'Double-Newtonian' rheological model for the two-dimensional Reynolds equation

In different mechanical applications, such as automotive engines, lubricants have undergone important changes over the past decades. Oil companies have added more and more additives to ensure correct performance of specific engine contacts, while increasing engine performance. Polymer additives are among these, used to increase viscosity at high temperatures and thus to flatten the viscosity temperature curve. This viscosity increase occurs at low shear rates, but at high shear rates, the polymers are less efficient and the viscosity diminishes. This viscosity reduction at high shear rate is due to the distortion and alignment of the polymer molecules, and their breakage for extreme shear rates. This article derives the 2D Rabinowitsch Reynolds equation. It then analyses the influence of the double Newtonian rheology on pressure, friction, and load-carrying capacity in a 2D linear contact. The influence of micro-geometrical features such as micro cavities is also studied.