,449.
Tam, C. K. W. 1969 J. Fluid Mech. 38,537.
Payne, L. E. & Pell, W. H. 1960 J. Fluid Mech. 7,529.
Savic, P. 1953 Nat. Res. Counc. Canada Rep. no. MT-22.
Haberman, W. L. & Sayre, R. M. 1958 David W. Taylor model basin Rep. no. 1143, Washington, D.C.
Smoluchowski, M. 1912 Proc. Fifth Int. Cong. Math. 2,192.
Burgers, J. M. 1941 Proc. Konigl. Wetenschap. (Amsterdam),44,1045.
Smoluchowski, M. 1911 Bull Int. Acad. Polonaise Sci. Lett. 1A, 28.
Tchen, C. 1954 J. Appl. Phys. 25,463.

Dates

Type	When
Created	19 years, 5 months ago (March 29, 2006, 6:08 a.m.)
Deposited	6 years, 2 months ago (May 31, 2019, 3:32 p.m.)
Indexed	2 weeks, 3 days ago (Aug. 12, 2025, 5:39 p.m.)
Issued	53 years, 8 months ago (Dec. 29, 1971)
Published	53 years, 8 months ago (Dec. 29, 1971)
Published Online	19 years, 5 months ago (March 29, 2006)
Published Print	53 years, 8 months ago (Dec. 29, 1971)

Funders 0

None

BibTeX

@article{Gluckman_1971, title={A new technique for treating multiparticle slow viscous flow: axisymmetric flow past spheres and spheroids}, volume={50}, ISSN={1469-7645}, url={http://dx.doi.org/10.1017/s0022112071002854}, DOI={10.1017/s0022112071002854}, number={4}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={Gluckman, Michael J. and Pfeffer, Robert and Weinbaum, Sheldon}, year={1971}, month=dec, pages={705–740} }

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