The shape of the film-vapor interface is found for a thin liquid film separating from a stationary surface and being swept away on an opposing moving surface. The analysis is for two-dimensional Newtonian flow, and includes the effects of gravity, inertia, and surface tension. The principal assumption is that of a quadratic tangential velocity distribution across the film. The solution shows that the entire separation phenomenon is completed in a distance of about one plate clearance from the stagnation point. Stagnation points occur on the vapor-liquid interface at the separation point and at a film height of 3h∞ (three times the film height on the moving plate far downstream). For a fixed separation height, the asymptotic film thickness h∞ is shown as a function of three dimensionless parameters. The results are in good agreement with published experimental data.
Another method has been developed for obtaining the rate of shear vs shearing stress curves of non-Newtonian fluids from concentric cylinder viscometer data. The mathematical expression developed is a rapidly converging power series in lns, where s is the cup to bob radius ratio. An estimate of error shows that under favorable conditions only two terms of the series are significant, and that terms past the third will hardly ever be needed.
In this paper a new turbulent lubrication analysis has been derived which takes into account certain well-established facts concerning turbulent shear flow. Consistent with lubrication-film theory, the nature of the local flow is taken to depend only on local film thickness, surface velocity, and pressure gradients. An eddy diffusivity treatment is used which incorporates the “law of wall” with the use of local (within the film) shear stress. Stress reversal phenomena are accommodated and isotropy of the turbulent exchange mechanism in the plane of the film is assured. Coefficients are developed for use in the generalized Reynolds (lubrication) equation, and computation procedures for the static and dynamic characteristics of turbulent, self-acting bearings have been prepared. The nonlinear effects due to the coupling of the shear induced flows and the flows due to the circumferential and axial pressure gradients are fully considered in this analysis. Thus, it is anticipated that it, unlike the previous linearized analysis, is directly applicable also to turbulent, externally pressurized, and hybrid bearings.
The purpose of this paper is to derive lubrication equations suitable for constant-property fluids exhibiting inelastic non-Newtonian characteristics. The analysis results in a slightly modified form of Reynolds equation. Fluid characteristics show up in this equation through an equivalent power-law. Data are presented for journal bearing performance over a range of L/D’s and rheological exponents.
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