Applications of Lubrication Theory

In any case, the very important conclusion from (5-81) is that the leading-order approximation to the solution in the thin-film region always can be determined completely without the need to determine anything about the velocity field in the rest of the domain where the geometry is much more complicated. This constitutes a very considerable simplification When the lubrication approximation can be made, we need focus our attention on only the lubrication equations within the thin gap, and in this region the general solutions (5-74) and (5-79) have been worked out already. We shall see in the next section that the dominant contributions to the forces or torques acting on a body near a second boundary always occur in the lubrication layer when e C 1. 

In this section we consider the detailed analysis for two applications of lubrication theory the classic slider-block problem that was depicted in the previous section and the motion of a sphere toward an infinite plane wall when the sphere is very close to the wall. It is the usual practice in lubrication theory to focus directly on the motion in the thin gap using (5-69)-(5-72), or their solutions (5-74) and (5-79), without any mention of the asymptotic nature of the problem or of the fact that these equations (and their solutions) represent only a first approximation to the full solution in the lubrication layer. We adopt the same approach here but with the formal justification of the preceding section. 

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A second example of the application of lubrication theory is its use in analyzing the motion of a sphere that is pushed by the action of an applied force / toward a solid plane boundary, when the gap between the sphere and the wall at the point of closest approach is small compared with the radius of the sphere.6 Although this problem is geometrically similar to the slider block in the sense that a body of finite dimensions is moving in the vicinity of an infinite plane boundary, the problem differs in that the motion is normal to the boundary rather than parallel to it and the gap width is time dependent. 

Booser, E. R., (Ed.) Handbook of Lubrication Theory and Practice of Tribology, 1, Application and Maintenance, CRC Press, Boca Raton, USA (1982)... 

Booser, E. R., ed. 1983-1994. CRC Handbook of Lubrication (Theory and Practice of Tribology). Boca Raton, FL CRC Press. This three-volume set from CRC is somewhat odd in design in that volumes one and two were issued in 1983 and 1984, respectively, then volume three was issued in 1994 and covers new developments and updates to the field in the decade since publication of the original two volumes. Volume one focuses on application and maintenance, volume two on theory and design, and volume three on monitoring, materials, synthetic lubricants, and applications. 

Matsuoka, H., andKato, T., "An Ultral-thin Liquid Film Lubrication Theory—Calculation Method of Solvation Pressure and Its Application to the EHL Problem, Trans. ASME, J. Tribol, Vol. 119,1997, pp. 217-226. 

We are now ready to formulate a criterion for when lubrication theory is applicable. We assume that it is and obtain the total viscous dissipation. The shear traction at the base of the blob is then... 

O. Reynolds, On the theory of lubrication and its application to Mr. Beauchamp Tower s experiments, including an experimental determination of viscosity of olive oil, Philos. Trans. R. Soc. London, Ser. A, 177, 157-234, 1886. 

In the foregoing treatments of the methodology of film thickness determination, the experimental results have been examined with respect to lubrication theory rather than direct engineering application. Still, the ultimate utility of establishing the validity of a theoretical relation is practical to predict the engineering limits for the existence of a fluid film, which in turn can be confirmed or tested by laboratory experiments amenable to close control and measurement, e.g. rolling/ sliding disk experiments. To be useful from both a theoretical and a practical viewpoint, the validity and accuracy of the film thickness measurements must be established on a primary basis. 

The conditions in which slow reactions of relative simplicity become accessible to precise measurement are not normally obvious, and have to be discovered. Even when they have been found, the phenomena which become apparent would be, in the eyes of many, little more than curiosities. Nevertheless, the development of any phenomenon in time has a fascination of its own, and the laws which it follows have an attraction to those interested in the quantitative aspect of things. The application of the so-called law of mass action led to the idea of reaction order, and provided a basis for a rational classification of slow chemical changes. Examples of reactions of different orders were sought and found, and indeed the existence of this convenient system of grouping not infrequently led to the oversimplification of the real relations. But the obvious molecular explanation of the order in terms of collision probability did not fail to arouse interest in the statistical theory of reaction rates. Even so, an unconscious tendency to compare chemical changes with phenomena of viscous flow or movement under friction persisted, terms such as chemical resistance were endowed with a fictitious significance, and catalysts were likened to lubricants. 

Reynolds, Osborne. On the Theory of Lubrication and Its Application to Mr. BEAUCHAMP TOWER S Experiments, Including an Experimental determination of the Viscosity of Olive Oil. Phil. Trans. Roy. Soc. 1886, 177, 157-234 with one plate. 

WARD, J. Some notes on the theory of lubrication with particular application to Mlchell thrust and journal Bearings Proc. Institution of Marine Engineers, Vol. 36, pp. 141 - 185, 1924. 

To determine the oil film thickness width the sealing zone precisely practically and theoretically, however, they are assumed to exist from 0.1 to 1 m approximately. This suggests the necessity for application of the elastohydrodynamic lubrication theory of thin film considering surface roughness or for the starved lubrication theory. 

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