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- Lubrication approximation for fluids with shear-dependent viscosityPublication . Pereira, Bruno M. M.; Dias, Gonçalo A. S.; Cal, Filipe S.; Rajagopal, Kumbakonam R.; Videman, Juha H.We 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.