Curved squeeze film with inertial effects — energy integral approach
TL;DR: In this paper, the laminar squeeze flow of an incompressible viscous fluid between a flat circular disk and a curved circular disk is analyzed by taking into account the effects of fluid inertia and curvature, using energy integral method.
About: This article is published in Fluid Dynamics Research.The article was published on 2002-03-01. It has received 14 citations till now. The article focuses on the topics: Laminar flow & Curvature.
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TL;DR: In this article, the deformations and stresses during squeeze flows are evaluated for a wider class of materials than previously covered in articles on this subject, including generalised Newtonian fluids, yield stress fluids, as well as elastic and viscoelastic materials.
Abstract: The deformations and stresses during squeeze flows are evaluated for a wider class of materials than previously covered in articles on this subject. These include generalised Newtonian fluids, yield stress fluids, as well as elastic and viscoelastic materials. Wherever possible, results are given in a compact mathematical form. The effect of different boundary conditions (no slip, perfect slip and partial slip) and how these interact with different types of material behaviour to give a variety of macroscopic responses is also discussed. The significance of this in using squeeze flow as a rheometry method is highlighted and a state-of-the-art view of squeeze flow rheometry is given.
384 citations
TL;DR: The force to squeeze a Herschel-Bulkley material without slip between two approaching surfaces of various curvature is calculated in this article, where concordant measurements are made of the yield stress τ 0 for two soft solids measured by the vane and by each squeeze-flow method.
Abstract: The force to squeeze a Herschel–Bulkley material without slip between two approaching surfaces of various curvature is calculated The Herschel–Bulkley yield stress requires an infinite force to make plane–plane and plane–concave surfaces touch However, for plane–convex surfaces this force is finite, which suggests experiments to access the mesoscopic thickness region (1–100 μm) of non-Newtonian materials using squeeze flow between a plate and a convex lens Compared to the plane–parallel surfaces that are used most often for squeeze flow, the dependence of the separation h′ and approach speed V on the squeezing-time is more complicated However, when the surfaces become close, a simplification occurs and the near-contact approach speed is found to vary as V ∝ h′0 if the Herschel–Bulkley index is n<1/3, and V ∝ h′(3n-1)/(2n) if n≥ 1/3 Using both plane–plane and plane–convex surfaces, concordant measurements are made of the Herschel–Bulkley index n and yield stress τ0 for two soft solids Good agreement is also found between τ0 measured by the vane and by each squeeze-flow method However, one of the materials shows a limiting separation and a V(h′) behaviour not predicted by theory for h′<10 μm, possibly owing to an interparticle structure of similar lengthscale
15 citations
Cites background or methods from "Curved squeeze film with inertial e..."
...Thus, Flanigan and Shull (1999) used a hemispherical indenter to measure the adhesive and elastic properties of thin gel layers, and Cua and Shaw (2002, 2004) measured the viscosity of HDPE melts squeezed between a plano-convex lens and an optical flat....
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...Although most workers use parallel-plate tools with typically millimetric separation, non-planar SF geometries have received considerable study (Hasegawa 1985; Phan-Thien and Zheng 1991; Dong Chen 1993; Rodin 1996; Hoffner et al. 2001; Huang et al. 2002; Lian et al. 2001; Usha and Vimila 2002; Matsoukas and Mitsoulis 2003), but they have been little-used experimentally....
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TL;DR: In this article, a numerical investigation of the hydrodynamic lubrication of a porous squeeze film between two circular discs is presented. And the results show that the effect of the porous disc is to reduce the lubricating properties of the fluid film and this effect is increased during the squeezing action.
Abstract: The present paper deals with a numerical investigation of the hydrodynamic lubrication of a porous squeeze film between two circular discs. To this purpose, the thin film (reduced) Navier Stokes equations and a generalised porous medium model are solved. The numerical results show that the effect of the porous disc is to reduce the lubricating properties of the fluid film. This effect is increased during the squeezing action. In addition, it is shown that the film pressure, the load-carrying capacity and the velocity field based only on the Darcy model are predicted higher than those obtained from the generalised porous medium model. Copyright © 2009 John Wiley & Sons, Ltd.
10 citations
TL;DR: In this paper, a theoretical investigation of the laminar squeeze flow of a couple-stress fluid between a flat circular static disk and an axisymmetric curved circular moving disk has been carried out using modified lubrication theory and microcontinuum theory.
Abstract: A theoretical investigation of the laminar squeeze flow of a couple-stress fluid between a flat circular static disk and an axisymmetric curved circular moving disk has been carried out using modified lubrication theory and microcontinuum theory. The combined effects of fluid inertia forces, curvature of the disk and non-Newtonian couple stresses on the squeeze film behavior are investigated analytically. Each of these effects and their combinations show a significant enhancement in the squeeze film behavior, and these are studied through their effects on the squeeze film pressure and the load carrying capacity of the fluid film as a function of time. Two different forms of the gapwidth between the disks have been considered, and the results have been shown to be in good agreement with the existing literature.
8 citations
TL;DR: In this article, the shape and extent of the core for the case of sinusoidal squeeze motion has been determined numerically for various values of the Bingham number, Reynolds number and for various amplitudes of squeeze motion.
Abstract: Lubricants with variable viscosity are assuming importance for their applications in polymer industry, thermal reactors and in biomechanics. With the bearing operations in machines being subjected to high speeds, loads, increasing mechanical shearing forces and continually increasing pressures, there has been an increasing interest to use non-Newtonian fluids characterized by an yield value. The most elementary constitutive equation in common use that describes a material which yields is that of Bingham fluid. In the present work, the problem of a circular squeeze film bearing lubricated with Bingham fluid under the sinusoidal squeeze motion has been analyzed. The shape and extent of the core for the case of sinusoidal squeeze motion has been determined numerically for various values of the Bingham number. Numerical solutions have been obtained for the bearing performances such as pressure distribution and load capacity for different values of Bingham number, Reynolds number and for various amplitudes of squeeze motion. The effects of fluid inertia, non-Newtonian characteristics, and the amplitudes of squeeze motion on the bearing performances have been discussed.
7 citations
Cites methods from "Curved squeeze film with inertial e..."
...[10] R. Usha and P. Vimala, Curved squeeze film with inertial effects-energy integral approach....
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...With sinusoidal squeeze motion, Usha and Vimala [10] have applied the energy integral approach to find the behavior of curved squeeze film bearing using a Newtonian lubricant....
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...The effects of fluid inertia forces and non-Newtonian characteristics of lubricants in the squeeze film bearings have been examined by several investigators, (Tichy and Winer [8], Covey and Stanmore [2], Gartling and Phan-Thien [4], Donovan and Tanner [7], Huang et al. [6], Usha and Vimala [9]) but there are few papers attempting to describe the combined effects of fluid inertia forces and non-Newtonian characteristics of lubricants (Elkough [3], Batra and Kandasamy [1]) ....
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...[9] R. Usha and P. Vimala, Inertia effects in circular squeeze films containing a central air bubble....
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References
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17 citations
15 citations
TL;DR: In this article, the problem of a squeeze film between a curved circular plate and a plane wall is studied theoretically and a perturbation solution is found in powers of ratio of the gap to the radius.
Abstract: The problem of a squeeze film between a curved circular plate and a plane wall is studied theoretically. The shape of the curved circular plate is assumed to be axisymmetric, that is, to be expressed by a function of only the radius coordinate. The circular plate is brought up to the wall under the action of a constant external force. The gap between the circular plate and the wall is assumed to be small compared with the radius of the circular plate. A perturbation solution is found in powers of ratio of the gap to the radius. This gap equation governing the gap is derived for a curved disk with any shape. This gap equation is solved numerically for the case of the curved disk with a parabolic shape. The properties of the squeeze film are clarified through the force-gap relation, the critical external force, the inertia effect and the pressure distribution.
10 citations
9 citations
TL;DR: In this article, a viscous incompressible fluid is contained between two parallel disks with arbitrarily shrinking width h(τ), and the solution is obtained as a power series in a single nondimensional parameter (squeeze number) S, for small values of S in contrast to the multifold series solution obtained by Ishizawa in terms of an infinite set of nondimensional parameters.
Abstract: A viscous incompressible fluid is contained between two parallel disks with arbitrarily shrinking width h(τ). The solution is obtained as a power series in a single nondimensional parameter (squeeze number) S, for small values of S in contrast to the multifold series solution obtained by Ishizawa in terms of an infinite set of nondimensional parameters. The gap width h(τ) is obtained for different states: when the top disk moves with constant velocity, constant force or constant power.
8 citations