Skip to main content
SpringerLink
Log in

A Deterministic Approach to Studying Liquid-Mediated Adhesion Between Rough Surfaces

  • Original Paper
  • Published:
Tribology Letters Aims and scope Submit manuscript

Abstract

In this work, a numerical method is developed to study the liquid-mediated adhesion between 3D rough surfaces. The presence of a wetting liquid between two rough surfaces generates a negative pressure inside the liquid film, which in turn induces tensile stresses in the contact region. Opposing these tensile stresses are the compressive stresses generated at solid–solid contact spots. An iterative deterministic contact model based on influence coefficients is employed to solve the equations of elasticity and capillarity simultaneously. Results for tensile (adhesive) force, wetted radius, average gap, and contact area between the rough surfaces are obtained. The results show that sudden changes in tensile force, average gap, and contact area occur with an increase in certain parameters, suggesting an elasto-capillary instability and surface collapse.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Abbreviations

a :

Radius of pressurized region (Eq. 8)

A n :

Nominal contact area between two rough surfaces

A r :

Real contact area between two rough surfaces

A *r :

Normalized contact area

C ijmn :

Influence coefficients

d :

Distance between rigid flat and mean of undeformed rough surface

Δp :

Capillary pressure drop

Δx :

Grid spacing in x direction

Δy :

Grid spacing in y direction

E :

Elastic modulus

\(E^{\prime }\) :

Reduced or effective elastic modulus

F c :

Compressive force between rough surfaces

F t :

Tensile force between rough surfaces

\(F_{\text{t}}^{*}\) :

Normalized tensile force

γ :

Surface tension of liquid

Γ :

Adhesion parameter

h fs :

Surface separation at the free surface of the liquid

\(\bar{h}\) :

Average surface separation

h * :

Normalized average surface separation

l c :

Correlation length

L :

Scan lengths in x and y directions

N :

Number of nodal points in x and y directions

υ :

Poisson’s ratio

p :

Pressure

p ij :

Nodal pressure

P :

External load applied to rough surfaces

P * :

Normalized external load

r w :

Radius of wetted region

R I,II :

Principal radii of curvature at the free surface of the liquid

σ :

Root mean square of rough surface heights

θ A,B :

Contact angles between the liquid and rough surfaces

u :

Surface deformation

u ij :

Nodal surface deformation

V 0 :

Liquid volume

V *0 :

Normalized liquid volume

z 0ij :

Nodal surface height of undeformed surface

z ij :

Nodal surface height of deformed surface

References

  1. Adamson, A.W., Gast, A.P.: Physical chemistry of surfaces. (1967)

  2. Bhushan, B., Dugger, M.: Liquid-mediated adhesion at the thin film magnetic disk/slider interface. ASME J. Tribol 112, 217–223 (1990)

    Article  Google Scholar 

  3. Yang, S.H., Nosonovsky, M., Zhang, H., Chung, K.-H.: Nanoscale water capillary bridges under deeply negative pressure. Chem. Phys. Lett. 451(1), 88–92 (2008)

    Article  Google Scholar 

  4. Yang, S.H., Zhang, H., Nosonovsky, M., Chung, K.-H.: Effects of contact geometry on pull-off force measurements with a colloidal probe. Langmuir 24(3), 743–748 (2008)

    Article  Google Scholar 

  5. Grobelny, J., Pradeep, N., Kim, D.-I., Ying, Z.: Quantification of the meniscus effect in adhesion force measurements. Appl. Phys. Lett. 88(9), 091906 (2006)

    Article  Google Scholar 

  6. Rabinovich, Y.I., Esayanur, M.S., Johanson, K.D., Adler, J.J., Moudgil, B.M.: Measurement of oil-mediated particle adhesion to a silica substrate by atomic force microscopy. J. Adhes. Sci. Technol. 16(7), 887–903 (2002)

    Article  Google Scholar 

  7. Rabinovich, Y.I., Adler, J.J., Esayanur, M.S., Ata, A., Singh, R.K., Moudgil, B.M.: Capillary forces between surfaces with nanoscale roughness. Adv. Colloid Interface Sci. 96(1), 213–230 (2002)

    Article  Google Scholar 

  8. Rabinovich, Y.I., Esayanur, M.S., Moudgil, B.M.: Capillary forces between two spheres with a fixed volume liquid bridge: theory and experiment. Langmuir 21(24), 10992–10997 (2005)

    Article  Google Scholar 

  9. Tian, H., Matsudaira, T.: The role of relative humidity, surface roughness and liquid build-up on static friction behavior of the head/disk interface. J. Tribol. 115(1), 28–35 (1993)

    Article  Google Scholar 

  10. Matthewson, M.J.: Adhesion of spheres by thin liquid films. Philos. Mag. A 57(2), 207–216 (1988)

    Article  Google Scholar 

  11. Zheng, J., Streator, J.L.: A micro-scale liquid bridge between two elastic spheres: deformation and stability. Tribol. Lett. 15(4), 453–464 (2003)

    Article  Google Scholar 

  12. Zheng, J., Streator, J.: A liquid bridge between two elastic half-spaces: a theoretical study of interface instability. Tribol. Lett. 16(1–2), 1–9 (2004)

    Article  Google Scholar 

  13. Megias-Alguacil, D., Gauckler, L.J.: Capillary forces between two solid spheres linked by a concave liquid bridge: regions of existence and forces mapping. AIChE J. 55(5), 1103–1109 (2009)

    Article  Google Scholar 

  14. Matthewson, M.J., Mamin, H.J.: Liquid mediated adhesion of ultra-flat solid surfaces. In: MRS Proceedings, vol. 119, pp. 87–92 (1988)

  15. Poon, C.Y., Bhushan, B.: Numerical contact and stiction analyses of Gaussian isotropic surfaces for magnetic head slider/disk contact. Wear 202(1), 68–82 (1996)

    Article  Google Scholar 

  16. Tian, X., Bhushan, B.: The micro-meniscus effect of a thin liquid film on the static friction of rough surface contact. J. Phys. D Appl. Phys. 29(1), 163 (1996)

    Article  Google Scholar 

  17. Streator, J.: A model of mixed lubrication with capillary effects. Tribol. Ser. 40, 121–128 (2002)

    Article  Google Scholar 

  18. Persson, B.: Capillary adhesion between elastic solids with randomly rough surfaces. J. Phys.: Condens. Matter 20(31), 315007 (2008)

    Google Scholar 

  19. Streator, J.L., Jackson, R.L.: A model for the liquid-mediated collapse of 2-D rough surfaces. Wear 267(9), 1436–1445 (2009)

    Article  Google Scholar 

  20. Streator, J.L.: A model of liquid-mediated adhesion with a 2D rough surface. Tribol. Int. 42(10), 1439–1447 (2009)

    Article  Google Scholar 

  21. Rostami, A., Streator, J.L.: Study of liquid-mediated adhesion between 3D rough surfaces: a spectral approach. Tribol. Int. 84, 36–47 (2015). doi:10.1016/j.triboint.2014.11.019

    Article  Google Scholar 

  22. Rostami, A., Streator, J.L.: A model for capillary flow between rough surfaces. STLE annual meeting (2014)

  23. Jackson, R.L., Streator, J.L.: A multi-scale model for contact between rough surfaces. Wear 261(11), 1337–1347 (2006)

    Article  Google Scholar 

  24. Rostami, A., Jackson, R.L.: Predictions of the average surface separation and stiffness between contacting elastic and elastic–plastic sinusoidal surfaces. Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol. 227(12), 1376–1385 (2013)

    Article  Google Scholar 

  25. Johnson, K.: Contact Mechanics, 1985. Cambridge University Press, Cambridge (1974)

    Google Scholar 

  26. Love, A.E.H.: The stress produced in a semi-infinite solid by pressure on part of the boundary. Philos. Trans. R. Soc. London. Ser. A, Contain. Pap. Math. Phys. Charact. 228, 377–420 (1929)

  27. Webster, M., Sayles, R.: A numerical model for the elastic frictionless contact of real rough surfaces. J. Tribol. 108(3), 314–320 (1986)

    Article  Google Scholar 

  28. Garcia, N., Stoll, E.: Monte Carlo calculation for electromagnetic-wave scattering from random rough surfaces. Phys. Rev. Lett. 52(20), 1798 (1984)

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the National Science Foundation (NSF) for support of this work.

Author information

Authors and Affiliations

  1. G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Amir Rostami & Jeffrey L. Streator

Authors
  1. Amir Rostami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jeffrey L. Streator
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amir Rostami.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rostami, A., Streator, J.L. A Deterministic Approach to Studying Liquid-Mediated Adhesion Between Rough Surfaces. Tribol Lett 58, 2 (2015). https://doi.org/10.1007/s11249-015-0497-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11249-015-0497-2

Keywords

Search

Navigation