Application of Theory of Super Lubricity of Minimum Entropy Welding

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From the viewpoint of mechanical engineering, the bacterial flagellar motor has several interesting features ; it rotates at a maximum speed of 17,000 HZ, and the diameter of the rotor is about 50 nm. In nature, the driving system using rotational motion is found only in single-celled organisms bacteria, while beating motion dominates the non-bacterial world.Since life chooses the more efficient mechanism in the process of evolution, it is interesting to know the reasons why bacteria chose rotational motion rather than beating motion.On the other hand, motors are widely used as driving systems in engineering. When we consider the difficulty of lubrication in microtribology which occurs in a world as small as bacteria, knowledge about the f1agellar motor will be useful to solve the problems.In the 20th century, tribology and lubrication engineering on the macroscale have reached a paradigm that most of the solid frictions in engineering can be well described by Coulomb-Amonton's law and … More that the best strategy of lubrication is fluid film lubrication. Here, deviations from Coulomb's law such as the friction of rubber or super-lubricity are considered to be exceptional cases.Now, entering the 21st century, the circumstances around tribology are drastically changing. Since the paradigm is not always applicable to newly emerging areas such as microtribology, we have to employ some other paradigms for friction and lubrication.In microtribology, friction between ideal crystalline surfaces may sometimes occur. Molecular forces would play an essential role in this kind of friction. Therefore, Coulomb's law is not powerful anymore ; as it is an experimental rule for solid friction. Molecular forces affect the behavior of liquids in molecularly thin liquid films. When thin film viscosity (or a viscosity rise) is duced by molecular forces, the fluid film lubrication method will not be the best anymore. Until now, we have not obtained enough knowledge about the lubrication in micromachines.In the flagellar motor of some bacterial species, there is a bushing, called the PL ring, which allows the rotating shaft to penetrate the rigid cell wall. The existence of the PL ring suggests that our classical method of lubrication might be still valid in microtribology. In a recent study, we calculated parameters in the tribology of the PL ring using theory of the classical hydrodynamic lubrication and the parameter values in thin film viscosity. The results showed that the friction values thus calculated are too high to operate the motor at high speeds, indicating invalidity of the classical method.In this study, we show that the ordinary theory for hydrodynamic lubrication is not an adequate tool for analysis of lubrication in the PL ring. We also calculate the scale invariance of the Stokes equation and consider other possible lubrication mechanisms. Less