The flow of a power-law liquid in a continuous-flow squeeze film

Consideration is given to the flow of an inelastic ‘power-law’ liquid in a continuous flow squeeze film. This simulates the flow in a conventional squeeze film by continuously injecting fluid into the narrow gap between two plates through the lower plate (Oliver et al. [6]). To zero order in the usual lubrication approximation the results are identical with those for the conventional squeeze film. To first order, useful corrections to the normal force due to the effects of inertia are obtained.     

An experimental test of equations predicting the load bearing capacity of squeeze films of elastico-viscous liquid

A form of squeeze film apparatus was recently described in which the movement of one plate towards the other was simulated by the continuous volume generation of liquid over the plate area. The liquid exuded from a large number of holes in the lower plate surface and formed a “continous flow” version of squeeze film apparatus with no moving parts [1]. A later paper gave derivations of equations from which squeeze film load bearing capacity could be evaluated, taking into account viscous, inertial and normal stress effects in the liquid film [2].In order to find the total load in a squeeze film system, it was necessary to obtain the relationship between the first normal stress difference and shear rate for the liquid in use, using an experimental method. At high shear rates, the jet thrust method provided these data [3,4] and from them the load bearing capacity of squeeze films of hot, polymer-thickened oil were predicted [2].A more complete test of the method is possible with a highly elastic liquid because considerable load enhancement due to extra stress is present at moderate deformation rates in squeeze film systems [1,5,6,7]. Thus a 0.1 per cent aqueous polyacrylamide solution gives well-defined load enhancement and (quite independently) the jet thrust method gives the relationship between normal stress and shear rate from which predictions of load enhancement may be made. Furthermore, convergent nozzles may be used in the jet thrust apparatus [3] to measure the stress development in an elastic liquid which is being simulateneously sheared and stretched, a situation which more closely resembles the squeeze film case than that of steady shear.     

Load enhancement effects by polymer-thickened oils in strip squeeze film flow

A modification to existing equipment is described which permits continuous squeeze-film flow to be obtained between parallel-sided strips of material rather than between disc-shaped surface. Squeeze film flow is simulated by having liquid move through one of the surfaces via an array of equispaced holes. The Squeeze-film behavior of a Newtonian base oil is first tested at temperatures of 24°C and 55°C. It is shwon that loads are in reasonable agreement with theretical predictions and that end effects (corrected by means of a guard ring) and fluid maldistribution effects are of small proporitons. At the very highest liquid flowrates, the rapid liquid flow through the holes may influence the measured load. The Polymer-thickened oils, representinhg 10 W/30 and 10 W/50 motor oils, are tested at temperatures of 24°C and 55°C. Both oils five marked load enhancement, compared with Newtonian oil under similar flow conditions, at the higher flowrates used. The 10 W/50 oil gives load enhancement of 76 per cent at 55°C, increasing rapidly with the simulated approach velocity. Fluid inertia effects in the squeeze film flow aslo increase the load significantly. The results confirm earlier data using disc-shaped surfaces; load enhancement is greater in the present work on strip squeeze films because the fluid deformation rates are greater (2000 s^t-1 in planar extention and 2 x 10⁵ s^t-1 in shear). It is suggested that the fuel consumption of cars could be improved by the development of elastic, shear stable oils of lower viscosity than those currently in use.     

The behavior of viscoelastic squeeze films subject to normal oscillations, including the effect of fluid inertia

The problem of the squeeze film flow of a viscoelastic fluid between parallel, circular disks is analyzed. The upper disk is subject to small, axial oscillations. Lodge's “rubber-like liquid” is used as the viscoelastic fluid model, and fluid inertia forces are included. An exact solution to the equations of motion is obtained involving in-phase and out-of-phase components of velocity field and load, with respect to the plate velocity. Peculiar resonance phenomena in the load amplitude are exhibited at high Deborah number. At certain combinations of Reynolds number and Deborah number, the in-phase and/or out-of-phase velocity field components may attain an unusual circulating type of motion in which the flow reverses direction across the film. In the low Deborah number limit, and in the low Reynolds number limit, the results of this study reduce to those obtained by other workers.     

Combined effects of non-Newtonian couple stresses and fluid inertia on the squeeze film characteristics between a long cylinder and an infinite plate

On the basis of the Stokes micro-continuum theory together with the averaged inertia principle, the combined effects of non-Newtonian couple stresses and convective fluid inertia forces on the squeeze film motion between a long cylinder and an infinite plate are presented. A closed-form solution has been derived for squeeze film characteristics including the film pressure, the load capacity and the response time. Comparing with the Newtonian-lubricant non-inertia case, the combined effects of couple stresses and convective inertia forces provide an increase in the film pressure, the load capacity and the response time. In addition, the quantitative effects of couple stresses and convective inertia forces are more pronounced for cylinder–plate system operating at a larger couple stress parameter and film Reynolds number, as well as a smaller squeeze film height. To guide the use of the present study, a numerical example is also illustrated for engineers when considering both the effects of non-Newtonian couple stresses and fluid convective inertia forces.     

An investigation of squeeze flow as a viable technique for determining the yield stress

A systematic study of squeeze flow (SF) was performed on different concentrations of Carbopol with varying yield stresses. A sample of constant volume was placed between two parallel plates and a series of constant force steps applied, following the plate separation as a function of time. Precise rheological measurements of the model yield stress fluids were performed in addition to the well-controlled SF tests. These rheological measurements were used in conjunction with the SF equations to determine the time-dependent plate separation, allowing a direct comparison of theory and experiment throughout the entire test. The limiting height achieved during constant force SF reveals information about the yield stress of the fluid as predicted by the theory. It appears that by carefully controlling the experimental conditions of the squeeze test one can obtain yield stress values that agree with the rheological measurements within 10%. Additionally, the validity of the lubricational theory was tested; not only for the determination of the yield stress but throughout the flow as well.     

Effect of lubricant inertia in bearings with a non-Newtonian lubricant

Summary The inertia effects in externally pressurized and squeeze film bearings with lubricants obeying a power law are considered. It is found that the inertia forces decrease the load capacity of the externally pressurized bearing with a given flow rate and the inertia effect increases with the flow behaviour index. At a given feeding pressure, on the other hand, the inertia increases or decreases the load capacity when the flow behaviour index is smaller than or greater than 3, respectively. For squeeze films between circular plates and rectangular plates, the rate of squeeze is slowed down by the inertia and the inertia effect is larger in dilatant lubricants than in pseudoplastic lubricants.Nomenclature 2a diameter of the bearing, width of rectangular plates - 2b diameter of the recess - 2h film thickness - 2h ₀ initial thickness of squeeze films - l length of the rectangular plates - m consistency index - n flow behaviour index - p pressure - p _e external pressure - p _i feeding pressure - q flow rate - r radial distance - t time - u velocity of the lubricant - v squeeze velocity - w load capacity - W dimensionless load capacity - axial distance - viscosity of the lubricant - density of the lubricant     

Instantaneous Squeeze-Film Force Between a Heat Exchanger Tube and a Support Plate for Arbitrary Tube Motion

The instantaneous squeeze-film force between a heat exchanger tube and a support plate is studied. Based on a two-dimensional rectangular plate model, a short-sleeve squeeze-film model for arbitrary tube motion is developed. The instantaneous squeeze-film force is expressed in normal and tangential directions. The normal squeeze-film force consists of four nonlinear terms, the viscous, unsteady inertia, convective inertia and centripetal inertia terms. Three nonlinear terms, the viscous, unsteady inertia and Coriolis inertia terms, make up the tangential squeeze-film force. An experimental apparatus was developed in order to evaluate the theoretical models against measurements of a finite length squeeze film. A modified model based on the experimental data is obtained where the viscous terms for both directions are multiplied by the instantaneous Reynolds number. All the inertia terms are multiplied by constant coefficients. The modified model is in good agreement with most experimental cases for unsymmetrical linear motion, approximate circular motion and elliptical motion. The form of the modified model is suitable for predicting instantaneous squeeze-film forces in the simulation of heat exchanger tube vibration. Further work using different sized components and fluid properties is required in order to finalize coefficient values.     

Inertia effects in hydromagnetic lubrication

Summary A theoretical investigation of inertia effects in a squeeze film bearing with an electrically conducting lubricant in the presence of a uniform transverse magnetic field is presented. The two cases of infinitely long rectangular plates and circular plates as bearing surfaces are considered. It is shown that the load supporting capacity of the bearing increases and the squeeze decreases if the lubricant inertia effects are taken into account. However, the inertia effect becomes smaller when the strength of the magnetic field increases.     

Free surface effects in squeeze flow of Bingham plastics

New results for the squeeze flow of Bingham plastics show the shape of the free surface in quasi-steady-state simulations, and its effect on the yielded/unyielded regions and the squeeze force. The present simulation results are obtained for both planar and axisymmetric geometries as in our previous paper [A. Matsoukas, E. Mitsoulis, Geometry effects in squeeze flow of Bingham plastics, J. Non-Newtonian Fluid Mech. 109 (2003) 231–240] and for aspect ratios ranging from 0.01 to 1. Bigger aspect ratios produce more free surface movement relative to the disk radius or plate length, but less movement relative to the gap. Planar geometries give more free surface movement than axisymmetric ones. Viscoplasticity serves to reduce the free surface movement and its deformation. In some cases of planar geometries and big aspect ratios, unyielded regions appear at the free surface, while the small unyielded regions near the center of the disks or plates are not affected. Including the free surface in the calculations of the squeeze force adds a small percentage to the values depending on aspect ratio and Bingham number. The previously fitted easy-to-use equations are corrected to account for that effect.     

Squeeze flow of Bingham fluids under slip with friction boundary condition

This paper develops a theoretical analysis of a Bingham fluid in slipping squeeze flow. The flow field decomposition consists in combining a central extensional flow zone in the plane of symmetry and shear flow zones near the plates. It is also considered that the slipping zone is located around a central sticking zone as previously shown from experiments. It is assumed that the shear stress at the plates is constant in the slipping zone and equals a fixed friction yield value. The squeeze force required to compress a Bingham fluid under the slipping behaviour as well as the radial evolution of the transition point between both sticking and slipping zones are finally determined.     

Derivation of two-dimensional couple-stress hydromagnetic squeeze film Reynolds equation and application to wide parallel rectangular plates

On the basis of Stokes couple-stress fluid model together with the hydromagnetic flow equations, a two-dimensional curved squeeze-film Reynolds equation has been derived. This equation can be applied to the study of squeeze film characteristics including the non-Newtonian hydromagnetic effects, in which the general film shape is h=h(x,z,t). To guide the application of the equation, an example of one-dimensional parallel rectangular plates lubricated with a non-Newtonian couple-stress, electrically conducting lubricant is illustrated. According to the results, the effects of couple stresses and external magnetic fields provide an increase in the load capacity and the response time as compared to the classical Newtonian hydrodynamic rectangular squeeze-film plates.     

Mathematical modeling of fractional derivatives for magnetohydrodynamic fluid flow between two parallel plates by the radial basis function method

Investigations into the magnetohydrodynamics of viscous fluids have become more important in recent years, owing to their practical significance and numerous applications in astro-physical and geo-physical phenomena. In this paper, the radial base function was utilized to answer fractional equation associated with fluid flow passing through two parallel flat plates with a magnetic field. The magnetohydrodynamics coupled stress fluid flows between two parallel plates, with the bottom plate being stationary and the top plate moving at a persistent velocity. We compared the radial basis function approach to the numerical method (fourth-order Range-Kutta) in order to verify its validity. The findings demonstrated that the discrepancy between these two techniques is quite negligible, indicating that this method is very reliable. The impact of the magnetic field parameter and Reynolds number on the velocity distribution perpendicular to the fluid flow direction is illustrated. Eventually, the velocity parameter is compared for diverse conditions α, Reynolds and position (y), the maximum of which occurs at α = 0.4. Also, the maximum velocity values occur in α=0.4 and Re=1000 and the concavity of the graph is less for α=0.8.     

An efficient method for vibration and stability analysis of rectangular plates axially moving in fluid

An efficient method is developed to investigate the vibration and stability of moving plates immersed in fluid by applying the Kirchhoff plate theory and finite element method.The fluid is considered as an ideal fluid and is described with Bernoulli’s equation and the linear potential flow theory.Hamilton’s principle is used to acquire the dynamic equations of the immersed moving plate.The mass matrix,stiffness matrix,and gyroscopic inertia matrix are determined by the exact analytical integration.The numerical results show that the fundamental natural frequency of the submersed moving plates gradually decreases to zero with an increase in the axial speed,and consequently,the coupling phenomenon occurs between the first-and second-order modes.It is also found that the natural frequency of the submersed moving plates reduces with an increase in the fluid density or the immersion level.Moreover,the natural frequency will drop obviously if the plate is located near the rigid wall.In addition,the developed method has been verified in comparison with available results for special cases.     

A method for the estimation of the film thickness and plate tilt angle in thin film misaligned plate–plate rheometry

This communication describes a general procedure for the estimation of the true gap and tilt angle in commercially available torsional flow plate–plate rheometers by simply measuring the torque and normal force acting on the plates when shearing a Newtonian fluid.     

Squeeze film flow of ideal elastic liquids

An exact solution is presented for the squeeze film flow of an Oldroyd B. fluid. The solution demonstrates that the flow kinematics is similar to the Newtonian (or Maxwellian) one. Theoretical predictions for constant velocity squeezing are compared to experimental observation for well characterized non-shear thinning elastic fluids. It is shown both theoretically and experimentally that the effect of elasticity in a constant velocity squeeze film flow is to always reduce the load relative to the inelastic (Newtonian) prediction and that this load reduction falls between the upper and lower asymptote prediction by the exact solution for the Oldroyd B fluid. The upper load asymptote is given by the Stefan solution for the viscosity of the polymer solution and the lower asymptote is given by the Stefan solution for the viscosity of the solvent. Experimental observations agree with the theoretical prediction for the Oldroyd B fluid at low shear rates where it is shown that the steady and dynamic flow properties of the test fluids used in the experimental program are well represented by the Oldroyd B constitutive equation. With the exception of the work of Lee et al. [6] for constant load squeezing of a Maxwell fluid, this work represents one of the few cases where experimental observation of large effects due to elasticity are indeed predicted with a constitutive equation which actually describes the steady and dynamic shear properties of the fluids used in the experimental program.     

Influence of inertia,topography and gravity on transient axisymmetric thin‐film flow

This study examines theoretically the development of early transients for axisymmetric flow of a thin film over a stationary cylindrical substrate of arbitrary shape. The fluid is assumed to emerge from an annular tube as it is driven by a pressure gradient maintained inside the annulus, and/or by gravity in the axial direction. The interplay between inertia, annulus aspect ratio, substrate topography and gravity is particularly emphasized. Initial conditions are found to have a drastic effect on the ensuing flow. The flow is governed by the thin‐film equations of the ‘boundary‐layer’ type, which are solved by expanding the flow field in terms of orthonormal modes in the radial direction. The formulation is validated upon comparison with the similarity solution of Watson (J. Fluid Mech 1964; 20 :481) leading to an excellent agreement when only 2–3 modes are included. The wave and flow structure are examined for high and low inertia. It is found that low‐inertia fluids tend to accumulate near the annulus exit, exhibiting a standing wave that grows with time. This behaviour clearly illustrates the difficulty faced with coating high‐viscosity fluids. The annulus aspect is found to be influential only when inertia is significant; there is less flow resistance for a film over a cylinder of smaller diameter. For high inertia, the free surface evolves similarly to two‐dimensional flow. The substrate topography is found to have a significant effect on transient behaviour, but this effect depends strongly on inertia. It is observed that the flow of a high‐inertia fluid over a step‐down exhibits the formation of a secondary wave that moves upstream of the primary wave. Gravity is found to help the film (coating) flow by halting or prohibiting the wave growth. The initial film profile and velocity distribution dictate whether the fluid will flow downstream or accumulate near the annulus exit. Copyright © 2004 John Wiley & Sons, Ltd.     

Squeezing flow of elastic liquids

The theoretical analysis is made of the relation between applied force and plate separation for squeezing flows of viscoelastic liquids between closely-spaced parallel disks. The lubrication approximation and the quasi-steady-state assumption are employed in the development. Elastic effects are incorporated through inclusion of normal stresses. Solutions are presented for liquids with power-law viscometric functions, and a numerical procedure is used for fluids having viscometric functions of arbitrary form. For fast and slow squeezing, calculated values of t_{$\text{1}\text{2}$}, the time required to squeeze out half the fluid, are found to agree with the constant force data of Leider [1,2].     

Computations of flow over a flexible plate using the hybrid Cartesian/immersed boundary method

A hybrid Cartesian/immersed boundary code is developed and applied to interactions between a flexible plate and a surrounding fluid. The velocities at the immersed boundary (IB) nodes are reconstructed by interpolations along local normal lines to an interface. A new criterion is suggested to distribute the IB nodes near an interface. The suggested criterion guarantees a closed fluid domain by a set of the IB nodes and it is applicable to a zero‐thickness body. To eliminate the pressure interpolation at the IB nodes, the hybrid staggered/non‐staggered grid method is adapted. The developed code is validated by comparisons with other experimental and computational results of flow around an in‐line oscillating cylinder. Good agreements are achieved for velocity profiles and vorticity and pressure contours. As applications to the fluid–structure interaction, oscillations of flexible plate in a resting fluid and flow over a flexible plate are simulated. The elastic deformations of the flexible plate are modelled based on the equations of motion for plates considering the fluid pressure as the external load on the plate. Two non‐dimensional parameters are identified and their effects on the damping of the plate motion are examined. Grid convergence tests are carried out for both cases. Copyright © 2007 John Wiley & Sons, Ltd.     

The squeeze flow of a bi-viscosity fluid between two rigid spheres with wall slip

In this paper, the squeeze flow between two rigid spheres with a bi-viscosity fluid is examined. Based on lubrication theory, the squeeze force is calculated by deriving the pressure and velocity expressions. The results of the normal squeeze force are discussed, and fitting functions of the squeeze and correction coefficients are given. The squeeze force between the rigid spheres increases linearly or logarithmically with the velocity when most or part of the boundary fluid reaches the yield state, respectively. Furthermore, the slip correction coefficient decreases with the increase in the velocity. The investigation may contribute to the further study of bi-viscosity fluids between rigid spheres with wall slip.