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The classical Reynolds theory reveals that a converging gap is the first necessary condition to generate a hydrodynamic pressure in a viscous fluid film confined between two solid surfaces with a relative sliding/rolling motion. For hundreds of years, the classical lubrication mechanics has been based on the frame of the Reynolds theory with no slip assumption. Recent studies show that a large boundary slip occurs on an ultrahydrophobic surface, which results in a very small friction drag. Unfortunately, such a slip surface also produces a small hydrodynamic pressure in a fluid film between two solid surfaces. This paper studies the lubrication behavior of infinite width slider bearings involving a mixed slip surface (MSS). The results of the study indicate that any geometrical wedges (gaps), i.e., a convergent wedge, a parallel gap, and even a divergent wedge, can generate hydrodynamic pressure in an infinite slider bearing with a mixed slip surface. It is found that with an MSS, the maximum fluid load support capacity occurs at a slightly divergent wedge (roughly parallel sliding gap) for an infinite width slider bearing, but not at a converging gap as what the classical Reynolds theory predicts. Surface optimization of a parallel sliding gap with a slip surface can double the hydrodynamic load support and reduce the friction drag by half of what the Reynolds theory predicts for an optimal wedge of a traditional slider bearing.

SUMMARYWall slip has been observed in a micro/nanometer gap during the past few years. It is difficult to make a mathematical analysis for the hydrodynamics of the fluid flowing in a gap with wall slip because the fluid velocity at the liquid-solid interface is not known a priori. This difficulty is met especially in a two-dimensional slip flow due to the non-linearity of the slip control equation. In the present paper we developed a multi-linearity method to approach the non-linear control equation of the two-dimensional slip gap flow. We used an amended polygon to approximate the circle yield (slip) boundary of surface shear stress. The numerical solution does not need an iterative process and can simultaneously give rise to fluid pressure distribution, wall slip velocity and surface shear stress. We analysed the squeeze film flow between two parallel discs and the hydrodynamics of a finite slider gap with wall slip. Our numerical solutions show that wall slip is first developed in the large pressure gradient zone, where a high surface shear stress is easily generated, and then the slip zone is enlarged with the increase in the shear rate. Wall slip dramatically affects generation of the hydrodynamic pressure.

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In the present paper, a multi-linearity method is used to address the nonlinear slip control equation for the hydrodynamic analysis of a two-dimensional (2-D) slip gap flow. Numerical analysis of a finite length slider bearing with wall slip shows that the surface limiting shear stress exerts complicated influences on the hydrodynamic behavior of the gap flow. If the slip occurs at either the stationary surface or the moving surface (especially at the stationary surface), there is a transition point in the initial limiting shear stress for the proportional coefficient to affect the hydrodynamic load support in two opposite ways: it increases the hydrodynamic load support at higher initial limiting shear stresses, but decreases the hydrodynamic load support at lower initial limiting shear stresses. If the slip occurs at the moving surface only, no fluid pressure is generated in the case of null initial limiting shear stress. If the slip occurs at both the surfaces with the same slip property, the hydrodynamic load support goes off after a critical sliding speed is reached. A small initial limiting shear stress and a small proportionality coefficient always give rise to a low friction drag.

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