Abstract
This paper investigates the axisymmetric sedimentation of a small slowly rotating and translating particle through a fluid-filled circular pore of finite length which communicates with two half-space chambers of fluid. In the quasi-steady Stokes approximation the particle is modelled by either a rotlet or Stokeslet, and potential-theoretic methods are used to reduce each problem to the solution of coupled infinite systems of linear equations. The numerical solutions of these sets of equations are used to compute approximations to the resistive torque and drag experienced by the particle.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. Shail and B.A. Packham, Some potential problems associated with the sedimentation of a small particle into a semi-infinite fluid-filled pore, IMA J. Appl. Math. 37 (1986) 37–66.
H. Brenner, Effect of finite boundaries on the Stokes resistance of an arbitrary particle, J. Fluid Mech. 12 (1962) 35–48.
A.M.J. Davis, M.E. O'Neill and H. Brenner, Axisymmetric Stokes flows due to a rotlet or Stokeslet near a hole in a plane wall: filtration flows, J. Fluid Mech. 103 (1981) 183–205.
Z. Dagan, S. Weinbaum and R. Pfeffer, An infinite-series solution for creeping motion through an orifice of finite length, J. Fluid Mech. 115 (1982) 505–523.
L.M. Keer, A class of non-symmetrical punch and crack problems, Q. Jl. Mech. Appl. Math. 17 (1964) 420–436.
H. Brenner, Slow viscous rotation of an axisymmetric body within a cylinder of finite length, Appl. Sci. Res. A 13 (1964) 81–120.
M.R. Hestenes and E. Stiefel, Method of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards 49 (1952) 404–436.
D. Shanks, Non-linear transformations of divergent and slowly convergent sequences, J. Math. Phys. 34 (1955) 1–42.
A.E. Green and W.A. Zerna, Theoretical Elasticity, Oxford, Clarendon Press (1954).
I.N. Sneddon, Mixed Boundary Value Problems in Potential Theory, Amsterdam, North Holland (1966).
R.M. Sonshine, R.C. Cox and H. Brenner, The Stokes translation of a particle of arbitrary shape along the axis of a circular cylinder filled to a finite depth with viscous liquid I, Appl. Sci. Res. 16 (1966) 273–300.
W.E. Williams, Boundary effects in Stokes flow, J. Fluid Mech. 24 (1966) 285–291.
R. Shail and B.A. Packham, Some asymmetric Stokes flow problems, J. Engng. Mathematics 21 (1987) 331–348.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shail, R., Warrilow, I.M. The sedimentation of a small particle through a fluid-filled pore of finite length. J Eng Math 22, 355–382 (1988). https://doi.org/10.1007/BF00058514
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00058514