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.

Viscous flow through a grating or lattice of cylinders

Abstract: Viscous flow perpendicular to a line (or ‘grating’) of evenly spaced identical cylinders is considered in the case when the spacing between the cylinders is much smaller than their cross-sectional dimensions. Lubrication theory is used to find the pressure drop across the grating and hence the force on each cylinder. A square array (or ‘lattice’) of closely packed cylinders is similarly treated.

An experimental and theoretical study of the squeeze-film deformation and flow of elastoplastic fluids

Abstract: Lubrication theory is commonly employed to analyse the squeeze-film flow of plastic fluids under no-slip wall boundary conditions. Solutions exist for both Bingham and Herschel-Bulkley fluids but they infer that there exists a rigid or unyielded core and flow zones adjacent to the platens; it has been recognised previously that such a velocity field is kinematically inconsistent. Furthermore, the pressure boundary condition at the edge of the platens is conventionally set to zero which is inconsistent with experimental data presented here for a model Herschel-Bulkley fluid (Plasticine). An attempt has been made to examine the lubrication theory in more detail by a comparison with equilibrium stress analysis for rigid-plastic solids. Squeeze-film measurements were carried out using a model Herschel-Bulkley fluid and the results were consistent with the theory, suggesting that it is a useful first approximation. Nevertheless, the approach does not resolve the kinematic inconsistency resulting in lubrication theory.

Dynamics and transport of a localized soluble surfactant on a thin film

Abstract: The flow induced by a localized droplet of soluble surfactant on the surface of a thin film is analysed, motivated by an interest in the interaction between inhaled droplets and the lung's thin liquid lining after an aerosol lands on its surface. The spreading is driven by gradients of surface tension and results in flow of the droplet and underlying liquid film. This induced flow field plays an important role in the transport of dissolved species from the droplet, through the film, and to the tissue for absorption.Evolution equations for the film thickness, surface and bulk liquid concentrations are derived using lubrication theory, since the depth of the film is much smaller than the characteristic radius of the droplet. Solutions are obtained numerically using the method of lines for a variety of surface Peclet numbers.We find that the effect of solubility is to decrease both film disturbances and surface concentrations, and to induce an absorption-driven backflow. In addition, there is a gravity-driven backflow from hydrostatics. At large surface Peclet numbers, large film disturbances are obtained and more surfactant is able to diffuse across the rigid permeable wall, while surface diffusion causes more rapid spreading and decreases film disturbances. Gravity acts as a restoring force by creating a bidirectional flow, and hence disenhances the vertical flux of surfactant across the air-liquid interface. This model may have implications for the delivery of drugs by aerosol inhalation.

Finite‐element analysis of Taylor flow

Abstract: A finite-element analysis of Taylor flow in a cylindrical capillary was performed using a commercial FEM program (FIDAP) to solve the fundamental fluid dynamics equations together with the capillary forces at the gas–liquid interface. A moving-surface formulation was used to calculate the bubble shape. The thickness of the liquid film surrounding the gas bubble, the degree of mixing in the liquid phase, and the slip velocity between the two phases were calculated. These parameters influence the performance of monolith reactors operating in the Taylor flow regime. On comparison with experimental results it was found that the FEM calculation generally predicts a thinner liquid film, which can possibly be explained in terms of a peripheral variation in surface tension. Moreover, the wavelength of the wiggles predicted in the liquid film near the tail end of the bubble was compared to those arising from a simplified mathematical analysis available in the literature. Good agreement was found for Ca < 0.005, while for higher Ca the FEM predicts significantly shorter wavelengths, indicating that the lubrication theory is not valid here.