The continuum theory of mixture was employed to derive a generalized form of the Reynolds equation for the lubrication problems involving lubricants that contain solid particles. The derivation of the governing equations and the boundary conditions are presented. The governing equations are two coupled partial differential equations that must be solved simultaneously for the solid volume fraction and the pressure distribution in a hydrodynamic bearing. The boundary conditions allow the particles to slip at the boundary surfaces. The formulation takes the interaction between the solid and the fluid constituents into consideration. Extensive numerical results are presented for the performance parameters in finite journal bearings lubricated with granular powder mixed with Newtonian oil.

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