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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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