Lubrication theory

About: Lubrication theory is a research topic. Over the lifetime, 1713 publications have been published within this topic receiving 50261 citations. The topic is also known as: Fluid bearing.

Stability of lubricated viscous gravity currents. Part 2. Global analysis and stabilisation by buoyancy forces

Abstract: The novel viscous fingering instability recently found in the experiments of Kowal & Worster (J. Fluid Mech., vol. 766, 2015, pp. 626–655), involving two superposed currents of viscous fluid, has been shown to originate at the lubrication front when the fluids are of equal density. However, when the densities are unequal, additional buoyancy forces associated with the underlying layer act to suppress this instability and are largest at the lubrication front, which is where the instability originates. In this paper, we investigate the interaction between the mechanism of the instability and the stabilising influence of these buoyancy forces by performing a global and fully time-dependent analysis, which does not use the frozen-time approximation. We determine a critical condition for instability in terms of the viscosity ratio and the density difference between the two layers. Consistently with the local analysis of the companion paper, instabilities occur when the jump in hydrostatic pressure gradient across the lubrication front is negative, or, equivalently, when the intruding fluid is less viscous than the overlying fluid, provided the two fluids are of equal densities. Once there is a non-zero density difference, these driving buoyancy forces suppress the instability for large wavelengths, giving rise to wavelength selection. As the density difference increases, the instability criterion requires higher viscosity ratios for any instability to occur, and the band of unstable wavenumbers becomes bounded. Large enough density differences suppress the instability completely.

Roll coating in the presence of a fixed constraining boundary

Abstract: When a cylindrical roll rotates about its axis while partially submerged in a liquid, as suggested in Figure 1, a layer of the liquid is entrained and withdrawn from the bath. In the absence of a constraining boundary the coating thickness H is found to exhibit a strong dependence on roll speed, as well as on the fluid viscosity and interfacial tension. In a previous publication (Middleman, 1978) from this laboratory we have presented experimental results and a successful data correlation for the case of a roll operating under such conditions that the boundaries of the fluid reservoir exert no influence on the coating dynamics. In this paper the effect of an adjacent constraining boundary is considered, a mathematical model based on lubrication theory is presented, and the data are found to exhibit the general features predicted by the model. Under some conditions it is observed that a uniform coating is not achieved. Instead, a regular set of lines or “ribs” is developed, in the direction of motion. Figu...

Physics of the granite sphere fountain

Abstract: A striking example of levitation is encountered in the “kugel fountain” where a granite sphere, sometimes weighing over a ton, is kept aloft by a thin film of flowing water. In this paper, we explain the working principle behind this levitation. We show that the fountain can be viewed as a giant ball bearing and thus forms a prime example of lubrication theory. It is demonstrated how the viscosity and flow rate of the fluid determine (i) the remarkably small thickness of the film supporting the sphere and (ii) the surprisingly long time it takes for rotations to damp out. The theoretical results compare well with measurements on a fountain holding a granite sphere of one meter in diameter. We close by discussing several related cases of levitation by lubrication.

An Influence of Inertia Forces on Stability of Turbulent Journal Bearings

Abstract: It is a purpose of this paper to discuss both turbulence and inertia effects on the static and dynamic characteristics of high speed journal bearings. Because of the difficulty of analysis, infinitely long and short width bearings are dealt with analytically instead of finite width bearings. It is found that the static characteristics such as the Sommerfeld number and the locus of shaft center are affected mainly by turbulence but the dynamic ones such as the spring, damping and acceleration coefficients of lubricant film and the stability of rotors are affected by inertia.