An isothermal theory of fluid-film flows of differential fluids of complexity n is developed on the basis of a complete dimensional analysis. Within that particular geometrical configuration and provided that the Deborah number is small, such fluids cannot be distinguished from the far more special Rivlin-Ericksen material of complexity 3. It is shown afterwards that the use of a method of resolution similar to that of Reynolds requires to reduce the field of rheological models or the number of geometrical dimensions. The corresponding “generalized Reynolds’ equations” are then deduced: one in 3 dimensions, available for general viscous fluids; one in 2 dimensions, available for Stokesian fluids.

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