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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: In this paper, the shape, velocity and lubrication film thickness distribution of a droplet rising in a vertical Hele-Shaw cell were studied experimentally, numerically and using a lubrication approach.
Abstract: We study here experimentally, numerically and using a lubrication approach, the shape, velocity and lubrication film thickness distribution of a droplet rising in a vertical Hele-Shaw cell. The droplet is surrounded by a stationary immiscible fluid and moves purely due to buoyancy. A low density difference between the two media helps to operate in a regime with capillary number . The experimental data show that in this regime the droplet velocity is not influenced by the thickness of the thin lubricating film and the dynamic meniscus. For iso-viscous cases, experimental and three-dimensional numerical results of the film thickness distribution agree well with each other. The mean film thickness is well captured by the Aussillous & Quere (Phys. Fluids, vol. 12 (10), 2000, pp. 2367–2371) model with fitting parameters. The droplet also exhibits the ‘catamaran’ shape that has been identified experimentally for a pressure-driven counterpart (Huerre et al., Phys. Rev. Lett., vol. 115 (6), 2015, 064501). This pattern has been rationalized using a two-dimensional lubrication equation. In particular, we show that this peculiar film thickness distribution is intrinsically related to the anisotropy of the fluxes induced by the droplet’s motion.

14 citations

Journal ArticleDOI
TL;DR: In this article, the authors revisited the Landau and Levich analysis of a coating flow in the case where the flow in thin liquid film is supported by a Rayleigh surface acoustic wave (SAW), propagating in the solid substrate.
Abstract: In this paper we revisit the Landau and Levich analysis of a coating flow in the case where the flow in the thin liquid film is supported by a Rayleigh surface acoustic wave (SAW), propagating in the solid substrate. Our theoretical analysis reveals that the geometry of the film evolves under the action of the propagating SAW in a manner that is similar to the evolution of films that are being deposited using the dip coating technique. We show that in a steady state the thin-film evolution equation reduces to a generalized Landau–Levich equation with the dragging velocity, imposed by the SAW, depending on the local film thickness. We demonstrate that the generalized Landau–Levich equation has a branch of stable steady state solutions and a branch of unstable solutions. The branches meet at a saddle-node bifurcation point corresponding to the threshold value of the SAW intensity. Below the threshold value no steady states were found and our numerical computations suggest a gradual thinning of the liquid film from its initial geometry.

14 citations

Journal ArticleDOI
TL;DR: In this paper, the hydrodynamic theory of lubrication is used to obtain an analytical solution which relates the flowrate, rotation rate, pressure drop and applied torque as functions of two geometric parameters for a viscous pump.
Abstract: A viscous pump is a device such that a cylindrical rotor is eccentrically placed in a channel, so that the viscous resistance between the small and large gaps between the cylinder and the channel walls generate a net flow along the channel. Assuming that the gaps between the cylinder and the channel walls are small compared to the radius of the rotor, the hydrodynamic theory of lubrication may be utilized to study the viscous pump. Here lubrication theory is used to obtain an analytical solution which relates the flowrate, rotation rate, pressure drop and applied torque as functions of two geometric parameters for a viscous pump. This analysis differs from a previous similar study in two ways. Firstly, certain integrals are evaluated explicitly, and secondly the standard no-slip boundary condition of fluid mechanics has been replaced with the Navier boundary condition which allows a degree of tangential velocity slip on all solid boundaries. Comparison with the prior known solution shows that the solution obtained in this study predicts a slightly improved pump performance for the case of no-slip. For the case of slip, our results demonstrate that the performance of the pump is significantly improved.

14 citations

Journal ArticleDOI
TL;DR: In this paper, a bilayer system has two unstable eigenmodes: squeezing and bending, and the system exhibits the avoided crossing behavior, where the two eigen modes are interchanged.
Abstract: Two superposed thin layers of fluids are prone to interfacial instabilities due to London-van der Waals forces. Evolution equations for the film thicknesses are derived using lubrication theory. Using the intrinsic scales, for a single layer, results in a system with parametric dependence of four ratios of the two layers: surface tension, Hamaker constant, viscosity, and film thickness. In contrast to the single layer case, the bilayer system has two unstable eigenmodes: squeezing and bending. For some particular parameter regimes, the system exhibits the avoided crossing behavior, where the two eigenmodes are interchanged. Based on numerical analysis, the system evolves into four different rupture states: basal layer rupture, upper layer rupture, double layer rupture, and mixed layer rupture. The ratio of Hamaker constants and the relative film thickness of the two layers control the system dynamics. Remarkably, the line of avoided crossing demarks the transition region of mode mixing and energy transfer...

14 citations

Journal ArticleDOI
TL;DR: In this article, a simulation of particle focusing in a corrugated tube is performed using a discrete-element method (DEM) and the results are compared to an asymptotic approximation valid for low Stokes numbers.
Abstract: A computational study is performed of the transport of a particulate suspension through a corrugated tube using a discrete-element method (DEM). The tube is axisymmetric with a radius that varies sinusoidally along the tube length, which, in the presence of a mean suspension flow, leads to periodic inward and outward acceleration of the advected particles. The oscillations in radial acceleration and straining rate lead to a net radial drift, with mean acceleration measuring about an order of magnitude smaller than the instantaneous radial acceleration, which over time focuses small particles within the tube. The foundations of particle focusing in this flow are examined analytically using lubrication theory, together with a low-Stokes-number approximation for the particle drift. This lubrication-theory solution provides the basic scaling for how the particle drift will vary with wave amplitude and wavelength. Computations are then performed using a finite-volume method for a fluid flow in the tube at higher Reynolds numbers over a range of amplitudes, wavelengths and Reynolds numbers, examining the effect of each of these variables on the averaged radial fluid acceleration. A DEM is used to simulate particle behaviour at finite Stokes numbers, and the results are compared to an asymptotic approximation valid for low Stokes numbers. At low tube Reynolds number (e.g. Re = 10), the drift velocity induced by the tube corrugations focuses the particles onto the tube centreline, in accordance with the low-Stokes-number approximation based on the axial-averaged fluid radial acceleration. At higher tube Reynolds numbers (e.g. Re = 100), the correlation between the particle radial oscillation and the fluid acceleration field leads the outermost particles to drift into a ring at a finite radius from the tube centre, with little net motion of the particles in the innermost part of the tube. At larger Stokes numbers, particles can be dispersed to the outer regions of the tube due to particle outward dispersion from the large instantaneous radial acceleration. The effects of eddy formation within the corrugation crests on particle focusing are also examined.

14 citations


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