Fluid flow through rock joints is commonly described by the parallel plate model where the volume flow rate varies as the cube of the joint aperture. However, deviations from this model are expected because real joint surfaces are rough and contact each other at discrete points. To examine this problem further, a computer simulation of flow between rough surfaces was done. Realistic rough surfaces were generated numerically using a fractal model of surface topography. Pairs of these surfaces were placed together to form a “joint” with a random aperture distribution. Reynolds equation, which describes laminar flow between slightly nonplanar and nonparallel surfaces, was solved on the two-dimensional aperture mesh by the finite-difference method. The solution is the local volume flow rate through the joint. This solution was used directly in the cubic law to get the so-called “hydraulic aperture.” For various surface roughnesses (fractal dimensions) the hydraulic aperture was compared to the mean separation of the surfaces. At large separations the surface topography has little effect. At small separations the flow is tortuous, tending to be channeled through high-aperture regions. The parameter most affecting fluid flow through rough joints is the ratio of the mean separation between the surfaces to the root-mean-square surface height. This parameter describes the distance the surface asperities protrude into the fluid and accounts for most of the disagreement with the parallel plate model. Variations in the fractal dimension produce only a second-order effect on the fluid flow. For the range of joint closures expected during elastic deformation these results show that the actual flow rate between rough surfaces is about 70–90% of that predicted by the parallel plate model.

Fluid flow through rock joints: The effect of surface roughness

We present measurements of the thickness as a function of time of liquid films as they are squeezed between molecularly smooth mica surfaces. Three Newtonian, nonpolar liquids have been studied: octamethylcyclotetrasiloxane, n‐tetradecane, and n‐hexadecane. The film thicknesses are determined with an accuracy of 0.2 nm as they drain from ∼1 μm to a few molecular layers. Results are in excellent agreement with the Reynolds theory of lubrication for film thicknesses above 50 nm. For thinner films the drainage is slower than the theoretical prediction, which can be accounted for by assuming that the liquid within about two molecular layers of each solid surface does not undergo shear. In very thin films the continuum Reynolds theory breaks down, as drainage occurs in a series of abrupt steps whose size matches the thickness of molecular layers in the liquid. The presence of trace amounts of water has a dramatic effect on the drainage of a nonpolar liquid between hydrophilic surfaces, causing film rupture whi...

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The drainage of thin liquid films between solid surfaces

The subject of this monograph is the fluid dynamics of liquid turbomachines, particularly pumps. Rather than attempt a general treatise on turbomachines, we shall focus attention on those special problems and design issues associated with the flow of liquid through a rotating machine. There are two characteristics of a liquid that lead to these special problems, and cause a significantly different set of concerns than would occur in, say, a gas turbine. These are the potential for cavitation and the high density of liquids that enhances the possibility of damaging unsteady flows and forces.

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Hydrodynamics of Pumps

The potential use of a new technology of laser surface texturing (LST) in parallel thrust bearings is theoretically investigated. The surface texture has the form of micro-dimples with pre-selected diameter, depth, and area density. It can be applied to only a portion of the bearing area (partial LST) or the full bearing area (full LST). Optimum parameters of the dimples, and best LST mode, are found in order to obtain maximum load carrying capacity for a thrust bearing having parallel mating surfaces. A comparison is made with optimum linear and stepped sliders showing that parallel LST sliders can provide similar load carrying capacity. Scheduled for Presentation at the 58th Annual Meeting in New York City April 28–May 1, 2003

A Laser Surface Textured Parallel Thrust Bearing

The archetypal feature of a viscoplastic fluid is its yield stress: If the material is not sufficiently stressed, it behaves like a solid, but once the yield stress is exceeded, the material flows like a fluid. Such behavior characterizes materials common in industries such as petroleum and chemical processing, cosmetics, and food processing and in geophysical fluid dynamics. The most common idealization of a viscoplastic fluid is the Bingham model, which has been widely used to rationalize experimental data, even though it is a crude oversimplification of true rheological behavior. The popularity of the model is in its apparent simplicity. Despite this, the sudden transition between solid-like behavior and flow introduces significant complications into the dynamics, which, as a result, has resisted much analysis. Over recent decades, theoretical developments, both analytical and computational, have provided a better understanding of the effect of the yield stress. Simultaneously, greater insight into the material behavior of real fluids has been afforded by advances in rheometry. These developments have primed us for a better understanding of the various applications in the natural and engineering sciences.

Yielding to Stress: Recent Developments in Viscoplastic Fluid Mechanics

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Theory of Hydrodynamic Lubrication

The effect of roughness of surfaces of a slider bearing on the load-carrying capacity and friction force, is studied. The distinction is made between waviness and roughness, the latter being treated as a random quantity which may be characterized by a probability density function, determined experimentally. Results can be obtained in closed form suitable for calculation if a Beta distribution is assumed. Actually, this can approximate quite closely a Gaussian distribution, yielding quite accurate results. However, the procedure developed can be carried out for any desired distribution.

Surface Roughness Effect on Slider Bearing Lubrication

An analytical method is developed for treating the flow of a non-Newtonian lubricant in a slider bearing. The difference between this treatment and earlier ones is in the type of constitutive equation used. This one satisfies the invariant conditions and is applicable to both pseudoplastic and dilotant fluids. The pressure distribution, oil flow, and friction force and load-carrying capacity are calculated, and the results are compared with the corresponding ones for a Newtonian fluid. Presented as an American Society of Lubrication Engineers paper at the Lubrication Conference held in Washington, D. C., October 13–16, 1964.

Edward Saibel

Papers

Theory of Hydrodynamic Lubrication

Surface Roughness Effect on Slider Bearing Lubrication

Slider Bearing Performance with a Non-Newtonian Lubricant

Nonlinear Viscosity Effects in Slider Bearing Lubrication

On the effects of surface roughness in the hydrodynamic lubrication theory of a short journal bearing