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.

The propagation of a liquid bolus along a liquid-lined flexible tube

Abstract: We use lubrication theory and matched asymptotic expansions to model the quasi-steady propagation of a liquid plug or bolus through an elastic tube. In the limit of small capillary number, asymptotic expressions are found for the pressure drop across the bolus and the thickness of the liquid film left behind, as functions of the capillary number, the thickness of the liquid lining ahead of the bolus and the elastic characteristics of the tube wall. These results generalise the well-known theory for the low-capillary-number motion of a bubble through a rigid tube (Bretherton 1961). As in that theory, both the pressure drop across the bolus and the thickness of the film it leaves behind vary like the two-thirds power of the capillary number. In our generalised theory, the coefficients in the power laws depend on the elastic properties of the tube. For a given thickness of the liquid lining ahead of the bolus, we identify a critical imposed pressure drop above which the bolus will eventually rupture, and hence the tube will reopen. We find that generically a tube with smaller hoop tension or smaller longitudinal tension is easier to reopen. This flow regime is fundamental to reopening of pulmonary airways, which may become plugged through disease or by instilled/aspirated fluids.

Non-isothermal flow of a liquid film on a horizontal cylinder

Abstract: We consider the flow of a viscous liquid film on the surface of a cylinder that is heated or cooled. Lubrication theory is used to study a thin film under the influence of gravity, capillary, thermocapillary, and intermolecular forces. We derive evolution equations for the interface shapes as a function of the azimuthal angle about the cylinder that govern the behaviour of the film subject to the above coupled forces. We use both analytical and numerical techniques to elucidate the dynamics and steady states of the thin layer over a wide range of thermal conditions and material properties. Finally, we extend our derivation to the case of three-dimensional dynamics and explore the stability of the film to small axial disturbances.

An Ultrathin Liquid Film Lubrication Theory—Calculation Method of Solvation Pressure and Its Application to the EHL Problem

Abstract: This paper describes a new method for calculating the solvation pressure that acts between solid surfaces when the surfaces approach each other to within a very small distance in a liquid medium. Solvation pressure is calculated by solving the transformed Ornstein-Zernike equation for hard-spheres in a two-phase system with Perram's method and using the Derjaguin approximation. Furthermore, the authors apply the new method to the elastohydrodynamic lubrication problem in which the film thickness is very small and solvation force and van der Waals force cannot be neglected. It will be shown that the calculation results agree well with experimental data. The results are then compared with two conventional solvation pressure models proposed so far, namely, Chan and Horn's model, and, Jang and Tichy's model. It is found that these two models neglect the elastic deformation of solid surface when obtaining the experimental parameter used in their models; thus they overestimate the solvation pressure resulting in the prediction of larger film thickness than the experiments.

Airway closure: surface-tension-driven non-axisymmetric instabilities of liquid-lined elastic rings

Abstract: This paper investigates the stability and large-displacement post-buckling behaviour of liquid-lined elastic rings. The fluid flow and the wall deformation are described by the free-surface Navier–Stokes equations and by geometrically nonlinear shell theory, respectively. The fluid–structure interaction problem is solved numerically by a finite element method. The compressive load on the ring is a combination of the external pressure and the effect of surface tension. Once this combined load exceeds a critical value, the subsequent non-axisymmetric collapse of the ring is controlled by the dynamics of the surface-tension-driven redistribution of fluid in the liquid lining. It is shown that, for sufficiently large surface tension, the ring can undergo a catastrophic collapse which leads to a complete occlusion of its lumen. A novel lubrication theory model, which ensures exact volume conservation for flows on strongly curved substrates, is developed and found to be capable of accurately describing the motion of the air–liquid interface and the fluid–structure interaction in the large-displacement regime, even in cases where the film thickness is large.The findings have important implications for the occurrence of airway closure in lung diseases (such as oedema) which cause an increase in the thickness of the airways' liquid lining. It is shown that under such conditions, airways can become occluded even if the volume of fluid in their liquid lining is much smaller than that required to occlude them in their axisymmetric state.