A generalized Reynolds-type lubrication equation valid for arbitrary Knudsen numbers, defined as the ratio of the molecular mean free path to the film thickness, is derived from a linearized Boltzmann equation by semi-numerically calculating the flow rates of fundamental flows in the lubrication film: Poiseuille flow, Couette flow, and thermal creep flow. Numerical analysis of the equation for high Knudsen numbers reveals three principal results. First, Burgdorfer’s modified Reynolds equation featuring the first-order velocity slip boundary condition overestimates load carrying capacities, while the approximation equation including both the first- and second-order velocity slip boundary condition underestimates them. Second, since the flow rate of the Couette flow, which is independent of Knudsen numbers, becomes dominant as the bearing number increases, all the lubrication equation results tend toward the same asymptotic value for an infinite bearing number. Third, a new kind of load carrying capacity caused by thermal creep flow occurs if temperature gradients at the boundaries exist in the flow direction.

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This paper proposes the use of a Poiseuille flow rate database for rapid calculation of a generalized lubrication equation for high Knudsen number gas films. The database is created by numerical calculations based on the linearized Boltzmann equation. The proposed interpolation method is verified to reduce calculation time to several tenths of that required to perform rigorous calculations with the same accuracy.

Carbon films whose hardness is comparable to diamond’s, but whose electrical conductivity is 19 orders of magnitude larger, have been discovered. The films were deposited onto silicon substrates by electron cyclotron resonance plasma sputtering. The bonding structure of the film was mainly sp2. The film consisted of sp2 nanocrystallites having parallel and curved graphene sheets vertically oriented to the film surface. The sp2 nanocrystallites were connected with adjacent crystallites by sp3 bonding, which gives the film both its high hardness and conductivity. These sp2 nanocrystallite films will have many applications.