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.

An insoluble surfactant model for a vertical draining free film with variable surface viscosity

Abstract: A mathematical model is constructed to study the evolution of a vertically oriented, thin, free liquid film draining under gravity when there is an insoluble surfactant, with finite variable surface viscosity, on its free surface. Lubrication theory for this free film results in three coupled nonlinear partial differential equations describing the free surface shape, the surface velocity and the surfactant transport, at leading order. In the limit of large surface viscosity and the Marangoni effect, the evolution of the free surface is that of a rigid film. For mobile films with small surface viscosity, transition from a mobile to an essentially immobile film is observed for large Marangoni effects. It is also verified that stable aqueous films can be formed in the regime of high surfactant concentrations. The theoretical results are compared with experiment; the purpose of both is to act as a model problem to evaluate the effectiveness of surfactants for potential use in foam-fabrication processes.

The effect of viscoelasticity on the stability of a pulmonary airway liquid layer

Abstract: The lungs consist of a network of bifurcating airways that are lined with a thin liquid film. This film is a bilayer consisting of a mucus layer on top of a periciliary fluid layer. Mucus is a non-Newtonian fluid possessing viscoelastic characteristics. Surface tension induces flows within the layer, which may cause the lung’s airways to close due to liquid plug formation if the liquid film is sufficiently thick. The stability of the liquid layer is also influenced by the viscoelastic nature of the liquid, which is modeled using the Oldroyd-B constitutive equation or as a Jeffreys fluid. To examine the role of mucus alone, a single layer of a viscoelastic fluid is considered. A system of nonlinear evolution equations is derived using lubrication theory for the film thickness and the film flow rate. A uniform film is initially perturbed and a normal mode analysis is carried out that shows that the growth rate g for a viscoelastic layer is larger than for a Newtonian fluid with the same viscosity. Closure occurs if the minimum core radius, Rmin(t), reaches zero within one breath. Solutions of the nonlinear evolution equations reveal that Rmin normally decreases to zero faster with increasing relaxation time parameter, the Weissenberg number We. For small values of the dimensionless film thickness parameter e, the closure time, tc, increases slightly with We, while for moderate values of e, ranging from 14% to 18% of the tube radius, tc decreases rapidly with We provided the solvent viscosity is sufficiently small. Viscoelasticity was found to have little effect for e>0.18, indicating the strong influence of surface tension. The film thickness parameter e and the Weissenberg number We also have a significant effect on the maximum shear stress on tube wall, max(τw), and thus, potentially, an impact on cell damage. Max(τw) increases with e for fixed We, and it decreases with increasing We for small We provided the solvent viscosity parameter is sufficiently small. For large e≈0.2, there is no significant difference between the Newtonian flow case and the large We cases.

Theoretical analysis of electrical double layer effects on the multiphase flow of Jeffrey fluid through a divergent channel with lubricated walls

Abstract: A theoretical study of two-phase non-Newtonian fluid with heat transfer is presented in this article. Jeffrey fluid model is used as the base liquid to form a multiphase suspension with the help of gold particles. Heating effects have also been applied on an electro-osmotic two-phase flow through a divergent channel. The lubrication effects have been applied to dampen the skin friction of the opposite walls. An analytical solution is obtained for the nonlinear multiphase fluid flow with heat transfer. Separate expressions for the volumetric flow rate of two-phase flow and pressure gradient are determined via a complex mathematical manipulation. A concise parametric study reveals that slippery walls of the channel have a prominent influence on the momentum of both phases.

Discrete Nature of Ultrathin Lubrication Film Between Mica Surfaces

Abstract: A new apparatus which can measure force and separation between surfaces accurately is developed. Ultrathin fluid lubrication film thickness between mica surfaces is measured using this apparatus. Octamethylcyclotetrasiloxane (OMCTS) is used as a lubricant. As a result of the experiment, it is found that when the film thickness is more than about 10 nm (ten times as large as the molecular diameter of OMCTS), there is good agreement with the conventional continuum fluid lubrication theory (EHL theory). In case of film thickness less than 10 nm, however, it deviates from the theoretical prediction and discretization of film thickness is observed. It is considered that this phenomenon is due to the solvation force (structural force), and that the molecular effect cannot be neglected in such an ultrathin lubrication phenomenon as in this experiment.