Journal of Engineering Mathematics

, Volume 8, Issue 1, pp 23–29 | Cite as

Fundamental singularities of viscous flow

Part I: The image systems in the vicinity of a stationary no-slip boundary
  • J. R. Blake
  • A. T. Chwang


The image system for the fundamental singularities of viscous (including potential) flow are obtained in the vicinity of an infinite stationary no-slip plane boundary. The image system for a: stokeslet, the fundamental singularity of Stokes flow; rotlet (also called a stresslet), the fundamental singularity of rotational motion; a source, the fundamental singularity of potential flow and also the image system for a source-doublet are discussed in terms of illustrative diagrams. Their far-fields are obtained and interpreted in terms of singularities. Both the stokeslet and rotlet have similar far field characteristics: for force or rotational components parallel to the wall a far-field of a stresslet typeO(r−2) is obtained, whereas normal components are of higher orderO(r−3).


Mathematical Modeling Image System Industrial Mathematic Rotational Motion Normal Component 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    G. K. Batchelor, Stress system in a suspension of force-free particles,J. Fluid Mech., 41 (1970) 545–570.ADSMATHMathSciNetGoogle Scholar
  2. [2]
    J. R. Blake, A note on the image system for a stokeslet in a no-slip boundary,Proc. Camb. Phil. Soc., 70 (1971) 303–310.MATHGoogle Scholar
  3. [3]
    J. Blake, A model for the micro-structure in ciliated organisms,J. Fluid Mech., 55 (1972) 1–23.ADSMATHGoogle Scholar
  4. [4]
    A. T. Chwang and T. Y. Wu, A note on the helical movements of micro-organisms,Proc. Roy. Soc., B178 (1971) 327–346.ADSGoogle Scholar
  5. [5]
    J. Happel and H. Brenner,Low Reynolds Number Hydrodynamics, Prentice Hall, Englewood Cliffs, N.J. (1965).Google Scholar
  6. [6]
    H. Lamb,Hydrodynamics, Cambridge and Dover (1932).Google Scholar
  7. [7]
    L. D. Landau and E. M. Lifshitz,Fluid Mechanics, Pergamon, N.Y. (1959).Google Scholar
  8. [8]
    H. A. Lorentz,Zittingsverlag. Akad. v. Wet., 5 (1896) 168–182.MATHGoogle Scholar
  9. [9]
    C. W. Oseen,Hydrodynamik, Leipzig (1927).Google Scholar

Copyright information

© Noordhoff International Publishing 1974

Authors and Affiliations

  • J. R. Blake
    • 1
  • A. T. Chwang
    • 1
  1. 1.Engineering Science DepartmentCalifornia Institute of TechnologyPasadena(U.S.A.)

Personalised recommendations