During the operation of hydrodynamically lubricated devices a fully formulated lubricant has the ability to form layers at the surfaces. A friction modifier's task is to adjust the interaction between lubricant and the surface so that friction is lowered. An antiwear additive creates a protective layer on the surface and this definitely influence the performance of the lubricated device. To gain fundamental understanding, models that address the modified liquid - solid interaction due to the formation of layers, but also models that may be used to study the effects of layers already formed on the contacting surfaces are required. In this paper, two non-Newtonian lubricant rheology models that may be used to simulate reacted layers resembling those created by lubricant additives are adopted for the simulation of the piston ring - cylinder liner lubrication problem. The possibility of layer to layer interaction, which is likely to occur in the convex conjunction between the ring and the liner, is considered and this extends the models found in the literature. The effects induced by this type of layering are studied by using a modified Reynolds' equation where the coefficients have been corrected with factors that accounts for the layer properties. This enables, effectively, studies of layers resembling those created by lubricant additives during the operation of the lubricated conjunction between a piston ring and a cylinder liner.