Skip to main content
×
Home
    • Aa
    • Aa

Particle motion in Stokes flow near a plane fluid–fluid interface. Part 2. Linear shear and axisymmetric straining flows

  • Seung-Man Yang (a1) and L. Gary Leal (a1)
Abstract

We consider the motion of a sphere or a slender body in the presence of a plane fluid–fluid interface with an arbitrary viscosity ratio, when the fluids undergo a linear undisturbed flow. First, the hydrodynamic relationships for the force and torque on the particle at rest in the undisturbed flow field are determined, using the method of reflections, from the spatial distribution of Stokeslets, rotlets and higher-order singularities in Stokes flow. These fundamental relationships are then applied, in combination with the corresponding solutions obtained in earlier publications for the translation and rotation through a quiescent fluid, to determine the motion of a neutrally buoyant particle freely suspended in the flow. The theory yields general trajectory equations for an arbitrary viscosity ratio which are in good agreement with both exact-solution results and experimental data for sphere motions near a rigid plane wall. Among the most interesting results for motion of slender bodies is the generalization of the Jeffrey orbit equations for linear simple shear flow.

Copyright
References
Hide All
Batchelor, G. K. 1970 Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44, 419.
Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16, 242.
Chwang, A. T. & Wu, T. Y-T. 1975 Hydrodynamics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows. J. Fluid Mech. 67, 787.
Cox, R. G. 1971 The motion of long slender bodies in a viscous fluid. Part 2. Shear flow. J. Fluid Mech. 45, 625.
Darabaner, C. L. & Mason, S. G. 1967 Particle motions in sheared suspensions. XXII: interactions of rigid sphere. Rheol. Acta 6, 273.
Dukhin, S. S. & Rulev, N. N. 1977 Hydrodynamic interaction between a solid spherical particle and a bubble in the elementary act of flotation. Colloid J. USSR 39, 270.
Faxén, H. 1921 Dissertation, Uppsala University.
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.
Goldman, A. J., Cox, R. G. & Brenner, H. 1967a Slow viscous motion of a sphere parallel to a plane wall. I. Motion through a quiescent fluid. Chem. Engng Sci. 22, 637.
Goldman, A. J., Cox, R. G. & Brenner, H. 1967b Slow viscous motion of a sphere parallel to a plane wall. II. Couette flow. Chem. Engng Sci. 22, 653.
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.
Jeffery, G. B. 1912 On a form of the solution of Laplace's equation suitable for problems relating to two spheres. Proc. R. Soc. Lond. A 87, 109.
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161.
Leal, L. G. 1975 The slow motion of slender rod-like particles in a second-order fluid. J. Fluid Mech. 69, 305.
Lee, S. H., Chadwick, R. S. & Leal, L. G. 1979 Motion of a sphere in the presence of a plane interface. Part 1. An approximate solution by generalization of the method of Lorentz. J. Fluid Mech. 93, 705.
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.
Lorentz, H. A. 1907 A general theory concerning the motion of a viscous fluid. Abhandl. Theor. Phys. 1, 23.
Spielman, L. A. 1977 Particle capture from low-speed laminar flows. Ann. Rev. Fluid Mech. 9, 297.
Wakiya, S. 1957 Viscous flows past a spheroid. J. Phys. Soc. Japan 12, 1130.
Yang, S.-M. & Leal, L. G. 1983 Particle motion in Stokes flow near a plane fluid—fluid interface. Part 1. Slender body in a quiescent fluid. J. Fluid Mech. 136, 393.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 21 *
Loading metrics...

Abstract views

Total abstract views: 156 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 22nd October 2017. This data will be updated every 24 hours.