Asymptotic Analysis of Ultra-Thin Gas Squeeze Film Lubrication for Infinitely Large Squeeze Number (Extension of Pan’s Theory to the Molecular Gas Film Lubrication Equation)

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Abstract
Ultra-thin gas squeeze film characteristics are analyzed by extending Pan’s asymptotic theory for infinite squeeze number to the molecular gas film lubrication equation which was derived from the linearized Boltzmann equation and is valid for arbitrary Knudsen numbers. The generalized asymptotic method is shown to solve the boundary value equation which contains the flow rate coefficient as a function of the product of pressure P and film thickness H. Numerical results are obtained for a circular squeeze film. The PH ratio and the load carrying capacity ratio to those of continuum flow both decrease when the average film thickness is less than several microns because of molecular gas effects.