FLUID-FILM FLOWS OF DIFFERENTIAL FLUIDS OF COMPLEXITY N DIMENSIONAL APPROACH - APPLICATIONS TO LUBRICATION THEORY

An isothermal theory of fluid-film flows of differential fluids of complexity eta 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 one 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.