The average flow model of Patir and Cheng [1, 2] for obtaining an average Reynolds equation in the presence of two dimensional surface roughness is extended and generalized. Expectation values of the flow factors appearing in the formalism are calculated by means of a perturbation expansion of the pressure in a nominal parallel film. Terms in the series are evaluated using the unperturbed Green function, which permits ensemble averaging to be performed directly on the solution. Calculations are carried to second order, which involves only two point correlation functions of the two rough surfaces. Perturbation results agree well with results of the earlier numerical simulation until surface contact becomes important when both approaches are inadequate. The theory displays the dependence of the flow factors on the roughness parameters in simple closed form, leading to improved understanding of the average flow method.

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