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.

Dynamics of elastocapillary rise

Abstract: We present the results of a combined experimental and theoretical investigation of the surface-tension-driven coalescence of flexible structures. Specifically, we consider the dynamics of the rise of a wetting liquid between flexible sheets that are clamped at their upper ends. As the elasticity of the sheets is progressively increased, we observe a systematic deviation from the classical diffusive-like behaviour: the time to reach equilibrium increases dramatically and the departure from classical rise occurs sooner, trends that we elucidate via scaling analyses. Three distinct temporal regimes are identified and subsequently explored by developing a theoretical model based on lubrication theory and the linear theory of plates. The resulting free-boundary problem is solved numerically and good agreement is obtained with experiments.

Models for gravitationally-driven free-film drainage

Abstract: The drainage of the thin fluids layers, or lamellae, in a foam may be modeled by a vertical draining thin liquid film. A sequence of mathematical models is described that attempts to explain some aspects of the drainage of the film. Lubrication theory is used to derive the nonlinear partial differential equations (PDE) that describe the film; all models assume an insoluble surfactant in this paper. The models include effects from gravity, viscosity, surface tension and its dependence on surface concentration (the Marangoni effect), and surface viscosity; they may also include nonlinear equations of state. The models are able to predict very well the fast and slow limits of the drainage observed experimentally; a limited range of intermediate drainage rates has been described by these models to date. The limitations of the models and possible extensions will be discussed.

Comparisons of Slip-Corrected Reynolds Lubrication Equations for the Air Bearing Film in the Head-Disk Interface of Hard Disk Drives

Abstract: Slip-corrected Reynolds equations have not been widely used in the air bearing simulations for the head-disk interface in hard disk drives since Fukui and Kaneko [Trans ASME J Tribol 110:253–262, 1988] published a more accurate generalized lubrication equation (FK model) based on the linearized Boltzmann equation for molecular gas lubrication. However, new slip models and slip-corrected Reynolds equations continue to be proposed with certain improvements or with the more physical basis of kinetic theory. Here, we reanalyze those slip models and lubrication equations developed after the FK model was published. It is found that all of the slip-corrected Reynolds equations are of limited use in the air bearing simulations, and that these new slip-corrected Reynolds equations cannot replace the FK model for calculating an accurate pressure distribution of molecular gas lubrication.