Curved squeeze film with inertial effects — energy integral approach

Squeeze flow theory and applications to rheometry: A review

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.

Flow of soft solids squeezed between planar and spherical surfaces

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

A general model for porous medium flow in squeezing film situations

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.

Theoretical Investigation of Couple Stress Squeeze Films in a Curved Circular Geometry

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.

Rheodynamic lubrication of a squeeze film bearing under sinusoidal 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.

Fluid inertia effects in squeeze films

Abstract: Fluid inertia effects in squeeze films are analyzed. Experimental results are also presented. The agreement between theory and experiment is very good.

The Unsteady Laminar Flow between Two Parallel Discs with Arbitrarily Varying Gap Width

Abstract: A theoretical analysis is presented for the unsteady laminar flow of an incompressible fluid in a narrow gap between two parallel discs of which gap-width h (t) varies arbitrarily with time. An infinite set of the non-dimensional time-dependent parameters [numerical formula], …… is introduced providing that the function h (t) is continuously differentiable, and the exact solutions of the Navier-Stokes equations and the thermal energy equation are obtained as the "multifold"series of these non-dimensional parameters. As an application, a detailed numerical study has been made of the fundamental case when the walls perform reciprocating harmonic oscillations with finite amplitudes {h (t)=h0 (1+asinωt)}. The flow characteristics are governed by the two non-dimensional parameters a and Rω=(h02ω)/υ. As compared with the sinusoidal velocity of the gap-width change, (dh)/(dt)=aωh0cosωt, the varying hydrodynamical force acting on the wall surface becomes more distorted in wave form as a increases, and becomes more advanced in phase as Rω increases. Heat is generated in the fluid between the walls through viscous friction : when the fluid is cooled by only one wall surface the fluid temperature becomes very much higher than when the cooling is done by both the two walls.