Nonlocal formulation of the Reynolds equation for rarefied gas flow with steep pressure variation

The current formulation of the Reynolds equation for lubrication problems in the rarefied gas flow regime breaks down when the pressure varies rapidly in the flow direction, which could often happen in the complicated modern hard-disk drive air bearings. In this paper the effect of rapid pressure change in a small distance is examined using a new nonlocal formulation of rarefied Poiseuille flow. The new formulation couples the pressure distribution and the velocity distributions via the Reynolds equation. Detailed numerical strategies required to solve the nonlocal pressure field are explained by analyzing a particular slider structure. Comparisons of the pressure field calculated using the proposed nonlocal formulation with the pressure predicted by the local formulation reveal significant differences between them in the region of large pressure variation. The nonlocal effect discussed in this paper could be significant for certain disk-drive air-bearing design that involves large pressure variations.

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