This solution immediately shows the major relations within the HL theory (but they also remain qualitatively true in elastohydrodynamic theory as well). Absence of the elastic deformations simplifies the problem as compared to EHL theory, but allows one to construct some important analytical solutions as will be shown further. It differs from elastohydrodynamic lubrication theory (EHL) due to negligible elastic deformation of the surfaces.

Derivation of Reynolds equation and possible solution methods are given here.

This equation carries his name and forms a foundation of the lubrication theory. Reynolds published famous equation of thin fluid film flow in the narrow gap between two solids ( Reynolds 1886). History of lubrication theory goes more than a century back to 1886 when O. Lubricant Film (From: Lubrication for Industry, by Ken Bannister, Industrial Press) Read further about the lubricant definition here. Most of the lubricants contain additives (5-30%) to improve their performance. A lubricant can be in liquid (oil, water, etc.), solid (graphite, graphene, molybdenum disulfide), gaseous (air) or even semisolid (grease) forms. Depending on its nature, lubricants are also used to eliminate heat and wear debris, supply additives into the contact, transmit power, protect, seal. Lubricant is a substance which is used to control (more often to reduce) friction and wear of the surfaces in a contact of the bodies in relative motion. The theory is developed within a field known as tribology.

This film separates the surfaces from direct contact and it in general reduces friction and consequently wear (but not always), since friction within the lubricant is less than between the directly contacting solids. The goal of hydrodynamic lubrication is to add a proper lubricant, so that it penetrates into the contact zone between rubbing solids and creates a thin liquid film, as shown in the figure below. Even mirror shining surfaces are composed of hills and valleys – surface roughness. For a vast majority of the surfaces encountered in nature and used in industry, the source of friction is the imperfections of the surfaces. This situation is often beneficial and lubrication is used to reduce friction and/or wear of rubbing solids with the aid of liquid (or semi-solid) lubricant. Hydrodynamic lubrication is a term that defines a situation in which two rubbing surfaces are separated by a thin film of a lubricant. Definition of Hydrodynamic Lubrication (HL)

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