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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.


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Journal ArticleDOI
TL;DR: A theoretical analysis is presented predicting the closure of small airways in the region of the terminal and respiratory bronchioles by a coupled capillary-elastic instability leading to liquid bridge formation, wall collapse or a combination of both.
Abstract: A theoretical analysis is presented predicting the closure of small airways in the region of the terminal and respiratory bronchioles. The airways are modelled as thin elastic tubes, coated on the inside with a thin viscous liquid lining. This model produces closure by a coupled capillary-elastic instability leading to liquid bridge formation, wall collapse or a combination of both. Nonlinear evolution equations for the film thickness, wall position and surfactant concentration are derived using an extended version of lubrication theory for thin liquid films. The positions of the air-liquid and wall-liquid interfaces and the surfactant concentration are perturbed about uniform states and the stability of these perturbations is examined by solving the governing equations numerically. Solutions show that there is a critical film thickness, dependent on fluid, wall and surfactant properties above which liquid bridges form. The critical film thickness, epsilon c, decreases with increasing mean surface-tension or wall compliance. Surfactant increases epsilon c by as much as 60 percent for physiological conditions, consistent with physiological observations. Airway closure occurs more rapidly with increasing film thickness and wall flexibility. The closure time for a surfactant rich interface can be approximately five times greater than an interface free of surfactant.

164 citations

Journal ArticleDOI
27 Jan 2015-ACS Nano
TL;DR: This study quantified the hydrophobic interaction in asymmetric system between air bubble and Hydrophobic surfaces, and provided a feasible method for synchronous measurements of the interaction forces with sub-nN resolution and the drainage dynamics of thin films down to nm thickness.
Abstract: A combination of atomic force microscopy (AFM) and reflection interference contrast microscopy (RICM) was used to measure simultaneously the interaction force and the spatiotemporal evolution of the thin water film between a bubble in water and mica surfaces with varying degrees of hydrophobicity. Stable films, supported by the repulsive van der Waals-Casimir-Lifshitz force were always observed between air bubble and hydrophilic mica surfaces (water contact angle, θ(w) < 5°) whereas bubble attachment occurred on hydrophobized mica surfaces. A theoretical model, based on the Reynolds lubrication theory and the augmented Young-Laplace equation including the effects of disjoining pressure, provided excellent agreement with experiment results, indicating the essential physics involved in the interaction between air bubble and solid surfaces can be elucidated. A hydrophobic interaction free energy per unit area of the form: WH(h) = -γ(1 - cos θ(w))exp(-h/D(H)) can be used to quantify the attraction between bubble and hydrophobized solid substrate at separation, h, with γ being the surface tension of water. For surfaces with water contact angle in the range 45° < θ(w) < 90°, the decay length DH varied between 0.8 and 1.0 nm. This study quantified the hydrophobic interaction in asymmetric system between air bubble and hydrophobic surfaces, and provided a feasible method for synchronous measurements of the interaction forces with sub-nN resolution and the drainage dynamics of thin films down to nm thickness.

164 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered boundary conditions, where the solid faces of the surfaces are near enough together to influence the physical properties of the lubricant, and the resistance varies directly with the viscosity of the surface.
Abstract: In what is often called complete lubrication, the kind of lubrication investigated by Towers and Osborne Reynolds, the solid surfaces are completely floated apart by the lubricant. There is, however, another kind of lubrication in which the solid faces are near enough together to influence directly the physical properties of the lubricant. This is the condition found with "dry" or "greasy" surfaces. What Osborne Reynolds calls ”boundary conditions” then operate, and the friction depends not only on the lubri­cant, but also on the chemical nature of the solid boundaries. Boundary lubrication differs so greatly from complete lubrication as to suggest that there is a discontinuity between the two states. In the former the surfaces have the property of static friction, and the resistance is some inverse function of the viscosity of the lubricant. In complete lubrication static friction is absent and the resistance varies directly with the viscosity of the lubricant. Boundary lubrication is alone considered in this paper. The enquiry is limited to the lubricating qualities of normal paraffins and their related acids and alcohols.The molecules of the substances employed, therefore, consist either of a simple chain of carbon atoms to which are attached atoms of hydrogen, or of such a chain loaded at one end with the hydroxyl group—OH, or the carboxyl group—COOH.

160 citations

Journal ArticleDOI
TL;DR: In this article, a generalized lubrication theory for highly deformable porous layers is developed using an effective medium approach (Brinkman equation), which is valid in the limit where the structure is so compressible that the normal forces generated by elastic compression of the fibres comprising the solid phase are negligible compared to the pressure forces generated within the porous layer.
Abstract: A generalized lubrication theory that is applicable to highly deformable porous layers is developed using an effective-medium approach (Brinkman equation). This theory is valid in the limit where the structure is so compressible that the normal forces generated by elastic compression of the fibres comprising the solid phase are negligible compared to the pressure forces generated within the porous layer. We assume that the deformation of the solid phase is primarily due to boundary compression as opposed to the motion of the fluid phase. A generalized Reynolds equation is derived in which the spatial variation of the Darcy permeability parameter, α = H/√K p , due to the matrix compression is determined by new local hydrodynamic solutions for the flow through a simplified periodic fibre model for the deformed matrix. Here H is the undeformed layer thickness and K p the Darcy permeability. This simplified model assumes that the fibres compress linearly with the deformed gap height in the vertical direction, but the fibre spacing in the horizontal plane remains unchanged. The model is thus able to capture the essential nonlinearity that results from large-amplitude deformations of the matrix layer. The new theory shows that there is an unexpected striking similarity between the gliding motion of a red cell moving over the endothelial glycocalyx that lines our microvessels and a human skier or snowboarder skiing on compressed powder. In both cases one observes an order-of-magnitude compression of the matrix layer when the motion is arrested and predicts values of α that are of order 100. In this large-α limit one finds that the pressure and lift forces generated within the compressed matrix are four orders-of-magnitude greater than classical lubrication theory. In the case of the red cell these repulsive forces may explain why red cells do not experience constant adhesive molecular interactions with the endothelial plasmalemma, whereas in the case of the skier or snowboarder the theory explains why a 70 kg human can glide through compressed powder without sinking to the base as would occur if the motion is arrested. The principal difference between the tightly fitting red cell and the snowboarder is the lateral leakage of the excess pressure at the edges of the snowboard which greatly diminishes the lift force. A simplified axisymmetric model is presented for the red cell to explain the striking pop out phenomenon in which a red cell that starts from rest will quickly lift off the surface and then glide near the edge of the glycocalyx and also for the unexpectedly large apparent viscosity measured by Pries et al. (1994) in vivo.

156 citations

Journal ArticleDOI
TL;DR: A scaling law that governs the coarsening rate is derived through the asymptotic reduction of the long-wave PDE governing the thin film to a set of ODEs for the evolution of the droplets.
Abstract: Lubrication theory for unstable thin liquid films on solid substrates is used to model the coarsening dynamics in the long-time behavior of dewetting films. The dominant physical effects that drive the fluid dynamics in dewetting films are surface tension and intermolecular interactions with the solid substrate. Instabilities in these films lead to rupture and other morphological changes that promote nonuniformity in the films. Following the initial instabilities, the films break up into near-equilibrium droplets connected by an ultrathin film. For longer times, the fluid will undergo a coarsening process in which droplets both move and exchange mass on slow time scales. The dynamics of this coarsening process will be obtained through the asymptotic reduction of the long-wave PDE governing the thin film to a set of ODEs for the evolution of the droplets. From this, a scaling law that governs the coarsening rate is derived.

154 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202325
202265
202155
202062
201970
201864