Generalized Newtonian viscosity functions for hydrodynamic lubrication

•Measurements which penetrate far into the shear-thinning regime.•Review of viscosity functions and their properties.•Review of superposition.•New viscosity function for multiple transitions which resolves issues with previous functions.

Among some of the generalized Newtonian viscosity functions used in hydrodynamic lubrication, the Cross and Ellis equations have a transition from the first Newtonian plateau to the power-law regime that is much broader than is typical of polymer-thickened oils. The Dobson method employs the Cross equation to extract the second Newtonian viscosity for a polymer-thickened oil from ambient pressure viscometry. This method will always produce a second Newtonian viscosity for a polymer thickened oil, even if none is present in the data. Shear-thinning measured at elevated pressure removes this issue.An improved viscosity function is offered which describes the shear-dependence of the polymer and of the base oil without the artifacts associated with a sum of individual viscosity equations.