Comparison of the Models for Multiscale Elastohydrodynamic Lubrication in a Line Contact

Document Type : Regular Article


1 School of Mechanics Technology, Wuxi Institute of Technology, Wuxi, Jiangsu Province, China

2 College of Mechanical Engineering, Changzhou University, Changzhou, Jiangsu Province, China



Two models are compared for calculating the surface separation in a multiscale elastohydrodynamic lubricated line contact for the same operating conditions. In the studied line contact, the surface separation is very low so that the effect of the adsorbed boundary layer is significant. Model I principally takes the continuum fluid film as intervening between the two adsorbed boundary layers. Model II takes the continuous phase transition both along the flow direction and across the whole surface separation; in this model, in the Hertzian contact zone there is only the adsorbed boundary layer, while in most of the inlet zone there is only the continuum fluid film (by neglecting the adsorbed boundary layer). The analytical results show that for the same case these two models give the close surface separations. The equivalence of these two models is shown.


Atkas, O. and N. R. Aluru (2002). A combined continuum/DSMC technique for multiscale analysis of microfluidic filters. Journal of Computational Physics 178, 342-372.##
Blake, T. D. and J. M. Haynes (1969). Kinetics of liquid/liquid displacement. Journal of Colloid and Interface Science 30, 421-423.##
Begelinger, A. and A. W. J. Gee de (1974). Thin film lubrication of sliding point contacts of AISI 52100 steel. Wear 28, 103-114.##
Begelinger, A. and A. W. J. Gee de (1976). On the mechanism of lubricant film failure in sliding concentrated steel contacts. Journal of Tribology 98(4), 575.##
Chan, D. Y. C. and R. G. Horn (1985). The drainage of thin liquid films between solid surfaces. Journal of Chemical Physics 83, 5311-5324.##
Gohar, R. and A. Cameron (1963). Optical measurement of oil film thickness under elasto-hydrodynamic lubrication. Nature 200, 458-459.##
Grubin, A. N. (1949). Fundamentals of the hydrodynamic theory of lubrication of heavily loaded cylindrical surfaces, in Kh. F. Ketova (Ed.). Central Scientific Research Institute for Technology and Mechanical Engineering, D.S.I.R. London Translations, Wellington 337, 115.##
Johnston, G. J., R. Wayte and H. A. Spikes (1991). The measurement and study of very thin lubricant films in concentrated contacts. Tribology Transactions 34, 187-194.##
Kalker, J. J. (1972). On elastic line contacts. Journal of Applied Mechanics 39, 1125-1132.##
Karim, A. M. and H. P. Kavehpour (2015). Dynamics of spreading on ultra-hydrophobic surfaces. Journal of Coating Technology Research 12, 959-964.##
Karim, A. M., S. H. Davis and H. P. Kavehpour (2016). Forced versus spontaneous spreading of liquids. Langmuir 32, 10153-10158.##
Karim, A. M., J. P. Rothstein and H. P. Kavehpour (2018). Experimental study of dynamic contact angles on rough hydrophobic surfaces. Journal of Colloid and Interface Science 518, 658-665.##
Karim, A. M., K. Fujii and H. P. Kavehpour (2021). Contact line dynamics of gravity driven spreading of liquids. Fluid Dynamics Research 53, 035503.##
Petrov, P. G. and J. G. Petrov (1992). A combined molecular-hydrodynamic approach to wetting kinetics. Langmuir 8, 1762-1767.##
Pinkus, O. and B. Sternlicht (1961). Theory of hydrodynamic lubrication. McGraw-Hill, New York.##
Yen, T. H., C. Y. Soong and P. Y. Tzeng (2007). Hybrid molecular dynamics-continuum simulation for nano/mesoscale channel flows. Microfluidics and Nanofluidics 3, 665-675.##
Zhang, Y. B., K. Tang and G. S. Lu (2003). Model of elastohydrodynamic lubrication with molecularly thin lubricating films: Part I-Development of analysis. International Journal of Fluid Mechanics Research 30, 542-557.##
Zhang, Y. B. and G. S. Lu (2003). Model of elastohydrodynamic lubrication with molecularly thin lubricating films: Part II-Results for an exemplary lubrication. International Journal of Fluid Mechanics Research 30, 558-571.##
Zhang, Y. B. (2016). The flow equation for a nanoscale fluid flow. International Journal of Heat and Mass Transfer 92, 1004-1008.##
Zhang, Y. B. (2020). Modeling of flow in a very small surface separation. Applied Mathematical Modelling 82, 573-586.##
Zhang, Y. B. (2021a). Multiscale mixed hydrodynamics in line contacts, Continuum Mechanics and Thermodynamics,
Zhang, Y. B. (2021b). Multiscale hydrodynamics in line contacts. Mechanics Research Communications 111, 103658.##