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.

Three-dimensional instabilities of liquid-lined elastic tubes : A thin-film fluid-structure interaction model

Abstract: We develop a theoretical model of surface-tension-driven, three-dimensional instabilities of liquid-lined elastic tubes—a model for pulmonary airway closure. The model is based on large-displacement shell theory, coupled to the equations of lubrication theory, modified to ensure the exact representation of the system’s equilibrium configurations. The liquid film that lines the initially uniform, axisymmetric tube can become unstable to a surface-tension-driven instability. We show that, if the surface tension of the liquid lining is sufficiently large (relative to the tube’s bending stiffness), the axisymmetric redistribution of fluid by this instability can increase the wall compression to such an extent that the system becomes unstable to a secondary, nonaxisymmetric instability which causes the tube wall to buckle. We establish the conditions for the occurrence of the nonaxisymmetric instability by a linear stability analysis and use finite element simulations to explore the system’s subsequent evoluti...

Forced spreading of films and droplets of colloidal suspensions

Abstract: When a thin film of a colloidal suspension flows over a substrate, uneven distribution of the suspended particles can lead to an uneven coating. Motivated by this phenomenon, we analyse the flow of perfectly wetting films and droplets of colloidal suspensions down an inclined plane. Lubrication theory and the rapid-vertical-diffusion approximation are used to derive a coupled pair of one-dimensional partial differential equations describing the evolution of the interface height and particle concentration. Precursor films are assumed to be present, the colloidal particles are taken to be hard spheres, and particle and liquid dynamics are coupled through a concentration- dependent viscosity and diffusivity. We find that for sufficiently high Peclet numbers, even small initial concentration inhomogeneities produce viscosity gradients that cause the film or droplet front to evolve continuously in time instead of travelling without changing shape as happens in the absence of colloidal particles. At high enough particle concentrations, particle diffusion can lead to the formation of long-lived secondary flow fronts in films. Our results suggest that particle concentration gradients can have a dramatic influence on interface evolution in flowing films and droplets, a finding which may be relevant for understanding the onset of patterns that are observed experimentally.

Dynamics of thin liquid films on vertical cylindrical fibres

Abstract: Recent experiments on thin films flowing down a vertical fibre with varying nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. We present a detailed analysis using a full lubrication model that includes slip boundary conditions, nonlinear curvature terms and a film stabilization term. This study brings to focus the presence of a stable liquid layer playing an important role in the full dynamics. We propose a combination of these physical effects to explain the observed velocity and stability of travelling droplets in the experiments and their transition to isolated droplets. This is also supported by stability analysis of the travelling wave solution of the model.

Initial rates of aggregation for dilute, granular flows of wet particles

Abstract: Molecular dynamics (MD) simulations are used to determine the agglomeration rates of wet grains (particles coated with a viscous, liquid layer) engaged in simple shear flow under dilute conditions. In this work, a closed-form model derived from the elastohydrodynamic theory describes the normal restitution coefficient for binary collisions. Unlike previous MD studies, the particle deformation is not assumed to depend on a particle “overlap” (penetration), but instead depends on the formal coupling of Hertzian deformation theory with lubrication theory. The initial rate of doublet formation is studied as a function of system properties and the energy input to the system. In addition to the system properties, the distribution of relative velocities in the system is found to be a key factor influencing the initial rates of clustering. A theory based on estimating the collision frequency and the critical velocity below which no rebound is observed—due to viscous dissipation—is found to provide a good approxim...