DOI: 10.1017/s0022112075001486. Stokes flow past a particle of arbitrary shape: a numerical method of solution

Stokes flow past a particle of arbitrary shape: a numerical method of solution

10.1017/s0022112075001486

Crossref journal-article

Cambridge University Press (CUP)

Journal of Fluid Mechanics (56)

Abstract

The problem of determining the slow viscous flow of an unbounded fluid past a single solid particle is formulated exactly as a system of linear integral equations of the first kind for a distribution of Stokeslets over the particle surface. The unknown density of Stokeslets is identical with the surface-stress force and can be obtained numerically by reducing the integral equations to a system of linear algebraic equations. This appears to be an efficient way of determining solutions for several external flows past a particle, since it requires that the matrix of the algebraic system be inverted only once for a given particle.The technique was tested successfully against the analytic solutions for spheroids in uniform and simple shear flows, and was then applied to two problems involving the motion of finite circular cylinders: (i) a cylinder translating parallel to its axis, for which the local stress force distribution and the drag were determined; and (ii) the equivalent axis ratio of a freely suspended cylinder, which was calculated by determining the couple on a stationary cylinder placed symmetrically in two different simple shear flows. The numerical results were found to be consistent with the asymptotic analysis of Cox (1970, 1971) and in excellent agreement with the experiments of Anczurowski & Mason (1968), but not with those of Harris & Pittman (1975).

Bibliography

Youngren, G. K., & Acrivos, A. (1975). Stokes flow past a particle of arbitrary shape: a numerical method of solution. Journal of Fluid Mechanics, 69(2), 377â403.

Authors 2

G. K. Youngren (first)
A. Acrivos (additional)

References 30 Referenced 410

Taylor, T. D. & Acrivos, A. 1964 The Stokes flow past an arbitrary particle – the slightly deformed sphere Chem. Engng Sci. 19,445.
Rosen, A. L. 1972 A computational algorithm for the Stokes problem. I. Methodology J. Inst. Math. Appl. 9,265. (10.1093/imamat/9.3.265)
Payne, L. E. & Pell, W. H. 1960 The Stokes flow problem for a class of axially symmetric bodies J. Fluid Mech. 7,529. (10.1017/S002211206000027X)
Odqvist, F. K. G. 1930 Rüber die Randwertaufgaben der Hydrodynamik Zräher Flrüssigkeiten Math. Z. 32,329. (10.1007/BF01194638)
O'BRIEN, V. 1968 Form factors for deformed spheroids in Stokes flow A.I.Ch.E. J. 14,870.
Oberbeck, A. J. 1876 Rüber stationräre Flrüssigkeitsbewgungen mit Berücksichtigung der inner Reibung J. reine angew. Math. 81,62.
Kantorovich, L. V. & Krylov, V. I. 1958 Approximate Methods of Higher Analysis ,Interscience.
Hunt, B. H. 1968 Numerical solution of an integral equation for flow from a circular orifice J. Fluid Mech. 31,361. (10.1017/S0022112068000200)
Nir, A. & Acrivos, A. 1973 On the creeping motion of two arbitrary-sized touching spheres in a linear shear field J. Fluid Mech. 59,209. (10.1017/S0022112073001527)
GÜNTER, N. M. 1967 Potential Theory and Its Application to Basic Problems of Mathematical Physics .Ungar.
Goldsmith, H. L. & Mason, S. G. 1967 The microrheology of dispersions. In Rheology (ed. Eirich ),pp.85–250.Academic. (10.1016/B978-1-4832-2941-6.50008-8)
Gluckman, M. J. , Weinbaum, S. & Pfeffer, R. 1972 Axisymmetric slow viscous flow past an arbitrary convex body of revolution J. Fluid Mech. 55,677. (10.1017/S0022112072002083)
Finlayson, B. A. 1972 The Method of Weighted Residuals and Variational Principles .
Cox, R. G. 1971 The motion of long slender bodies in a viscous fluid. Part 2. Shear flow J. Fluid Mech. 45,625. (10.1017/S0022112071000259)
Chang, Y. P. , Kang, C. S. & Chen, D. J. 1973 The use of fundamental Green's functions for the solution of problems of heat conduction in anisotropic media Int. J. Heat Mass Transfer,16,1905. (10.1016/0017-9310(73)90208-1)
Brenner, H. 1966 Hydrodynamic resistance of particles Adv. in Chem. Eng. 6,287. (10.1016/S0065-2377(08)60277-X)
Brenner, H. 1964b The Stokes resistance of an arbitrary particle. III. Shear fields.Chem. Engng Sci. 19,631. (10.1016/0009-2509(64)85052-1)
Brenner, H. 1964a The Stokes resistance of a slightly deformed sphere.Chem. Engng Sci. 19,519. (10.1016/0009-2509(64)85045-4)
Bowen, B. D. & Masliyah, J. H. 1973 Drag force on isolated axisymmetric particles in Stokes flow Can. J. Chem. Engng,51,8.
Anczurowski, E. & Mason, S. G. 1968 Particle motions in sheared suspensions. IV. Rotation of rigid spheroids and cylinders Trans. Soc. Rheol. 12,209. (10.1122/1.549106)
Ladyzhenskaya, O. A. 1963 The Mathematical Theory of Viscous Incompressible Flow .Gordon & Breach.
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid.Proc. Roy. Soc. A102,161. (10.1098/rspa.1922.0078)
Smith, A. M. O. & Hess, J. L. 1966 Calculation of potential flow about arbitrary bodies Prog. Aero. Sci. 8,1. (10.1016/0376-0421(67)90003-6)
Lamb, H. 1932 Hydrodynamics .Cambridge University Press.
Harris, J. B. & Pittman, J. F. T. 1975 Equivalent ellipsoidal axis ratios of slender rod-like particles J. Colloid Interface Sci. 50,280. (10.1016/0021-9797(75)90231-3)
Cruse, T. A. 1969 Numerical solutions in three-dimensional elastostatics Int. J. Solids Struct. 5,1259. (10.1016/0020-7683(69)90071-7)
Cox, R. G. 1970 The motion of long slender bodies in a viscous fluid. Part 1. General theory J. Fluid Mech. 44,791. (10.1017/S002211207000215X)
Sampson, R. A. 1891 On Stokes's current function.Phil. Trans. A182,449. (10.1098/rsta.1891.0012)
Stokes, G. G. 1851 On the effect of the internal friction of fluids on pendulums Trans. Camb. Phil. Soc. 9,8.
Batchelor, G. K. 1970 Slender-body theory for particles of arbitrary cross-section in Stokes flow J. Fluid Mech. 44,419. (10.1017/S002211207000191X)

Dates

Type	When
Created	19 years, 5 months ago (March 29, 2006, 3:59 a.m.)
Deposited	6 years, 4 months ago (April 17, 2019, 9:45 a.m.)
Indexed	1 month ago (Aug. 6, 2025, 9:32 a.m.)
Issued	50 years, 3 months ago (May 27, 1975)
Published	50 years, 3 months ago (May 27, 1975)
Published Online	19 years, 5 months ago (March 29, 2006)
Published Print	50 years, 3 months ago (May 27, 1975)

Funders 0

None

BibTeX

@article{Youngren_1975, title={Stokes flow past a particle of arbitrary shape: a numerical method of solution}, volume={69}, ISSN={1469-7645}, url={http://dx.doi.org/10.1017/s0022112075001486}, DOI={10.1017/s0022112075001486}, number={2}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={Youngren, G. K. and Acrivos, A.}, year={1975}, month=may, pages={377–403} }

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