The fluid motion between surfaces with different radii of curvature and velocities is studied, assuming that the viscous fluid is carried by the solid surfaces but does not fill up the whole space. The boundary conditions at the inlet are examined in connection with those at the outlet of the fluid film. It is shown that only a part of the fluid carried by the surfaces, depending on the velocities and the initial rates of flow ratio, penetrates into the contact zone. Thus an interpretation of the flow field is proposed, differering from the usually assumed shape of the streamlines, by assuming the existence of a counterflow at the inlet. By using some physical conditions in various representative situations, as well as an equilibrium condition for the vortex flow, the real quantity of fluid and the entry and exit points are determined. Thereafter, the film extent, pressure distribution, load-carrying capacity, and minimum film thickness are obtained. Tables are given with the characteristic angles of the fluid film as functions of the minimum film thickness-radius of curvature ratio. The calculated values are in a satisfactory agreement with the experiments of other authors, especially when using the Prandtl-Hopkins conditions at the outlet.

The momentum equations are written for viscous fluids exhibiting magnetic stresses. The velocity profiles are deduced; then from continuity, a pressure differential equation, equivalent to Reynolds equation is obtained. This equation is discussed with emphasis on the case when magnetic stresses derive from a potential, also when the pyromagnetic coefficient vanishes. The boundary conditions for lubrication problems are then formulated. In particular, short bearings with ferromagnetic lubricants are considered. A numerical example yields the pressure diagrams at low and moderate eccentricity ratios and for different speeds. In conclusion, it is shown that ferromagnetic lubricants may improve substantially the performance of bearings operating under low loads and/or at low speeds. However, a correct variation of the magnetic field, toward the center of the lubricated area, is required. Under such conditions, the extent of the active area of the film is increased and bearing stiffness and stability are improved.

Microscopic effects, generated by micromotions of particles in suspension in a viscous fluid, drastically change the character of the flow between solid walls. To the modified momentum and continuity equations, an equation of angular (spin) particle momentum is added. A vectorial system of equations is presented, for variable material coefficients. General properties of this system are discussed and differential equations for pressure and velocity field are derived. For constant viscosity and micropolar coefficients across the lubricating film, important simplifications lead to easier workable expressions. Under this assumption, the short bearing performance has been analyzed. The fluid pressure increase (compared to Newtonian flow) is represented by a surface depending on two groups of micropolar parameters; the overall bearing characteristics also exhibit larger values with respect to simple Newtonian lubricants. However, for similar gap geometries, the friction coefficient has lower values. Some formulas, regarding the velocity field, friction stresses and side flow, are general and may be applied to any bearing length-diameter ratio.

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