Second Order Effects in Non-Newtonian Lubrication Theory. A General Perturbation Approach

This paper is a theoretical investigation into the problem of the isothermal laminar flow of a Rivlin-Ericksen fluid of complexity n between arbitrary two bidimensional surfaces separated by a small gap. Nonlinear viscosity effects and normal-stress effects have both been taken into account. It had been recently proved that the use of a method of resolution similar to that of Reynolds imposes to reduce the field of rheological models; a “generalized Reynolds equation,” available for Stokesian fluids was then derived. Returning now to the most general differential fluid, an analytic approximate solution has been searched under the form of perturbation expansions for the normal stress and velocity fields, respectively. The corresponding set of differential equations has been given. An example has been worked out in order to compare our approximate solution with an exact solution which exists in the considered particular case. At that occasion, a discussion is opened about the choice of adequate boundary conditions at the ends of the lubricant film.