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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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Dissertation
01 Jan 2003
TL;DR: In this paper, the authors used a multigrid algorithm to solve the Navier-Stokes equations in a more tractable form, namely a coupled set of partial differential equations.
Abstract: Considerable progress in the understanding of thin film flow over surfaces has been achieved thanks to lubrication theory which enables the governing Navier-Stokes equations to be reduced to a more tractable form, namely a coupled set of partial differential equations. These are solved numerically since the flows of interest involve substrates containing heterogeneities in the form of wetting patterns and/or topography. An efficient and accurate numerical method is described and used to solve two classes of problem: droplet spreading in the presence of wetting and topographic heterogeneities; gravity-driven flow of continuous thin liquid films down an inclined surface containing well defined topographic features. The method developed, employs a Full Approximation Storage (FAS) multigrid algorithm, is fully implicit and has embedded within it an adaptive time-stepping scheme that enables the same to be optimised in a controlled manner subject to a specific error tolerance. Contact lines are ubiquitous in the context of droplet spreading and the wellknown singularity which occurs there is alleviated by means of a disjoining pressure model. The latter allows prescription of a local equilibrium contact angle and three dimensional numerical simulations reveal how droplets can be forced to either wet or dewet a region containing topography depending on the surface wetting characteristics. The growth of numerical instabilities, in the contact line region, which can lead to the occurrence of non-physical, negative film thicknesses is avoided by using a Positivity Preserving Scheme. A range of two- and three-dimensional problems is explored featuring the gravity-driven flow of a continuous thin liquid film over a non-porous inclined flat surface containing topography. Important new results include: the quantification of the validity range of the lubrication approximation for step-up and step-down topographies; description of the "bow wave" triggered by localised topography and an explanation, in terms of the local flow rate, of the accompanying "downstream surge": an assessment of linear superposition as a means of examining free surface response to topographies. In addition, the potential of local mesh refinement as a means of reducing computational time is highlighted. Finally, more complex liquids composed of a non-volatile resin dissolved in a solvent and allowed to evaporate are considered. An evaporation model based on the wellmixed approximation is utilised. Results show that localised topographies produce defects in dried continuous films which persist far downstream of the topography, while with respect to droplet motion, solvent evaporation is found to be responsible for contact line pinning and thus a reduction in spreading.

10 citations

Journal ArticleDOI
TL;DR: In this article, the spread of a gravity current consisting of a fluid of non-Newtonian power law rheology along a rigid horizontal plane, under a shallow layer with a free surface consisting of Newtonian fluid, is investigated.
Abstract: In this paper we investigate the spread of a gravity current consisting of a fluid of non-Newtonian power law rheology along a rigid horizontal plane, under a shallow layer with a free surface consisting of a Newtonian fluid. We apply the lubrication theory approximation to establish a two-layer model which couples the dynamics of the two layers. The problem corresponding to the release of a constant volume is solved numerically and the solution compared to exact similarity solutions in a limiting case. The effect of the various physical parameters is analyzed and comparison is made with the results of the single-layer model.

10 citations

Journal ArticleDOI
TL;DR: The present work could explain the strong persistence of the waves observed in adhered cells using differential inference contrast (DIC) microscopy and the observation that the wavelengths decrease shortly after leading edge retraction.
Abstract: Membrane waves have been observed near the leading edge of a motile cell. Such phenomenon is the result of the interplay between hydrodynamics and adhesive dynamics. Here we consider membrane dynamics on a thin fluid gap supported by adhesive bonds. Using coupled lubrication theory and adhesive dynamics, we derive an evolution equation to account for membrane tension, bending, adhesion, and viscous lubrication. Four adhesion scenarios are examined: no adhesion, uniform adhesion, clustered adhesion, and focal adhesion. Two contrasting traveling wave types are found, namely, tension and adhesion waves. Tension waves disperse with time and space, whereas adhesion waves show increased amplitudes and are highly persistent. We show that the transition from tension to adhesion waves depends on a necessary, but insufficient, criterion that the wave amplitude must exceed a critical gap height, which is dependent on adhesion binding probability. We also show that strong adhesion results in sharp tension-to-adhesion wave transitions. The present work could explain the strong persistence of the waves observed in adhered cells using differential inference contrast (DIC) microscopy and the observation that the wavelengths decrease shortly after leading edge retraction.

10 citations

Journal ArticleDOI
TL;DR: In this article, a new kind of acoustic prototype driven by standing waves utilizing reverse hydrodynamic effects of non-parallel squeeze film was proposed in order to realize contactless levitation and movement of precision components.

10 citations

Journal ArticleDOI
01 Feb 2008
TL;DR: In this paper, a theory that includes the coupled effects of electric double layer (EDL) and boundary slip near the solid surface increases and decreases apparent viscosity, respectively.
Abstract: A lubrication theory that includes the coupled effects of electric double layer (EDL) and boundary slip is developed. The consideration of EDL (electro-viscous effect) and boundary slip near the solid surface increases and decreases apparent viscosity, respectively. Both effects are important for flow within microscales and lubrication problems. Under the usual assumptions of lubrication and Debye—Huckel approximation for low surface potential, the Navier—Stokes equation with body force due to the electrical potential, as well as the Navier slip boundary conditions, is utilized to derive the velocity distributions, apparent viscosity, and modified Reynolds equation. The apparent viscosity is expressed explicitly as functions of the Debye length, the electro-viscosity, and the slip length. The coupled effects of EDL and boundary slip on the apparent viscosity and one-dimensional slider-bearing performance are analysed and discussed. Results show that the load capacity increases as a decrease in inverse Deb...

10 citations


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