Topic
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 motion of a rigid disk-shaped particle with rounded edges, which fits closely in the space between two parallel flat plates, and which is suspended in a viscous fluid subject to an imposed pressure gradient, is analyzed.
Abstract: The motion of a rigid disk-shaped particle with rounded edges, which fits closely in the space between two parallel flat plates, and which is suspended in a viscous fluid subject to an imposed pressure gradient, is analysed. This problem is relevant to the squeezing of red blood cells through narrow slot-like channels which are found in certain tissues. Mammalian red cells, although highly flexible, conserve volume and surface area as they deform. Consequently, a red cell cannot pass intact through a channel which is narrower than some minimum width. In channels that are just wide enough to permit cell passage, the cell is deformed into its ‘critical’ shape: a disk with rounded edges. In this paper, the fluid mechanical aspects of such motions are considered, and the particle is assumed to be rigid with the critical shape. The channel cross-section is assumed to be rectangular. The flow of the suspending fluid is described using lubrication theory. Use of lubrication theory is justified by considering the motion of a circular cylinder between parallel plates. For disk-shaped particles, approximate solutions are obtained by applying lubrication equations throughout the flow domain. In the region beyond the particle, this is equivalent to assuming a Hele-Shaw flow. More accurate solutions are obtained by including effects of boundary layers around the particle and at the sides of the channel. Pressure distributions and particle velocities are computed as functions of geometrical parameters, and it is shown that the particle may move faster or slower than the mean velocity of the surrounding fluid, depending on the channel dimensions.
18 citations
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TL;DR: In this article, the axisymmetric spreading of drops on a pre-existing horizontal layer of the same viscous fluid is studied and the authors employ lubrication theory to analyse the drop's ultimate long-term behaviour and show that all drops ultimately enter an asymptotic regime when their excess height falls below the thickness of the undisturbed layer.
Abstract: We study the axisymmetric spreading of drops deposited on a pre-existing horizontal layer of the same viscous fluid. Using a combination of experiments, numerical modelling based on the axisymmetric free-surface Navier–Stokes equations and scaling analyses, we explore the drops’ behaviour in a regime where the flow is driven by gravitational and/or capillary forces while inertial effects are small. We find that during the early stages of the drops’ evolution there are three distinct spreading behaviours depending on the thickness of the liquid layer. For thin layers the fluid ahead of a clearly defined spreading front is at rest and the overall behaviour resembles that of a drop spreading on a dry substrate. For thicker films, the spreading is characterised by an advancing wedge which is sustained by fluid flow from the drop into the layer. Finally, for thick layers the drop sinks into the layer, accompanied by significant flow within the layer. As the drop keeps spreading, the evolution of its shape becomes self-similar, with a power-law behaviour for its radius and its excess height above the undisturbed fluid layer. We employ lubrication theory to analyse the drop’s ultimate long-term behaviour and show that all drops ultimately enter an asymptotic regime which is reached when their excess height falls below the thickness of the undisturbed layer.
18 citations
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18 citations
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TL;DR: In this paper, a deformation-induced lateral migration of a bubble slowly rising near a vertical plane wall in a stagnant liquid is numerically and theoretically investigated for a situation with a short clearance c between the bubble interface and the wall.
Abstract: Deformation-induced lateral migration of a bubble slowly rising near a vertical plane wall in a stagnant liquid is numerically and theoretically investigated. In particular, our focus is set on a situation with a short clearance c between the bubble interface and the wall. Motivated by the fact that numerically and experimentally measured migration velocities are considerably higher than the velocity estimated by the available analytical solution using the Faxen mirror image technique for a/(a + c) ≪ 1 (here a is the bubble radius), when the clearance parameter ϵ(=c/a) is comparable to or smaller than unity, the numerical analysis based on the boundary-fitted finite-difference approach solving the Stokes equation is performed to complement the experiment. The migration velocity is found to be more affected by the high-order deformation modes with decreasing ϵ. The numerical simulations are compared with a theoretical migration velocity obtained from a lubrication study of a nearly spherical drop, which describes the role of the squeezing flow within the bubble–wall gap. The numerical and lubrication analyses consistently demonstrate that when ϵ ≤ 1, the lubrication effect makes the migration velocity asymptotically μVB12/(25ϵγ) (here, VB1, μ and γ denote the rising velocity, the dynamic viscosity of liquid and the surface tension, respectively).
18 citations
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TL;DR: In this article, a simple yet rather general mathematical model is presented for predicting the distribution of condensate layer thickness when aerodynamic shear is the dominant mechanism of liquid flow along the surface.
Abstract: A simple yet rather general mathematical model is presented for predicting the distribution of condensate layer thickness when aerodynamic shear is the dominant mechanism of liquid flow along the surface. The Newtonian condensate film is treated using well-known thin-layer (lubrication theory) approximations, and condensate supply is taken to be the result of either convective diffusion or inertial impaction. Illustrative calculations for a circular cylinder in a crossflow at Re = 100,000 reveal the consequences of alternate condensate arrival mechanisms and the existence of thicker reverse-flow films behind the position of gas boundary-layer separation. The present formulation is readily generalized to include transient liquid layer flows on noncircular objects of variable surface temperature, as encountered in turbine-blade materials testing or operation.
18 citations