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Axisymmetric Stokes flows due to a rotlet or stokeslet near a hole in a plane wall: filtration flows

Published online by Cambridge University Press:  20 April 2006

A. M. J. Davis ,
M. E. O'Neill  and
H. Brenner
A. M. J. Davis
Affiliation:
Department of Mathematics, University College London, London WC1E 6BY, England
M. E. O'Neill
Affiliation:
Department of Mathematics, University College London, London WC1E 6BY, England
H. Brenner
Affiliation:
Department of Chemical Engineering, University of Rochester, Rochester, New York 14627, U.S.A.
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Abstract

The axially symmetric Stokes-flow problems occurring when a point source, rotlet or stokeslet is situated along the axis through the centre of a circular hole in a solid plane wall are examined. Exact solutions of the governing equations are obtained in terms of toroidal coordinates and their use in modelling the flows caused by a small particle translating and rotating near to a filter pore is considered. First-order expressions are derived for the effects of the wall and hole upon the hydrodynamic force and torque on the particle for situations in which the particle dimensions are small in comparison with its distance from the solid portion of the plane wall. The resulting expressions apply to any centrally symmetric particle, not necessarily axisymmetric. Finally, expressions are derived for the motion of a neutrally buoyant sphere suspended in a flow through a hole. It is demonstrated that such a particle will generally migrate across the streamlines of the undisturbed flow - away from or towards the symmetry axis of the flow, according as the particle is approaching or receding from the hole. Such migratory motion may be of importance in the flow of suspensions through orifices and stenoses.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 103 , February 1981 , pp. 183 - 205
Copyright
© 1981 Cambridge University Press

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References

Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16, 242–251.Google Scholar
Brenner, H. 1962a Effect of finite boundaries on the Stokes resistance of an arbitrary particle. J. Fluid Mech. 12, 35–48.Google Scholar
Brenner, H. 1962b Dynamics of a particle in a viscous fluid. Chem. Engng Sci. 17, 435–446.Google Scholar
Brenner, H. 1964a Effect of finite boundaries on the Stokes resistance of an arbitrary particle. II. Asymmetrical orientations. J. Fluid Mech. 18, 144–158.Google Scholar
Brenner, H. 1964b Slow viscous rotation of an axisymmetric body in a circular cylinder of finite length. Appl. Sci. Res. (ser. A) 13, 81–120.Google Scholar
Cox, R. G. & Brenner, H. 1967 Effect of finite boundaries on the Stokes resistance of an arbitrary particle. III. Translation and rotation. J. Fluid Mech. 28, 391–411.Google Scholar
Happel, J. & Brenner, H. 1973 Low Reynolds Number Hydrodynamics. Noordhoff-Sijthoff.
Jeffrey, G. B. 1915 On the steady rotation of a solid of revolution in a viscous fluid. Proc. Lond. Math. Soc. 14, 327–338.Google Scholar
Payne, L. E. & Pell, W. H. 1960 The Stokes flow problem of a class of axially symmetric bodies. J. Fluid Mech. 7, 520–549.Google Scholar
Schneider, J. C., O'neill, M. E. & Brenner, H. 1973 On the slow viscous rotation of a body straddling the interface between two immiscible semi-infinite fluids. Mathematika 20, 175–196.Google Scholar
Sneddon, I. N. 1966 Mixed Boundary Value Problems in Potential Theory. North-Holland.
Sonshine, R. M., Cox, R. G. & Brenner, H. 1966 The Stokes translation of a particle of arbitrary shape along the axis of a circular cylinder filled to a finite depth with viscous fluid. I. Appl. Sci. Res. 16, 273–300.Google Scholar