Physics of lubricated impact of a sphere on a plate in a narrow continuum to gaps of molecular dimensions

This paper investigates the phenomenon of lubricated impact dynamics of ellipsoidal bodies upon semi-infinite elastic solids, giving rise to Hertzian contact conditions. The analysis conforms to the numerical predictions and experimental findings of others, when the physics of motion of the lubricant can be described through Newtonian continuum mechanics, with the dominant viscous action embodied in the transient solution of Reynolds' equation. The equivalence of squeeze film action under impacting conditions with that of a converging gap in pure entraining motion is shown. This concept is extended to study the accelerative nature of the lubricant film surface, and its concordance with Reynolds' assumption through use of a relativistic frame of reference and hyperbolic geometry. When the investigation is extended to the case of ultra-thin film conjunctions of the order of a few to several molecular diameters of the intervening fluid layer, the physics of fluid film motion through impact involves more complex kinetic interactions. These include the effect of structural force of solvation, as well as that of a meniscus force, formed in such narrow conjunctions. The former, through active dispersion, tends to promote a structureless environment, whilst the latter through wetting action encourages the formation of a coherent film. This paper shows the interplay between these competing kinetics.

[1]  B. Derjaguin,et al.  Untersuchungen über die Reibung und Adhäsion, IV , 1934 .

[2]  Roland Larsson,et al.  Elastohydrodynamic Lubrication at Impact Loading , 1994 .

[3]  M. Lozada-Cassou,et al.  A simple theory for the force between spheres immersed in a fluid , 1986 .

[4]  E. Lifshitz.  The theory of molecular attractive forces between solids , 1956 .

[5]  R. Larsson,et al.  Numerical Simulation of a Ball Impacting and Rebounding a Lubricated Surface , 1995 .

[6]  R. Evans,et al.  Liquids at interfaces: what can a theorist contribute? , 1990 .

[7]  I. Snook,et al.  Solvent structure and solvation forces between solid bodies , 1979 .

[8]  B. Bhushan,et al.  A Meniscus Model for Optimization of Texturing and Liquid Lubrication of Magnetic Thin-Film Rigid Disks , 1995 .

[9]  H. D. Conway,et al.  Impact of a Lubricated Surface by a Sphere , 1975 .

[10]  Hertz.  On the Contact of Elastic Solids , 1882 .

[11]  Shizhu Wen,et al.  Experimental method for quantitative analysis of transient EHL , 1991 .

[12]  Duncan Dowson,et al.  An analysis of the normal bouncing of a solid elastic ball on an oily plate , 1994 .

[13]  Derek Y. C. Chan,et al.  The drainage of thin liquid films between solid surfaces , 1985 .

[14]  D. Dowson,et al.  A Numerical Solution to the Elasto-Hydrodynamic Problem , 1959 .

[15]  Homer Rahnejat,et al.  Ultra-thin lubricating films under transient conditions , 2001 .

[16]  W. Russel,et al.  Simplified predictions of hamaker constants from Lifshitz theory , 1988 .

[17]  R. Gohar,et al.  Oil Film Thickness and Pressure Distribution in Elastohydrodynamic Point Contacts , 1982 .

[18]  H. Matsuoka.  An Ultrathin Liquid Film Lubrication Theory. Calculation Method of Solvation Pressure and its Application to the EHL Problem , 1995 .

[19]  H. Rahnejat,et al.  Nano-lubricant film formation due to combined elastohydrodynamic and surface force action under isothermal conditions , 2001 .

[20]  W. 0. Winer,et al.  Correlational Aspects of the Viscosity-Temperature-Pressure Relationship of Lubricating Oils(Dr In dissertation at Technical University of Delft, 1966) , 1966 .

[21]  H. Cheng,et al.  The Pressure and Deformation Profiles Between Two Normally Approaching Lubricated Cylinders , 1973 .

[22]  Lubricant Entrapment between Approaching Elastic Solids , 1967, Nature.

[23]  H. Matsuoka,et al.  Discrete Nature of Ultrathin Lubrication Film Between Mica Surfaces , 1996 .

[24]  E. Verwey,et al.  Theory of the stability of lyophobic colloids : the interaction of sol particles having and electric double l layer , 1948 .

[25]  Patricia McGuiggan,et al.  Measurements of and Relation Between the Adhesion and Friction of Two Surfaces Separated by Molecularly Thin Liquid Films , 1989 .

[26]  P. Tarazona,et al.  A model for density oscillations in liquids between solid walls , 1985 .

[27]  H. Christensen,et al.  The oil film in a closing gap , 1960, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[28]  H. Christensen,et al.  Elastohydrodynamic Theory of Spherical Bodies in Normal Approach , 1970 .

[29]  Shizhu Wen,et al.  The Behavior of Non-Newtonian Thermal EHL Film in Line Contacts at Dynamic Loads , 1992 .

[30]  The squeeze-film lubrication of ellipsoids , 1992 .

[31]  J. Israelachvili,et al.  Direct measurement of structural forces between two surfaces in a nonpolar liquid , 1981 .

[32]  B. Bhushan.  Contact mechanics of rough surfaces in tribology: multiple asperity contact , 1998 .

[33]  Duncan Dowson,et al.  Elastohydrodynamic Lubrication of Elliptical Contacts for Materials of Low Elastic Modulus I—Fully Flooded Conjunction , 1978 .

[34]  R. Gohar,et al.  Pressure Distribution Under a Ball Impacting a Thin Lubricant Layer , 1986 .