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.

Droplet levitation over a moving wall with a steady air film

Abstract: In isothermal non-coalescence behaviours of a droplet against a wall, an air film of micrometre thickness plays a crucial role. We experimentally study this phenomenon by letting a droplet levitate over a moving glass wall. The three-dimensional shape of the air film is measured using an interferometric method. The mean curvature distribution of the deformed free surface and the distributions of the lubrication pressure are derived from the experimental measurements. We vary experimental parameters, namely wall velocity, droplet diameter and viscosity of the droplets, over a wide range; for example, the droplet viscosity is varied over two orders of magnitude. For the same wall velocity, the air film of low-viscosity droplets shows little shape oscillation with constant film thickness (defined as the steady state), while that of highly viscous droplets shows a significant shape oscillation with varying film thickness (defined as the unsteady state). The droplet viscosity also affects the surface velocity of a droplet. Under our experimental conditions, where the air film shape can be assumed to be steady, we present experimental evidence showing that the lift force generated inside the air film balances with the droplet’s weight. We also verify that the lubrication pressure locally balances with the surface tension and hydrostatic pressures. This indicates that lubrication pressure and the shape of the free surface are mutually determined. Based on the local pressure balance, we discuss a process of determining the steady shape of an air film that has two areas of minimum thickness in the vicinity of the downstream rim.

The effect of wall slip on the dewetting of ultrathin films on solid substrates: Linear instability and second-order lubrication theory

Abstract: The influence of wall slip on the instability of a non-wetting liquid film placed on a solid substrate is analyzed in the limit of negligible inertia. In particular, we focus on the stability properties of the film, comparing the performance of the three lubrication models available in the literature, namely, the weak, intermediate, and strong slip models, with the Stokes equations. Since none of the aforementioned leading-order lubrication models is shown to be able to predict the growth rate of perturbations for the whole range of slipping lengths, we develop a parabolic model able to accurately predict the linear dynamics of the film for arbitrary slip lengths.

Mechanism of Boundary Lubrication and the Edge Effect

Abstract: Experimental work was carried out on the boundary lubrication of a copper-copper couple with pure cetane, palmitic acid solution of cetane, and some other organic materials. The purpose was to get information about α and μlube , which appear in the friction equation: μ = αμsolid + (1 − α)μlube, by using two different kinds of copper surface, a clean surface, and an oxidized surface. α was found to be small with palmitic acid solution, and the estimated shear strength of palmitic acid was high under the examined condition. α and μlube seemed to be properties which are independent of each other. α is closely related to the attraction force between the lubricant and the substrate, whereas μlube is related to the complexity of molecular structure of the lubricant. A comparison was made of bulk-liquid and thin-film lubrication. μlube was smaller in thin-film lubrication than it was in bulk-liquid lubrication. This suggests that the frictional resistance may be partly contributed by liquid in the edge space around the real contact.

Inertial effects at moderate Reynolds number in thin-film rimming flows driven by surface shear

Abstract: In this paper, we study two-dimensional thin-film flow inside a stationary circular cylinder driven by an imposed surface shear stress. Modelling is motivated by a need to understand the cooling and film dynamics provided by oil films in an aero-engine bearing chamber characterised by conditions of very high surface shear and additional film mass flux from oil droplets entering the film through the surface. In typical high-speed operation, film inertial effects can provide a significant leading-order mechanism neglected in existing lubrication theory models. Inertia at leading-order is included within a depth-averaged formulation where wall friction is evaluated similar to hydraulic models. This allows key nonlinear inertial effects to be included while retaining the ability to analyse the problem in a mathematically tractable formulation and compare with other approaches. In constructing this model, a set of simplified mass and momentum equations are integrated through the depth of the film yielding a spatially one-dimensional depth-averaged formulation of the problem. An a priori assumed form of velocity profile is needed to complete the system. In a local Stokes flow analysis, a quadratic profile is the exact solution for the velocity field though it must be modified when inertial effects become important. Extension of the velocity profile to a cubic profile is selected enabling specification of a wall friction model to include the roughness of the cylinder wall. A modelling advantage of including the inertia term, relevant to the applications considered, is that a smooth progression in solution can be obtained between cases of low Reynolds number corresponding to lubrication theory, and high Reynolds number corresponding to uniform rimming-flow. Importantly, we also investigate the effect of inertia on some typical solutions from other studies and present a greater insight to existing and new film solutions which arise from including inertia effects.