# Thermo-molecular gas-film lubrication (t-MGL) considering temperature distributions and accommodation coefficients: analyses by quasi-free-molecular t-MGL equation

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## Abstract

In the present paper, the air-bearing characteristics of a fixed plane inclined slider (Case 1) and a step slider flying in either air or He (Case 2) over a running boundary wall with local temperature distributions and imperfect surface accommodation coefficients, the molecular reflections at the surface of which are a mixture of diffuse reflection (*α*) and specular reflection (1−*α*) (Maxwell-type reflection), are analyzed using the thermo-molecular gas-film lubrication (t-MGL) equation. In particular, since the minimum spacing is ultra-small (~ 1 nm), the quasi-free-molecular t-MGL equation, in which the gas temperature, *τ*_{G}, is assumed to be that in the free molecular limit, *τ*_{Gfm}, defined by temperatures and accommodation coefficients at the disk, *τ*_{W0} and *α*_{0}, respectively, and those at the slider, *τ*_{W1} and *α*_{1}, respectively, is used. For a plane inclined slider (Case 1), the fundamental static and dynamic characteristics are analyzed numerically and are compared with the approximation results for an infinite bearing number (t-MGL_{qfm}, _{Λ→∞}). When the spacing is ultra-small and only the running boundary (disk) has a local temperature distribution, the additional static pressure produced by the local boundary temperature distribution is approximately proportional to the equivalent accommodation coefficient \( \gamma_{\alpha } \equiv \alpha_{0} (2 - \alpha_{1} )/[2\{ 1 - (1 - \alpha_{0} )(1 - \alpha_{1} )\} ] \). For a step slider (Case 2), the following results are revealed: (1) the spacing decreases occur as the accommodation coefficient of the disk, *α*_{0}, decrease *i.e*., the ratio of specular reflection at the disk increases, (2) the increases in the minimum spacing due to local temperature distribution are negligible in both air and He because the heat spot size is very small, (3) the decreases in the minimum spacing for a slider flying in He are significant, and (4) the spacing fluctuation caused by a running wavy disk varies according to both the surface accommodation coefficients and the ambient gas (air/He) and can be estimated precisely.

## Notes

## References

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