Abstract
The flow between rough surfaces in sliding motion with contacts between these surfaces, is analyzed through the volume averaging method. Assuming a Reynolds (lubrication) approximation at the roughness scale, an average flow model is obtained combining spatial and time average. Time average, which is often omitted in previous works, is specially discussed. It is shown that the effective transport coefficients, traditionally termed ‘flow factors’ in the lubrication literature, that appear in the average equations can be obtained from the solution to two closure problems. This allows for the numerical determination of flow factors on firmer bases and sheds light on some arguments to the literature. Moreover, fluid flows through fractures form an important subset of problems embodied in the present analysis, for which macroscopisation is given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adler, P. M. and Brenner, H.: 1985, Spatially periodic suspensions of convex particles in linear shear flows i., Int. J. Multiphase Flow 11(3), 361–385.
Adler, P. M., Zukovsky, M. and Brenner, H.: 1985, Spatially periodic suspensions of convex particles in linear shear flows ii., Int. J. Multiphase Flow 11, 387–417.
Adler, P. M. and Thovert, J. F.: 1999, Fractures and Fracture Network, Kluwer Academic Publishers.
Bayada, G. and Chambat, M.: 1988, New models in the theory of the hydrodynamic lubrication of rough surfaces, J. Tribology 110, 402–407.
Bayada, G. and Faure, J. B.: 1989, A double scale analysis approach of the reynolds roughness. comments and application to the journal bearing, J. Tribol. 111, 323–330.
Chow, L. S. H. and Cheng, H. S.: 1976, The effect of surface roughness on the average film thickness between lubricated rollers, J. Lubric. Technol. 98, 117–124.
Christensen, H.: 1970, Stochastic models for hydrodynamics lubrication of rough surfaces, Int. J. Mech. Eng. 104, 1022–1033.
Elrod, H. G.: 1979, A general theory for laminar lubrication with reynolds roughness, J. Lubric. Technol. 101, 8–14.
Frankel, T.: 1997, The Geometry of Physics: An Introduction, Cambridge University Press.
Gray, W. G.: 1993, Mathematical Tools for Changing Spatial Scales in the Analysis of Physical Systems, CRC Press.
Gray, W. R.: 1975, A derivation of the equations for multiphase transport, Chem. Eng. Sci. 30, 229–233.
Howes, S. and Whitaker, S.: 1985, The spatial averaging theorem revisited, Chem. Eng. Sci. 40, 1387–1392.
Knoll, G., Rienacker, A., Lagemann, V. and Lechtape-Gruter, R.: 1998, Effect of contact deformation on flow factors, J. Tribology 120, 140–142.
Letalleur, N., Plouraboué, F. and Prat, M.: 2000, Average flow model of rough surface lubrication: Flow factors for sinusoidal surfaces, submitted to J. of Tribology.
Lunde, L. and Tonder, K.: 1997, Numerical simulation of the effects of three-dimensional roughness on hydrodynamic lubrication: Correlation coefficients, J. Tribology 119, 315–322.
Mei, C. C. and Auriault, J. L.: 1989, Mechanics of heterogeneous porous media with several spatial scales, Proc. Roy. Soc. A. 426(91).
Quintard, M. and Whitaker, S.: 1994, Transport in ordered and disordered porous media v:geometrical results for two-dimensional systems, Transport in Porous Media 15, 183–196.
Patir, N. and Cheng, H. S.: 1978, An average flow model for determining effects of three dimensional roughness on partial hydrodynamic lubrication, J. Lubric. Technol. 100, 12–17.
Patir, N. and Cheng, H. S.: 1979, Application of average flow model to lubrication between rough sliding surfaces, J. Lubric. Technol. 101, 220–229.
Peeken, H. J., Knoll, G., Rienacker, A., Lang, J. and Schonen, R.: 1997, On the numerical determination of flow factors, J. Tribology 119, 259–264.
Quintard, M. and Whitaker, S.: 1987, Ecoulement monophasique en milieu poreux:effet des heterogeneites locales, J. de Mecanique Theorique et Appliquée 6, 691–726.
Whitaker, S.: 1999, The Method of Volume Averaging, Kluwer Academic Punlishers.
Teale, J. L. and Lebeck, A. O.: 1980, An evaluation of the average flow model for surface roughness effects in lubrication, J. Lubric. Technol. 102, 360–367.
Tripp, J. H.: 1983, Surface roughness effects in hydrodynamic lubrication: the flow factor method, J. Lubric. Technol. 105, 458–465.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Prat, M., Plouraboué, F. & Letalleur, N. Averaged Reynolds Equation for Flows between Rough Surfaces in Sliding Motion. Transport in Porous Media 48, 291–313 (2002). https://doi.org/10.1023/A:1015772525610
Issue Date:
DOI: https://doi.org/10.1023/A:1015772525610