Pereira, Bruno M. M.Dias, Gonçalo A. S.Cal, Filipe S.Rajagopal, Kumbakonam R.Videman, Juha H.2019-07-302019-07-302019-06PEREIRA, Bruno M. M.; [et al] – Lubrication approximation for fluids with shear-dependent viscosity. Fluids. ISSN 2311-5521. Vol. 4, N.º 2 (2019), pp. 1-172311-5521http://hdl.handle.net/10400.21/10387We present dimensionally reduced Reynolds type equations for steady lubricating flows of incompressible non-Newtonian fluids with shear-dependent viscosity by employing a rigorous perturbation analysis on the governing equations of motion. Our analysis shows that, depending on the strength of the power-law character of the fluid, the novel equation can either present itself as a higher-order correction to the classical Reynolds equation or as a completely new nonlinear Reynolds type equation. Both equations are applied to two classic problems: the flow between a rolling rigid cylinder and a rigid plane and the flow in an eccentric journal bearing.engPower-law fluidShear-dependent viscosityReynolds equationLubrication approximationjournal article10.3390/fluids4020098