Based on the principles of continuum mechanics, we drive the governing
equations for the hydrodynamic lubrication involving the mixture of T
wo incompressible fluids. The governing equations are general in the s
ense that they can be applied to the mixture of any simple non-Newtoni
an fluid with a Newtonian fluid. A mixture thus formed is considered t
o 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 c
ases of the theory presented in this paper. As an example, results are
presented for journal bearing performance lubricated with a mixture o
f a power-law fluid mixed with Newtonian oil.