Showing papers on "Lubrication theory published in 1997"

Stokes flow in collapsible tubes: computation and experiment

Abstract: This paper is concerned with the problem of viscous flow in an elastic tube. Elastic tubes collapse (buckle non-axisymmetrically) when the transmural pressure (internal minus external pressure) falls below a critical value. The tube's large deformation during the buckling leads to a strong interaction between the fluid and solid mechanics.In this study, the steady three-dimensional Stokes equations are used to analyse the slow viscous flow in such a tube whose deformation is described by geometrically nonlinear shell theory. Finite element methods are used to solve the large-displacement fluid–structure interaction problem. Typical wall deformations and flow fields in the strongly collapsed tube are shown. Extensive parameter studies illustrate the tube's flow characteristics (e.g. volume flux as a function of the applied pressure drop through the tube) for boundary conditions corresponding to the four fundamental experimental setups. It is shown that lubrication theory provides an excellent approximation of the fluid traction while being computationally much less expensive than the solution of the full Stokes equations. Finally, the computational predictions for the flow characteristics and the wall deformation are compared to the results obtained from an experiment.

Displacement of fluid droplets from solid surfaces in low-Reynolds-number shear flows

Abstract: The yield conditions for the displacement of fluid droplets from solid boundaries are studied through a series of numerical computations. The study includes gravitational and interfacial forces, but is restricted to two-dimensional droplets and low-Reynolds-number flow. A comprehensive study is conducted, covering a wide range of viscosity ratio λ, Bond number Bd, capillary number Ca and contact angles θA and θR. The yield conditions for drop displacement are calculated and the critical shear rates are presented as functions Ca(λ, Bd, θA, Δθ) where Δθ=θA−θR is the contact angle hysteresis. The numerical solutions are based on the spectral boundary element method, incorporating a novel implementation of Newton's method for the determination of equilibrium free surface profiles. The numerical results are compared with asymptotic theories (Dussan 1987) based on the lubrication approximation. While excellent agreement is found in the joint asymptotic limits Δθ[Lt ]θA[Lt ]1, the useful range of the lubrication models proves to be extremely limited. The critical shear rate is found to be sensitive to viscosity ratio with qualitatively different results for viscous and inviscid droplets. Gravitational forces normal to the solid boundary have a significant effect on the displacement process, reducing the critical shear rate for viscous drops and increasing the rate for inviscid droplets. The low-viscosity limit λ→0 is shown to be a singular limit in the lubrication theory, and the proper scaling for Ca at small λ is identified.

A mathematical model for drying paint layers

Abstract: Many industrial processes involve the coating of substrates with thin layers of paint. This paper is concerned with modelling the variations in layer thickness which may occur as a paint layer dries. Firstly, a systematic derivation is provided of a model based on classical lubrication theory for a drying paint layer consisting of a non-volatile resin and a volatile solvent. The effects of variable surface tension, viscosity, solvent diffusivity and solvent evaporation rate are all included in the model. This analysis makes explicit the validity of the physically intuitive approximations made by earlier authors and hence clarifies when the model is appropriate. Secondly, the model is used to analyse the evolution of small perturbations to the thickness of, and the concentration of solvent in, a drying paint layer. This analysis provides an analytical description of the ‘reversal’ of an initial perturbation to the thickness of the layer and the appearance of a perturbation to an initially flat layer caused by an initial perturbation to the concentration of solvent. Thirdly, it is shown how a simplified version of the model applicable to the case of surface-tension-gradient-dominated flow can be derived and solved as an initial-value problem. Fourthly, the applicability of the present theory developed for solvent-based high-gloss alkyd paints to waterborne coatings is discussed. Finally, the results obtained are summarised and the practical implications of the work are discussed.

An Ultrathin Liquid Film Lubrication Theory—Calculation Method of Solvation Pressure and Its Application to the EHL Problem

Abstract: This paper describes a new method for calculating the solvation pressure that acts between solid surfaces when the surfaces approach each other to within a very small distance in a liquid medium. Solvation pressure is calculated by solving the transformed Ornstein-Zernike equation for hard-spheres in a two-phase system with Perram's method and using the Derjaguin approximation. Furthermore, the authors apply the new method to the elastohydrodynamic lubrication problem in which the film thickness is very small and solvation force and van der Waals force cannot be neglected. It will be shown that the calculation results agree well with experimental data. The results are then compared with two conventional solvation pressure models proposed so far, namely, Chan and Horn's model, and, Jang and Tichy's model. It is found that these two models neglect the elastic deformation of solid surface when obtaining the experimental parameter used in their models; thus they overestimate the solvation pressure resulting in the prediction of larger film thickness than the experiments.

Inertial effects on contact line instability in the coating of a dry inclined plate

Abstract: It has been observed that when a thin liquid film coats an initially dry inclined plane, a spanwise instability occurs at the leading edge. Here we develop a model for the evolution of this coating film which includes inertia, gravity, surface tension and the contact angle at the leading edge of the film. A Karman–Pohlhausen method is used to include inertia. We determine steady state profiles of the film and investigate their stability. The predictions of the model are compared to some recent experiments and we find good agreement. This theory gives improvement over a lubrication theory in experiments where Reynolds numbers are significantly larger than one.

Steep wave fronts on extrudates of polymer melts and solutions: lubrication layers and boundary lubrication

Abstract: Steep wave fronts tend to develop in many regimes of lubricated, slipping flows in which waves appear. Problems of slip, spurt, fracture and extrudate distortion can be framed in terms of lubrication theory with paradigms arising from the lubrication of heavy oil with water for some problems and concepts from the theory of boundary lubrication for others. In water-lubricated pipelines, high pressures are produced at the front side of a wave on the oil when water is forced through the wavecrest and the wall, low pressures develop at the back of the wave where the gap opens. The steep waves which develop on cores of heavy oil lubricated by water are irregular and look like melt fracture. Direct numerical simulation of regular periodic waves give rise to sharkskin solutions in which the wave length decreases with the wave amplitude as the gap size decreases, preserving the steep wave front. Wave steepening seems always to occur in extrusion when the polymers slip, in the abrasion of rubber samples and in Schallamach's waves of detachment.

A Numerical Study on Motion of a Sphere Coated With a Thin Liquid Film at Intermediate Reynolds Numbers

Abstract: The steady viscous flow past a sphere coated with a thin liquid film at low and intermediate Reynolds numbers (Re < 200) was investigated numerically. The influences of fluid physical properties, film thickness, and Reynolds number on the flow pattern were clarified. Temperature field around the compound drop was also analyzed. The strong dependence of flow pattern on the characteristics of heat transfer was recognized. The empirical equation of the drag coefficient for the compound drop was proposed. Furthermore, the explicit adaptability of the drag coefficient equation for a gas bubble, a liquid drop, and a rigid sphere in the range of Reynolds number Re ≤ 1000 was confirmed.

Elastohydrodynamic Lubrication Model of Connecting Rod Big-End Bearings: Application to Real Engines

Abstract: This study presents an elastohydrodynamic (EHD) lubrication model of connecting rod big-end bearings developed taking into consideration the effects of inertia and oil holes. In this model, the effect of inertia, namely the body force, on load and deformation is practically and rationally expressed based on engine dynamics and a structural model ofa connecting rod. A method of defining the deformation of bearings has been proposed to simplify numerical analysis. The effect of oil holes, namely an oil feed hole in a journal and an oil jet hole in a bearing, is considered as a boundary condition in the EHD lubrication theory. Calculations of oil flow rate and potter loss are also included.

Thin film core-annular flow of upper-convected maxwell liquids

Abstract: Pressure-driven pipe flow of two upper-convected Maxwell liquids in a vertical core-annular arrangement is studied. The annulus and core liquids have different relaxation times and viscosities. Weakly nonlinear evolution equations which describe the interface shape are derived. Lubrication theory is used in the annulus but not in the core. Motions periodic in the streamwise direction are addressed, with the aim of describing short-time behavior driven by capillary forces. Numerical and analytical results for the spatio-temporal dynamics are given for two subcases. In the first case, the liquids have the same viscosity. White noise non-axisymmetric initial data are found to evolve into axisymmetric motion. When axisymmetry is assumed, the evolution equation is a Kuramoto-Sivashinsky equation; the bifurcation parameter depends on the fluid elasticities, interfacial tension, Reynolds number and Weissenberg number. The second case concerns axisymmetric motions with wavelengths in the axial direction that are long compared with the annulus thickness. This asymptotic analysis places a restriction on the size of the Weissenberg number. A jump in the viscosities introduces dispersion, which may be enhanced by fluid elasticity; this can lead to a transition from an unstable regime or a chaotic regime to one in which organized traveling wave pulses move in the axial direction.

Lubrication theory for a fibre suspension

Abstract: The steady inertialess flow of a semi-dilute fibre suspension through a planar channel having slowly varying cross-section is considered. For large enough fibre concentrations, flow separation occurs at the wall near the widest part of the channel, and regions of asymptotically stagnant fluid develop over a significant fraction of the channel. These stagnant zones contain very thin sub-layers which are difficult to resolve numerically. Lubrication theory breaks down when flow separation occurs. A new theory is developed which enables the stagnant regions to be removed from the numerical computation, with jump conditions that stitch together the flowing regions on either side. The analysis predicts a region of very weak reversed flow near the wall and a stagnant layer which, in the lubrication limit extends to the wall. The lubrication results are compared with a full numerical solution.

Equations used in hydrodynamic lubrication

Abstract: Development of an oil film of adequate thickness is the prime requirement for long lived journal bearings. Hydrodynamic lubrication is the most important lubrication phenomenon, and the best understood. In this article Professor Sun is presenting the equations of hydrodynamic lubrication as taught at his university. The article is clearly basic lubrication engineering, and thus, is suitable for the Back to Basics series in this journal. This paper teaches basics of the mechanics of an oil film in a bearing, including: the oil film thickness; the pressure developed that determines the load that can be carried; the temperature created by the flow of oil in the film; the amount of oil that flows through the bearing; the factors of fluid fraction, and the coefficient of friction. The author prefers the term fluid film lubrication. He explains, The term hydrodynamic lubrication has been prevailing since Osborne Reynolds in 1886 proposed the idea of a hydrodynamic theory of lubrication. However, the word hydrodynamic in fluid mechanics carries a connotation of being nonviscous, while the development of a fluid film between two solid surfaces is precisely due to viscosity. Besides, one often encounters the term hydrostatic lubrication which is fluid film flow generated by external pressurization, and the term elastohydrodynaic lubrication which combines fluid film flow with the elastic deformation of bearing surfaces. Since the articles deals with the equations of fluid film flow that are applicable to all these modes of lubrication, the author prefers the term fluid film lubrication which will be used in the text. Obviously the article requires a working knowledge of differential equations and fluid mechanics. But even without those skills, an understanding may be gleaned by reading the article.

Thermo-optical mirror on a free ferrofluid surface

Abstract: Here we report on the first, to our knowledge, direct experimental observation of giant thermo-optical mirror effect on the free surface of ferrofluid under He-Ne laser excitation. In our experiment a slightly focused laser beam of power in mW range is incident nearly normally to the surface, and a characteristic diffraction ring pattern has been observed in reflection mode. Concave surface deformation has been clearly observed at laser irradiated spot and has been explained in terms of lubrication theory approach for laser driven thermocapillary motion in thin layer of light absorbing fluid.

Lubrication theory for a fibre suspension: Part 2: flow in a journal bearing

Abstract: The steady intertialess flow of a semi-dilute fibre suspension in a journal bearing is examined by asymptotic and numerical methods. For sufficiently large fibre concentrations, a stagnant layer appears, identical to that for pressure-driven flow (Sykes, P. and Rallison J.M., Lubrication theory for a fibre suspension; Part 1: pressure-driven flow in a planar channel having slowly-varying cross-section, J. Non-Newtonian Fluid Mech., 71 (1997) 109–136). In low eccentricity bearings, for which the Stokes flow is unseparated, high concentrations of fibres are needed to affect the flow. In large eccentricity bearings a new phenomenon is observed: the fibres modify the flow at significantly lower concentrations. This effect is seen in a more extreme form in a journal bearing containing a barrier, for which the Stokes flow is necessarily separated everywhere. For separated flow of this kind, including the larger eccentricity journal bearing, we find a asymptotic regime for which a detached stagnant layer occupies a significant fraction of the channel, but with Newtonian flowing regions on either side. Good agreement is shown between the lubrication solutions and a full numerical solution.

Study on the Adhesion Force of Lubricants—Adhesion Force Characteristics Under Boundary Lubrication

Abstract: The mechanisms that generate adhesion forces in liquid lubricants are studied under various experimental conditions. These forces occur between two surfaces when they are detached in the normal direction under static boundary lubrication conditions. The adhesion force is not influenced by the speed at which the upper specimen is pulled up, but is influenced by the viscosity of the lubricant. The adhesion force under boundary lubrication is much greater than that under hydrodynamic lubrication, and it is closely related to the compressibility of the lubricant.

On the transition of lubrication regimes

Abstract: It is found that the critical transition film thicknesses from elasohydrodynamic lubrication (EHL) to the thin film lubrication (TFL) and from the thin film lubrication to the boundary lubrication (BL) are related to the initial viscosity of lubricant, surface energy of substrates, etc.. In order to complete lubrication theory system, a lubrication model is proposed in this paper. In the model, three basic films, i.e. the dynamic film, the ordered lubricant film and static film, are proposed to represent the hydrodynamic lubrication, thin film lubrication and boundary lubrication. According to the division, we can tell different regimes from the friction of each basic film in the whole film. Since these basic films have their thickness region, the transitions between EHL, TFL and BL can be determined when the molecular structure of a lubricant is known.

Power Steering Actuator Lipseal에서의 유체/구조 상호작용에 관한 수치해석적 연구

Abstract: In this study, a numerical approach has been taken to analyze the interaction between fluid and structure in power steering actuator lipseal by using FEM method. Typical elastomer lipseal material was used to simulate the material behavior in elasto-hydrodynamic lubrication in power steering actuator. Lubrication oil was a heavy paraffin oil of kinematic viscosity of 66.7mm Is. Reynolds number based on gap distance was 2.856×l0^-5. Lubrication equation was solved along with FEM solution. The maximum pressure difference between the lubrication theory and the full Navier-Stokes equation was about 18% or less. With the second order lubrication theory the maximum pressure difference was 12%. The full Navier-Stokes code predicts consistently higher than the lubricaton theory. The bottom flat piston surface was pulled at a constant speed of 1 inch/sec and pressure at both inlet and exit were fixed at 0 relative pressure. The maximum deformation of elastomer was observed at the minimum gap area(throat). The magnitude of deformation in x-direction was about 0.0208 - 0.0289 lre! . The normal stress was about 30% higher than those of x-direction stress: σ_xx= - 0.7 ~0.7, σyy = -1.0 ~1.0 prej. Dissipating elastomer modeling such as Arruda-Boyce model will be studied further.

Displacement of fluid droplets from solid surfaces in low-Reynolds-number shear flows

Abstract: The yield conditions for the displacement of fluid droplets from solid boundaries are studied through a series of numerical computations. The study includes gravitational and interfacial forces, but is restricted to two-dimensional droplets and low-Reynoldsnumber flow. A comprehensive study is conducted, covering a wide range of viscosity ratio , Bond number Bd, capillary number Ca and contact angles A and R. The yield conditions for drop displacement are calculated and the critical shear rates are presented as functions Ca(;Bd;A;) where = A R is the contact angle hysteresis. The numerical solutions are based on the spectral boundary element method, incorporating a novel implementation of Newton’s method for the determination of equilibrium free surface proles. The numerical results are compared with asymptotic theories (Dussan 1987) based on the lubrication approximation. While excellent agreement is found in the joint asymptotic limits A 1, the useful range of the lubrication models proves to be extremely limited. The critical shear rate is found to be sensitive to viscosity ratio with qualitatively dierent results for viscous and inviscid droplets. Gravitational forces normal to the solid boundary have a signicant eect on the displacement process, reducing the critical shear rate for viscous drops and increasing the rate for inviscid droplets. The low-viscosity limit ! 0 is shown to be a singular limit in the lubrication theory, and the proper scaling for Ca at small is identied. The displacement of liquid droplets from solid substrates is a fundamental problem of fluid mechanics. This problem has application in numerous areas including distillation, spray coating, packed towers and a variety of multiphase flow operations in the chemical process industry. Our interest in the problem focuses on drop displacement in viscous shear flows at low Reynolds number. This regime has relevance in coating operations and in enhanced oil recovery. In the coating industry, the presence of small liquid droplets or gas bubbles on solid surfaces is a major concern in the design of process equipment, because even a small flow disturbance is sucient to destroy the uniformity required in precision lm coating. In the petroleum industry, enhanced oil recovery techniques are strongly dependent on the interaction of oil and water in immiscible two-phase mixtures, and the success of such operations depends on the displacement of small oil droplets attached to solid surfaces. The fundamental issues associated with viscous drop displacement from rigid boundaries have been addressed in a series of papers by Dussan and coworkers (Dussan & Chow 1983; Dussan 1985, 1987). These authors developed yield criteria