Overlapping layers in a gas lubrication problem.

*(English)*Zbl 1107.76320Summary: This investigation considers the operation of a one-dimensional squeeze slider bearing, operating under so-called slip flow conditions. At large values of the bearing and squeeze numbers, slide and squeeze effects in the pressure field in the bearing’s interior are confined to narrow layer regions at the leading and trailing edges of the bearing, with squeeze layers at both edges, while a single slide layer is located at the trailing edge, coincident with the squeeze layer there. The structure of these layers is analyzed for appropriately large values of these parameters, and the method of matched expansions is applied to construct a leading-order expression for the pressure field throughout the bearing gap. It is found that squeeze effects at the trailing edge are transmitted to the bearing’s (layer-free) interior via the (thicker) slide layer.

##### MSC:

76D08 | Lubrication theory |

35B25 | Singular perturbations in context of PDEs |

35K57 | Reaction-diffusion equations |

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\textit{E. Aliu} and \textit{J. J. Shepherd}, J. Comput. Appl. Math. 166, No. 1, 1--12 (2004; Zbl 1107.76320)

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##### References:

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[3] | White, J.W., The effect of two-dimensional surface roughness on the load-carrying capacity of a thin compressible gas film, J. tribol., 115, 246-252, (1993) |

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