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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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TL;DR: In this article, the most unstable values of the wave-number, n (characterizing the disturbance), are calculated as functions of the dimensionless variable T/μU0, and of the geometry of the system; T is the surface tension, μ the viscosity and U 0 a representative velocity of the fluid.
Abstract: When a thin film of viscous fluid is produced by passing it through a small gap between a roller or spreader and a flat plate, it often presents a waved, or ribbed, surface. An analysis is given here in terms of lubrication theory to show why in many cases flow leading to a uniform film is unstable. Account is taken of surface tension which proves to be a stabilizing factor. The most unstable values of the wave-number, n (characterizing the disturbance), are calculated as functions of the dimensionless variable T/μU0, and of the geometry of the system; T is the surface tension, μ the viscosity and U0 a representative velocity of the fluid. For the particular case of a spreader in the form of a wide-angled wedge, these predictions are compared with experimental observations. Agreement is obtained for values of T/μU0 between about 10 and 0.1, but for smaller values of T/μU0 it is clear that other considerations, involving only viscous and pressure forces, determine the nature of the secondary flow.

121 citations

Journal ArticleDOI

121 citations

Journal ArticleDOI
TL;DR: In this article, the authors review viscoplastic flow over inclined surfaces, focusing on constant-flux extrusions from small vents and the slumping of a fixed volume of material.
Abstract: We review viscoplastic flow over inclined surfaces, focusing on constant-flux extrusions from small vents and the slumping of a fixed volume of material. Lubrication theory is used for shallow and slow flows to reduce the governing equations to a nonlinear diffusion-type equation for the local fluid depth; this model is used as the basis for exploration of the problem. Theory is compared to experiments. A number of complications and additional physical effects are discussed that enrich real situations.

121 citations

Journal ArticleDOI
TL;DR: In this paper, the steady three-dimensional Stokes equations are used to analyse the slow viscous flow in an elastic tube whose deformation is described by geometrically nonlinear shell theory.
Abstract: This paper is concerned with the problem of viscous flow in an elastic tube. Elastic tubes collapse (buckle non-axisymmetrically) when the transmural pressure (internal minus external pressure) falls below a critical value. The tube's large deformation during the buckling leads to a strong interaction between the fluid and solid mechanics.In this study, the steady three-dimensional Stokes equations are used to analyse the slow viscous flow in such a tube whose deformation is described by geometrically nonlinear shell theory. Finite element methods are used to solve the large-displacement fluid–structure interaction problem. Typical wall deformations and flow fields in the strongly collapsed tube are shown. Extensive parameter studies illustrate the tube's flow characteristics (e.g. volume flux as a function of the applied pressure drop through the tube) for boundary conditions corresponding to the four fundamental experimental setups. It is shown that lubrication theory provides an excellent approximation of the fluid traction while being computationally much less expensive than the solution of the full Stokes equations. Finally, the computational predictions for the flow characteristics and the wall deformation are compared to the results obtained from an experiment.

119 citations

Journal ArticleDOI
TL;DR: In this paper, a semi-analytical model based on lubrication analysis is derived to predict the effect of tow shape and intra-tow permeability on the overall bed permeability for flow through rectangular arrays of porous elliptical cylinders.
Abstract: The permeability of preform materials used in liquid moulding processes such as resin transfer moulding and structural reaction injection moulding is a complex function of weave pattern, packing characteristics, tow structure and intra-tow properties. The development of tools for predicting permeability as a function of these parameters is of great practical importance because such capability would speed process design and optimization, and provide a step towards establishing processing-performance relations. In this study, transverse flow in aligned fibrous porous media has been investigated. A semi-analytical model based on lubrication analysis is derived to predict the effect of tow shape and intra-tow permeability on the overall bed permeability for flow through rectangular arrays of porous elliptical cylinders. The Brinkman equation is used to model flow inside the porous structures, and the Stokes equation to model flow in the open media between the structures. The model predictions are verified by comparing with rigorous finite element calculations. The model shows that the influence of the intra-tow permeability on the overall bed permeability increases with inter-tow packing, and increasing degree of tow ellipticity. The influence is particularly critical for ‘stacked’ geometries for which previous models predict a zero permeability. A method for predicting intra-tow permeability is also proposed and investigated by comparing the model predictions for overall bed permeability with some experimental data for flow in a model porous medium. The comparison shows that use of the method enables the experimentally measured permeability value to be properly bounded.

118 citations


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