Surface roughness effects in hydrodynamic lubrication involving the mixture of two fluids

In this paper, the relations expressing the ejfects of surface roughness and homogeneous mixture (the mixture of power-law fluid inserted into a Newtonian fluid) on the roughness-induced flow factors are derived. A coordinate transformation is utilized to simplify the derivation. By using the perturbation approach incorporated with Green function technique, the flow factors and shear stress factors are derived and expressed as functions of the volume fraction of the power-law fluid in the mixture (υp), the viscosity ratio of the power-law fluid to that of the Newtonian fluid (N or μp*), the flow behavior index of the power-law fluid (n), the Peklenik numbers (γ_i) and the standard deviations (σ_i) of each surface. A form of the average Reynolds equation is then obtained. It is shown that a number of currently available models are special cases of the theory presented here. Finally, the performance of a journal bearing is discussed.