Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-09T05:56:07.804Z Has data issue: false hasContentIssue false
  • English
  • Français

Particle motion in Stokes flow near a plane fluid-fluid interface. Part 1. Slender body in a quiescent fluid

Published online by Cambridge University Press:  20 April 2006

Seung-Man Yang  and
L. Gary Leal
Seung-Man Yang
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125
L. Gary Leal
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125
Get access Rights & Permissions [Opens in a new window]

Abstract

The present study examines the motion of a slender body in the presence of a plane fluid–fluid interface with an arbitrary viscosity ratio. The fluids are assumed to be at rest at infinity, and the particle is assumed to have an arbitrary orientation relative to the interface. The method of analysis is slender-body theory for Stokes flow using the fundamental solutions for singularities (i.e. Stokeslets and potential doublets) near a flat interface. We consider translation and rotation, each in three mutually orthogonal directions, thus determining the components of the hydrodynamic resistance tensors which relate the total hydrodynamic force and torque on the particle to its translational and angular velocities for a completely arbitrary translational and angular motion. To illustrate the application of these basic results, we calculate trajectories for a freely rotating particle under the action of an applied force either normal or parallel to a flat interface, which are relevant to particle sedimentation near a flat interface or to the processes of particle capture via drop or bubble flotation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 136 , November 1983 , pp. 393 - 421
Copyright
© 1983 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

Aderogba, K. & Blake, J. R. 1978 Action of a force near the planar surface between two semi-infinite immiscible liquids at very low Reynolds’ numbers Bull. Austral. Math. Soc. 18, 345.Google Scholar
Batchelor, G. K. 1970 Slender-body theory for particles of arbitrary cross-section in Stokes flow J. Fluid Mech. 44, 419.Google Scholar
Berdan, C. & Leal, L. G. 1982 Motion of a sphere in the presence of a deformable interface. I. Perturbation of the interface from flat: the effect on drag and torque. J. Colloid Interface Sci. 87, 62.Google Scholar
Cox, R. G. 1970 The motion of long slender bodies in a viscous fluid. Part 1. General theory. J. Fluid Mech. 44, 419, 791.Google Scholar
Cox, R. G. 1971 The motion of long slender bodies in a viscous fluid. Part 2. Shear flow J. Fluid Mech. 45, 625.Google Scholar
Fulford, G. R. & Blake, J. R. 1983 On the motion of a slender body near an interface between two immiscible liquids at very low Reynolds number J. Fluid Mech. 127, 203.Google Scholar
Goren, S. L. & O'NEILL, M. E. 1971 On the hydrodynamic resistance to a particle of a dilute suspension when in the neighborhood of a large obstacle Chem. Engng Sci. 26, 325.Google Scholar
Happel, J. & Brenner, H. 1973 Low Reynolds Number Hydrodynamics. Noordhoff.
Johnson, R. 1980 An improved slender-body theory for Stokes flow J. Fluid Mech. 99, 411.Google Scholar
Johnson, R. E. & Wu, T. Y. 1979 Hydrodynamics of low-Reynolds-number flow. Part 5. Motion of a slender torus J. Fluid Mech. 95, 263.Google Scholar
Keller, J. B. & Rubinow, S. I. 1976 Slender-body theory for slow viscous flow J. Fluid Mech. 75, 705.Google Scholar
Lee, S. H., Chadwick, R. S. & Leal, L. G. 1979 Motion of a sphere in the presence of a plane interface. Part 1. An approximation solution by generalization of the method of Lorentz J. Fluid Mech. 93, 705.Google Scholar
Lee, S. H. & Leal, L. G. 1980 Motion of a sphere in the presence of a plane interface. Part 2. An exact solution in bipolar coordinates J. Fluid Mech. 98, 193.Google Scholar
Lee, S. H. & Leal, L. G. 1982 The motion of a sphere in the presence of a deformable interface. II. A numerical study of the translation of a sphere normal to an interface J. Colloid Interface Sci. 87, 81.Google Scholar
Russel, W. B., Hinch, E. J., Leal, L. G. & Tieffenbruck, G. 1977 Rods falling near a vertical wall J. Fluid Mech. 83, 273.Google Scholar
Tillett, J.P. K. 1970 Axial and transverse Stokes flow past slender axisymmetric bodies J. Fluid Mech. 44, 401.Google Scholar
Tuck, E. O. 1964 Some methods for flows past blunt slender bodies J. Fluid Mech. 18, 619.Google Scholar
Supplementary material: PDF

Yang and Leal supplementary material

Supplementary Appendix

Download Yang and Leal supplementary material(PDF)
PDF 804.4 KB