Abstract
The dynamics of fluid flow at the interface between elastic solids with rough surfaces depends sensitively on the area of real contact, in particular close to the percolation threshold, where an irregular network of narrow flow channels prevails. In this paper, numerical simulation and experimental results for the contact between elastic solids with isotropic and anisotropic surface roughness are compared with the predictions of a theory based on the Persson contact mechanics theory and the Bruggeman effective medium theory. The theory predictions are in good agreement with the experimental and numerical simulation results and the (small) deviation can be understood as a finite-size effect. The fluid squeeze-out at the interface between elastic solids with randomly rough surfaces is studied. We present results for such high contact pressures that the area of real contact percolates, giving rise to sealed-off domains with pressurized fluid at the interface. The theoretical predictions are compared to experimental data for a simple model system (a rubber block squeezed against a flat glass plate), and for prefilled syringes, where the rubber plunger stopper is lubricated by a high-viscosity silicon oil to ensure functionality of the delivery device. For the latter system we compare the breakloose (or static) friction, as a function of the time of stationary contact, to the theory prediction.
Similar content being viewed by others
References
N. Patir, H.S. Cheng, J. Tribol., Trans. ASME 100, 12 (1978).
N. Patir, H.S. Cheng, J. Tribol., Trans. ASME 101, 220 (1979).
J.A. Greenwood, J.B.P. Williamson, Proc. R. Soc. London, Ser. A 295, 300 (1966).
A.W. Bush, R.D. Gibson, T.R. Thomas, Wear 35, 87 (1975).
B.N.J. Persson, J. Phys.: Condens. Matter 20, 312001 (2008).
C. Campañá, M.H. Müser, M.O. Robbins, J. Phys.: Condens. Matter 20, 354013 (2008).
B.N.J. Persson, Phys. Rev. Lett. 99, 125502 (2007).
C. Yang, B.N.J. Persson, J. Phys.: Condens. Matter 20, 215214 (2008).
B. Lorenz, B.N.J. Persson, J. Phys.: Condens. Matter 201, 015003 (2009).
F. Sahlin, A. Almqvist, R. Larsson, S. Glavatskih, Tribol. Int. 40, 1025 (2007).
J.H. Tripp, ASME J. Lubrication Technol. 105, 485 (1983).
M. Scaraggi, B.N.J. Persson, G. Carbone, D. Dini, Soft Matter 7, 10395 (2011).
B.N.J. Persson, J. Phys.: Condens. Matter 22, 265004 (2010).
B.N.J. Persson, O. Albohr, U. Tartaglino, A.I. Volokitin, E. Tosatti, J. Phys.: Condens. Matter 17, R1 (2005).
D. Bruggeman, Ann. Phys. (Leipzig) 24, 636 (1935).
S. Kirkpatrick, Rev. Mod. Phys. 45, 574 (1973).
M. Sahimi Heterogeneous Materials I (Springer, New York, 2003).
B. Lorenz, B.N.J. Persson, Eur. Phys. J. E 31, 159 (2010).
B.N.J. Persson, J. Chem. Phys. 115, 3840 (2001).
B.N.J. Persson, Surf. Sci. Rep. 61, 201 (2006).
A. Almqvist, C. Campañá, N. Prodanov, B.N.J. Persson, J. Mech. Phys. Solids 59, 2355 (2011).
B. Lorenz, B.N.J Persson, J. Phys.: Condens. Matter 23, 355005 (2011).
B. Lorenz, B.N.J. Persson, Eur. Phys. J. E 32, 281 (2010).
W. Humphrey, A. Dalke, K. Schulten, J. Molec. Graph. 14, 33 (1996).
C. Yang, U. Tartaglino, B.N.J. Persson, Eur. Phys. J. E 19, 47 (2006).
M. Griebel, S. Knapek, G. Zumbusch, Numerical Simulation in Molecular Dynamics (Springer, Berlin, Heidelberg, 2007).
D.C. Rapaport, The Art of Molecular Dynamics Simulation, second edition (Cambridge University Press, Cambridge, 2004).
Y. Mo, K.T. Turner, I. Szlufarska, Nature 457, 1116 (2009).
J. Schmelzer Jr., S.A. Brown, A. Wurl, M. Hyslop, R.J. Blaikie, Phys. Rev. Lett. 88, 226802 (2002).
A.D. Pogrebnjak, A.P. Shpak, N.A. Azarenkov, V.M. Beresnev, Phys. Usp. 52, 29 (2009).
A. Kapitulnik, A. Aharony, G. Deutscher, D. Stauffer, J. Phys. A: Math. Gen. 16, L269 (1983).
W.J. Boudville, T.C. McGill, Phys. Rev. B 39, 369 (1989).
C. Vanneste, A. Gilabert, D. Sornette, Phys. Lett. A 155, 174 (1991).
A.I. Olemskoi, V.F. Klepikov, Phys. Rep. 338, 571 (2000).
B.A. Krick, J.R. Vail, B.N.J. Persson, W.G. Sawyer, Tribol. Lett. 45, 185 (2011).
B.N.J. Persson, Eur. Phys. J. E 8, 385 (2002).
N. Rathore, P. Pranay, B. Eu, W. Ji, E. Wallis, PDA J. Pharm. Sci. Tech. 65, 468 (2011).
S. Yamada, Tribol. Lett. 13, 167 (2002).
L. Bureau, Phys. Rev. Lett. 104, 218302 (2010).
B. Lorenz, B.N.J. Persson, S. Dieluweit, T. Tada, Eur. Phys. J. E 34, 129 (2011).
I. Sivebaek, V. Samoilov, B.N.J. Persson, Phys. Rev. Lett. 108, 036102 (2012).
B.N.J. Persson, F. Mugele, J. Phys.: Condens. Matter 16, R295 (2004).
B.N.J. Persson, C. Yang, J. Phys.: Condens. Matter 20, 315011 (2008).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Persson, B.N.J., Prodanov, N., Krick, B.A. et al. Elastic contact mechanics: Percolation of the contact area and fluid squeeze-out. Eur. Phys. J. E 35, 5 (2012). https://doi.org/10.1140/epje/i2012-12005-2
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2012-12005-2