Based on the principles of continuum mechanics, we drive the governing equations for the hydrodynamic lubrication involving the mixture of two incompressible fluids. The governing equations are general in the sense that they can be applied to the mixture of any simple non-Newtonian fluid with a Newtonian fluid. A mixture thus formed is considered to be nonhomogeneous and non-Newtonian. In the theoretical development, the interaction between the constituents is taken into consideration. It is shown that a number of currently available models are special cases of the theory presented in this paper. As an example, results are presented for journal bearing performance lubricated with a mixture of a power-law fluid mixed with Newtonian oil.

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