Skip to main content
Log in

Hydrodynamic interaction of rough spheres

  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract.

The approach of two spheres along their line of centres is analyzed assuming that each sphere is covered by a porous layer. The slip of the fluid at the surface of the porous layers then permits the spheres to touch without a singularity in the associated force. In a corresponding analysis for flat surfaces, an analytical formula for the force is obtained. This force is also finite for vanishing gap width. It is shown how the properties of the porous layers can be related to the statistics of spatial distributions of surface asperities. Finally, it is emphasised that a finite force is associated with a finite asperity height.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Gelbard, F., Mondy, L.A., Ohrt, S.E.: A new method for determining hydrodynamic effects on the collision of two spheres. J. Stat. Phys. 62, 945–960 (1991)

    Google Scholar 

  2. Zeng, S., Kerns, E.T., Davis, R.H.: The nature of particle contacts in sedimentation. Phys. Fluids 8, 1389–1396 (1996)

    Google Scholar 

  3. Davis, R.H.: Effects of surface roughness on a sphere sedimenting through a dilute suspension of neutrally buoyant spheres. Phys. Fluids A 4(12), 2607–2619 (1992)

    Google Scholar 

  4. Wilson, H.J., Davis, R.H.: The viscosity of a dilute suspension of rough spheres. J. Fluid Mech. 421, 339–367 (2000)

    Google Scholar 

  5. Leighton, D., Acrivos, A.: The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 177, 109–131 (1987)

    Google Scholar 

  6. Acrivos, A., Batchelor, G.K., Hinch, E.J., Koch, D.L., Mauri, R.: Longitudinal shear-induced diffusion of spheres in dilute suspension. J. Fluid Mech. 240, 651–657 (1992)

    Google Scholar 

  7. McTigue, D.F., Jenkins, J.T.: Channel Flow of a concentrated suspension. In: Shen, H.H. (ed.), Advances in Micromechanics of Granular Materials, Elsevier, New York, 1992, pp. 381–390

  8. Nott, P.R., Brady, J.F.: Pressure driven flow of suspensions: Simulation and theory. J. Fluid Mech. 275, 157–199 (1994)

    Google Scholar 

  9. Da Cunha, F.R., Hinch, E.J.: Shear-induced dispersion in a dilute suspension of rough spheres. J. Fluid Mech. 309, 211–223 (1996)

    Google Scholar 

  10. Kim, S., Karrila, S.J.: Microhydrodynamics: principles and selected applications. Butterworth-Heineman, Boston (1991)

  11. Smart, J.R., Leighton, D.T.: Measurement of the hydrodynamic surface roughness of non-colloidal spheres. Phys. Fluids A 1(1), 52–60 (1989)

    Google Scholar 

  12. Patir, N., Cheng, H.S.: An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication. Journal of Lubrication Technology 100, 12–17 (1978)

    Google Scholar 

  13. Saffman, P.G.: On the boundary condition at the surface of a porous medium. Studies in Applied Mathematics L(2), 93–101 (1971)

    Google Scholar 

  14. Vasin, S.I., Starov, V.M., Filippov, A.N.: The motion of a solid spherical particle covered with a porous layer in a liquid. Colloid Journal 58(1), 282–290 (1996)

    Google Scholar 

  15. Landau, L.D., Lifschitz, E.M.: Lehrbuch der theoretischen Physik. VI Hydrodynamik, Akademie Verlag, Berlin (1981)

  16. Wells, J., Tsuji, Y.: Modelling normal collision of rough elastic spheres in liquid. Proc JSME Kansai Branch Meeting, Kobe, Japan, February, 1994, pp. 1–3

  17. Lamb, H.: Hydrodynamics 6th ed, Cambridge University Press, London (1975)

  18. Thompson, P.A., Troian, S.M.: A general boundary condition for liquid flow at solid surfaces. Nature 389, 360–362 (1997)

    Google Scholar 

  19. Cheng, J.T., Giordano, N.: Fluid flow through nanometer-scale channels. Phys. Rev. E 65, 031206 (2002)

    Google Scholar 

  20. Britsanis, I., Magda, J.J., Tirrell, M., Davis, H.T.: Molecular dynamics of flow in micropores. J. Chem. Phys. 87(3), 1733–1750 (1987)

    Google Scholar 

  21. Travis, K.P., Gubbins, K.E.: Poiseuille flow of Leonard-Jones fluids in narrow slit pores. J. Chem. Phys. 112(4), 1984–1994 (2000)

    Google Scholar 

  22. Sherwood, J.D.: The force on a sphere pulled away from a permeable half-space. Physicochemical Hydrodynamics 10(1), 3–12 (1988)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jenkins, J., Koenders, M. Hydrodynamic interaction of rough spheres. Granular Matter 7, 13–18 (2005). https://doi.org/10.1007/s10035-004-0193-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10035-004-0193-7

Keywords

Navigation