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Fluid friction describes the friction between layers of a viscous fluid that are moving relative to each other. [7] [8] Lubricated friction is a case of fluid friction where a lubricant fluid separates two solid surfaces. [9] [10] [11] Skin friction is a component of drag, the force resisting the motion of a fluid across the surface of a body.
Since the Painlevé paradoxes are based on a mechanical model of Coulomb friction, where the calculated friction force can have multiple values when the contact point has no tangential velocity, this is a simplified model of contact. It does, nevertheless, encapsulate the main dynamical effects of friction, such as sticking and slipping zones.
Jean Le Rond d'Alembert, Nouvelles expériences sur la résistance des fluides, 1777. In fluid dynamics, friction loss (or frictional loss) is the head loss that occurs in a containment such as a pipe or duct due to the effect of the fluid's viscosity near the surface of the containment.
First steps towards solving the paradox were made by Saint-Venant, who modelled viscous fluid friction. Saint-Venant states in 1847: [11] But one finds another result if, instead of an ideal fluid – object of the calculations of the geometers of the last century – one uses a real fluid, composed of a finite number of molecules and exerting in its state of motion unequal pressure forces or ...
This theory is exact for the situation of an infinite friction coefficient in which case the slip area vanishes, and is approximative for non-vanishing creepages. It does assume Coulomb's friction law, which more or less requires (scrupulously) clean surfaces. This theory is for massive bodies such as the railway wheel-rail contact.
As for friction, it is a result of both microscopic adhesion and chemical bond formation due to the electromagnetic force, and of microscopic structures stressing into each other; [3] in the latter phenomena, in order to allow motion, the microscopic structures must either slide one above the other, or must acquire enough energy to break one ...
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The reason why the form of the friction curve for liquid lubricated surfaces was later attributed to Stribeck – although both Thurston and Martens achieved their results considerably earlier – may be because Stribeck published his findings in the most important technical journal in Germany at that time, Zeitschrift des Vereins Deutscher ...