Some discussion on the flow factor tensor-considerations of roughness orientaton and flow rheology

Relations expressing the effects of roughness orientations (θ_i) and flow behavior index (n) of the power-law fluid on the flow factors of area-distributed random roughness in hydrodynamic lubrication are derived. By using a mapping function, the generalized average Reynolds equation contains non-diagonal terms, and the flow factor tensor is symmetrical but not necessarily diagonal according to the coordinate system. Finally, the conditions that two rough surfaces act as though they were perfectly smooth are discussed for some particular combinations.