Skip to main content
SpringerLink
Log in

A polar fluid estimate of relative force

Eine Polarflüssigkeitsschätzung der Relativkraft

  • Contributed Papers
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

A general expression for the relative force on a fluid's microstructure is derived. It is shown that for polar fluids this force reduces to the lateral force proposed by Segré and Silberberg to cause the migration of a suspended particle.

Zusammenfassung

Für die Relativkraft auf der Mikrostruktur einer Flüssigkeit wird eine allgemeine Beziehung angegeben. Es wird gezeigt, daß sich diese Kraft für Polarflüssigkeiten auf die von Segré und Silberberg vorgeschlagene seitliche Kraft, die den Zug eines suspendierten Partikels verursacht, reduziert.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kline, K.A.: Predictions from polar fluid theory which are independent of spin boundary condition. Trans. Soc. Rheol.19, 139 (1975).

    Google Scholar 

  2. Karnis, A., Goldsmith, H. L., Mason, S. G.: The kinetics of flowing dispersions. I. Concentrated suspensions of rigid particles. J. Colloid Interface Sci.22, 531 (1966).

    Google Scholar 

  3. Segré, G., Silberberg, A.: Behavior of macroscopic rigid spheres in Poiseuille flow. Part 1. Determination of local concentration by statistical analysis of particle passages through crossed light beams. J. Fluid Mech.14, 115 (1962).

    Google Scholar 

  4. Segré, G., Silberberg, A.: Behavior of macroscopic rigid spheres in Poiseuille flow. Part 2. Experimental results and interpretation. J. Fluid Mech.14, 136 (1962).

    Google Scholar 

  5. Takano, M., Goldsmith, H. L., Mason, S. G.: The flow of suspensions through tubes. VIII. Radial migration of particles in pulsatile flow. J. Colloid Interface Sci.27, 253 (1968).

    Google Scholar 

  6. Ho, B. P., Leal, L. G.: Inertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech.65, 365 (1974).

    Google Scholar 

  7. Cox, R. G., Brenner, H.: The lateral migration of solid particles in Poiseuille flow-I Theory. Chem. Engng. Sci.23, 147 (1968).

    Google Scholar 

  8. Popel, A. S., Regirer, S. A., Usick, P. I.: A continuum model of blood flow. Biorheology11, 427 (1974).

    Google Scholar 

  9. Allen, S. J., DeSilva, C. N., Kline, K. A.: A theory of simple deformable directed fluids. Phys. Fluids10, 2551 (1967).

    Google Scholar 

  10. Eringen, A. C.: Simple microfluids. Int. J. Engng. Sci.2, 205 (1964).

    Google Scholar 

  11. Eringen, A. C., Suhubi, E. S.: Nonlinear theory of simple micro-elastic solids. Int. J. Engng. Sci.2, 189 (1964).

    Google Scholar 

  12. Mindlin, R. D.: Micro-structure in linear elasticity. Arch. Rat. Mech. Anal.16, 51 (1964).

    Google Scholar 

  13. Kline, K. A.: The Reynolds-Orr energy equation, with applications to the stability of polar fluid motions. Trans. Soc. Rheol.14, 335 (1970).

    Google Scholar 

  14. Allen, S. J., Kline, K. A.: Fluid suspensions: Flow near an oscillating plate. Trans. Soc. Rheol.14, 39 (1970).

    Google Scholar 

  15. Brenner, H.: Annual Review of Fluid Mechanics 2, p. 137 (van Dyke, M., Vincenti, W. G., eds.), Palo Alto, California: Annual Reviews, Inc. 1970.

    Google Scholar 

  16. Nikolaevskii, V. N., Afanasiev, E. F.: On some examples of media with microstructure of continuous particles. Int. J. Solids Structures5, 671 (1969).

    Google Scholar 

  17. Karnis, A., Goldsmith, H. L., Mason, S. G.: The flow of suspensions through tubes. V. Inertial effects. Can. J. Chem. Engng.44, 181 (1966).

    Google Scholar 

  18. Kline, K. A., Allen, S. J.: Concentration effects in oscillatory blood flow. Biorheology6, 99 (1969).

    Google Scholar 

  19. Womersley, J. R.: Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J. Physiol.127, 553 (1955).

    Google Scholar 

  20. Halow, J. S., Wills, G. B.: Radial migration of spherical particles in Couette systems. A.I.Ch.E.J.16, 281 (1970).

    Google Scholar 

  21. Halow, J. S., Wills, G. B.: Experimental observations of sphere migration in Couette systems. Ind. Eng. Chem. Fund.9, 603 (1970).

    Google Scholar 

  22. Cowin, S. C., Pennington, C. J.: On the steady rotational motion of polar fluids. Rheol. Acta9, 307 (1970).

    Google Scholar 

  23. Serrin, J.: On the stability of viscous fluid motions. Arch. Ratl. Mech. Anal.3, 1 (1959).

    Google Scholar 

  24. Batchelor, G. K.: An Introduction to Fluid Dynamics. London: Cambridge University Press. 1967.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering Sciences, Wayne State University, 48202, Detroit, MI, USA

    K. A. Kline & T. K. Sandberg

Authors
  1. K. A. Kline
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. K. Sandberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

With 9 Figures

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kline, K.A., Sandberg, T.K. A polar fluid estimate of relative force. Acta Mechanica 26, 201–222 (1977). https://doi.org/10.1007/BF01177147

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01177147

Keywords

Search

Navigation