Showing papers on "Lubrication theory published in 2010"

Fluid Film Lubrication

Abstract: Fluid film bearings are machine elements that should be studied within the broader context of tribology. The three subfields of tribology - friction, lubrication, and wear - are strongly interrelated. The last decade has witnessed significant advances in the area of fluid film lubrication and its applications, and this second edition offers a look at some of these advances. This edition adds to the fundamentals of fluid film lubrication, a discourse on surface effects and the inclusion of treatment of flow with significant inertia within the section on turbulence. Basic ideas of the multigrid method are conveyed along with multilevel multi-integration in the treatment of elastohydrodynamic lubrication. New chapters have been included on ultra-thin films, both liquid and gaseous, and lubrication of articulating joints and their replacement. Some of the most recent literature is discussed.

Spatial rigid-multibody systems with lubricated spherical clearance joints: modeling and simulation

Abstract: The dynamic modeling and simulation of spatial rigid-multibody systems with lubricated spherical joints is the main purpose of the present work. This issue is of paramount importance in the analysis and design of realistic multibody mechanical systems undergoing spatial motion. When the spherical clearance joint is modeled as dry contact; i.e., when there is no lubricant between the mechanical elements which constitute the joint, a body-to-body (typically metal-to-metal) contact takes place. The joint reaction forces in this case are evaluated through a Hertzian-based contact law. A hysteretic damping factor is included in the dry contact force model to account for the energy dissipation during the contact process. The presence of a fluid lubricant avoids the direct metal-to-metal contact. In this situation, the squeeze film action, due to the relative approaching motion between the mechanical joint elements, is considered utilizing the lubrication theory associated with the spherical bearings. In both cases, the intra-joint reaction forces are evaluated as functions of the geometrical, kinematical, and physical characteristics of the spherical joint. These forces are then incorporated into a standard formulation of the system’s governing equations of motion as generalized external forces. A spatial four bar mechanism that includes a spherical clearance joint is considered here as an example. The computational simulations are carried out with and without the fluid lubricant, and the results are compared with those obtained when the system is modeled with perfect joints only. From the general results, it is observed that the system’s performance with lubricant effect presents fewer peaks in the kinematic and dynamic outputs, when compared with those from the dry contact joint model.

Flow and instability of thin films on a cylinder and sphere

Abstract: We investigate the dynamics of thin films driven by gravity on the outer surface of a cylinder and sphere. The surface is rigid, stationary and the axis of the cylinder is horizontal. An instantaneous release of a constant volume of fluid at the top of the cylinder or sphere results initially in a two-dimensional or axisymmetric current respectively. The resultant flow of a thin film of fluid is described using lubrication theory when gravity and viscous forces govern the dynamics. We show that the thickness of the flow remains uniform in space and decreases in time like t ―1/2 near the top of both the cylinder and the sphere. Analytic solutions for the extent of the flow agree well with our experiments until the advancing front splits into a series of rivulets. We discuss scalings of the flow at the onset of the instability as a function of the Bond number, which characterizes the relative importance of gravity and surface tension. The experiments, conducted within an intermediate range of Bond numbers, suggest that the advancing front becomes unstable after it has propagated a critical distance, which depends primarily and monotonically on the volume of fluid and not on the viscosity of fluid. Releasing a sufficiently large volume of fluid ensures that rivulets do not develop on either a cylinder or sphere.

Asymptotic analysis of the dewetting rim

Abstract: Consider a film of viscous liquid covering a solid surface, which it does not wet. If there is an initial hole in the film, the film will retract further, forming a rim of fluid at the receding front. We calculate the shape of the rim as well as the speed of the front using lubrication theory. We employ asymptotic matching between the contact line region, the rim, and the film. Our results are consistent with simple ideas involving dynamic contact angles and permit us to calculate all free parameters of this description, previously unknown

Tear film dynamics on an eye-shaped domain. Part 2. Flux boundary conditions

Abstract: We model the dynamics of the human tear film during relaxation (after a blink) using lubrication theory and explore the effects of viscosity, surface tension, gravity and boundary conditions that specify the flux of tear fluid into or out of the domain. The governing nonlinear partial differential equation is solved on an overset grid by a method of lines using finite differences in space and an adaptive second-order backward difference formula solver in time. Our simulations in a two-dimensional domain are computed in the Overture computational framework. The flow around the boundary is sensitive to both our choice of flux boundary condition and the presence of gravity. The simulations recover features seen in one-dimensional simulations and capture some experimental observations of tear film dynamics around the lid margins. In some instances, the influx from the lacrimal gland splits with some fluid going along the upper lid towards the nasal canthus and some travelling around the temporal canthus and then along the lower lid. Tear supply can also push through some parts of the black line near the eyelid margins.

Inertial lubrication theory.

Abstract: Thin fluid films can have surprising behavior depending on the boundary conditions enforced, the energy input and the specific Reynolds number of the fluid motion. Here we study the equations of motion for a thin fluid film with a free boundary and its other interface in contact with a solid wall. Although shear dissipation increases for thinner layers and the motion can generally be described in the limit as viscous, inertial modes can always be excited for a sufficiently high input of energy. We derive the minimal set of equations containing inertial effects in this strongly dissipative regime.

Tear film dynamics on an eye-shaped domain I: pressure boundary conditions

Abstract: We study the relaxation of a model for the human tear film after a blink on a stationary eye-shaped domain corresponding to a fully open eye using lubrication theory and explore the effects of viscosity, surface tension, gravity and boundary conditions that specify the pressure. The governing non-linear partial differential equation is solved on an overset grid by a method of lines using a finite-difference discretization in space and an adaptive second-order backward-difference formula solver in time. Our 2D simulations are calculated in the Overture computational framework. The computed flows show sensitivity to both our choices between two different pressure boundary conditions and the presence of gravity; this is particularly true around the boundary. The simulations recover features seen in 1D simulations and capture some experimental observations including hydraulic connectivity around the lid margins.

Adhesion of yield stress fluids

Abstract: The different regimes of flow when separating two solid rough surfaces in contact via a layer of a simple yield stress fluid are identified. Generic scalings for the adhesion energy and for the geometrical characteristics of the final deposits (after separation) as a function of the initial aspect ratio of the sample are found. We show that there is a strong pinning effect which might be at the origin of an adhesion energy significantly larger (by a factor about 2) than that estimated from the lubrication theory. We also observe that the conditions of development of viscous fingering are not at all predicted by the conventional Saffman–Taylor instability theory taking into account the specific non-Newtonian character of the fluid. This again suggests that for pastes the pinning effect plays a significant stabilizing role.

Plasto-Elastohydrodynamic Lubrication (PEHL) in Point Contacts

Abstract: Elastohydrodynamic lubrication (EHL) is an important branch of the lubrication theory, describing lubrication mechanisms in nonconformal contacts widely found in many mechanical components such as various gears, rolling bearings, cams and followers, metal-rolling tools, traction drives, and continuous variable transmissions. These components. often transmit substantial power under heavy loading conditions. Also, the roughness of machined surfaces is usually of the same order of magnitude as, or greater than, the estimated average EHL film thickness. Consequently, most components operate in mixed lubrication regime with significant asperity contacts. Due to very high pressure concentrated in small areas, resulted from either heavy external loading or severe asperity contacts, or often a combination of both, subsurface stresses may exceed the material yield limit, causing considerable plastic deformation, which may not only permanently change the surface profiles and contact geometry but also alter material properties through work hardening as well. In the present study, a three-dimensional plasto-elastohydrodynamic lubrication (PEHL) model has been developed by taking into account plastic deformation and material work-hardening. The effects of surface/subsurface plastic deformation on lubricant film thickness, surface pressure distribution, and subsurface stress field have been investigated. This paper briefly describes the newly developed PEHL model and presents preliminary results and observed basic behavior of the PEHL in smooth-surface point contacts, in comparison with those from corresponding EHL solutions under the same conditions. The results indicate that plastic deformation may greatly affect contact and lubrication characteristics, resulting in significant reductions in lubricant film thickness, peak surface pressure and maximum subsurface stresses.

The effect of viscoelasticity on the stability of a pulmonary airway liquid layer

Abstract: The lungs consist of a network of bifurcating airways that are lined with a thin liquid film. This film is a bilayer consisting of a mucus layer on top of a periciliary fluid layer. Mucus is a non-Newtonian fluid possessing viscoelastic characteristics. Surface tension induces flows within the layer, which may cause the lung’s airways to close due to liquid plug formation if the liquid film is sufficiently thick. The stability of the liquid layer is also influenced by the viscoelastic nature of the liquid, which is modeled using the Oldroyd-B constitutive equation or as a Jeffreys fluid. To examine the role of mucus alone, a single layer of a viscoelastic fluid is considered. A system of nonlinear evolution equations is derived using lubrication theory for the film thickness and the film flow rate. A uniform film is initially perturbed and a normal mode analysis is carried out that shows that the growth rate g for a viscoelastic layer is larger than for a Newtonian fluid with the same viscosity. Closure occurs if the minimum core radius, Rmin(t), reaches zero within one breath. Solutions of the nonlinear evolution equations reveal that Rmin normally decreases to zero faster with increasing relaxation time parameter, the Weissenberg number We. For small values of the dimensionless film thickness parameter e, the closure time, tc, increases slightly with We, while for moderate values of e, ranging from 14% to 18% of the tube radius, tc decreases rapidly with We provided the solvent viscosity is sufficiently small. Viscoelasticity was found to have little effect for e>0.18, indicating the strong influence of surface tension. The film thickness parameter e and the Weissenberg number We also have a significant effect on the maximum shear stress on tube wall, max(τw), and thus, potentially, an impact on cell damage. Max(τw) increases with e for fixed We, and it decreases with increasing We for small We provided the solvent viscosity parameter is sufficiently small. For large e≈0.2, there is no significant difference between the Newtonian flow case and the large We cases.

Contact in a viscous fluid. Part 2. A compressible fluid and an elastic solid

Abstract: A lubrication theory is presented for the effect of fluid compressibility and solid elasticity on the descent of a two-dimensional smooth object falling under gravity towards a plane wall through a viscous fluid. The final approach to contact, which takes infinite time in the absence of both effects, is determined by numerical and asymptotic methods. Compressibility can lead to contact in finite time either during inertially generated oscillations or if the viscosity decreases sufficiently quickly with increasing pressure. The approach to contact is invariably slowed by allowing the solids to deform elastically; specific results are presented for an underlying elastic wall modelled as a foundation, half-space, membrane or beam.

Interfacial Thermal Fluid Phenomena in Thin Liquid Films

Abstract: Films are ubiquitous in nature and play an important role in our daily life. The paper focuses on the recent progress that has been achieved in the interfacial thermal fluid phenomena in thin liquid films and rivulets through conducting experiments and theory. Phase shift schlieren technique, fluorescence method and infrared thermography have been used. A spanwise regular structures formation was discovered for films falling down an inclined plate with a built-in local rectangular heater. If the heating is low enough, a stable 2D flow with a bump at the front edge of the heater is observed. For lager heat flux this primary flow becomes unstable, and the instability leads to another steady 3D flow, which looks like a regular structure with a periodically bent leading bump and an array of longitudinal rolls or rivulets descending from it downstream. The heat flux needed for the onset of instability grows almost linearly with the increase of Re number. Strong surface temperature gradients up to 10–15 K/mm, both in the streamwise and spanwise directions have been measured. For a wavy film it was found that heating may increase the wave amplitude because thermocapillary forces are directed from the valley to the crest of the wave. Thin and very thin (less than 10 μm) liquid films driven by a forced gas/vapor flow (stratified or annular flows), i.e. shear-driven liquid films in a narrow channel are a promising candidate for the thermal management of advanced semiconductor devices in earth and space applications. Development of such technology requires significant advances in fundamental research, since the stability of joint flow of locally heated liquid film and gas is a rather complex problem. Experiments with water and FC-72 in flat channels (height 0.2–2 mm) have been conducted. Maps of flow regimes were plotted. It was found that stratified flow exists and stable in the channels with 0.2 mm height and 40 mm width. The critical heat flux for a shear driven film may be up to 10 times higher than that for a falling liquid film, and reaches 400 W/cm2 in experiments with water at atmospheric pressure. Some experiments have been done during parabolic flight campaigns of the European Space Agency under microgravity conditions. It was found that decreasing of gravity leads to a flow destabilization.Copyright © 2010 by ASME

Effects of surface topography on lubrication film formation within elastohydrodynamic and mixed lubricated non-conformal contacts:

Abstract: This article focuses on the effects of surface topography modifications on lubrication film thickness within non-conformal lubricated contact. An optical test rig is used to study lubricant...

A Study of Worn Hybrid Journal Bearing System With Different Recess Shapes Under Turbulent Regime

Abstract: The objective of the present paper is to study analytically the influence of wear on the performance of a capillary-compensated, four-pocket, hybrid journal bearing system operating in a turbulent regime by considering various geometric shapes of recess. The present study deals with bearings having four different geometric shapes of recess, i.e., square, circular, elliptical, and triangular recessed bearings. The wear on the bearing surface is modeled using Dufrane's abrasive wear model. The Reynolds equation based on Constantinescu's turbulent lubrication theory has been solved using finite element method along with a restrictor flow equation as a constraint together with appropriate boundary conditions. The numerically simulated results have been presented for a wide range of nondimensional external loads, wear depth parameters, and Reynolds numbers. The numerically simulated results suggest that the combined influence of wear, turbulence, and geometric shape of recess significantly affects the bearing performance. It has been observed that a triangular recessed bearing provides a greater value of minimum fluid film thickness when operating in a turbulent regime. It is also noticed that direct fluid film stiffness coefficients get reduced significantly when bearings operate in a turbulent regime compared with a laminar regime. Further, it is observed that from the viewpoint of fluid film stiffness, a square recessed bearing is found to be most suitable when operating in a turbulent regime.

Contact in a viscous fluid. Part 1. A falling wedge

Abstract: Computations are presented of the upward force on a two-dimensional wedge descending towards a plane surface due to the Stokes flow of an intervening viscous fluid. The predictions are compared with those of lubrication theory and an approximate analytical solution; all three predict a logarithmic divergence of the force with the minimum separation. An object falling vertically under gravity will therefore make contact with an underlying plane surface in finite time if roughened by asperities with sharp corners (with smooth surfaces, contact is made only after infinite time). Contact is still made in finite time if the roughened object also moves horizontally or rotates as it falls.

Direct verification of the lubrication force on a sphere travelling through a viscous film upon approach to a solid wall

Abstract: Experiments were performed to observe the motion of a solid sphere approaching a solid wall through a thin layer of a viscous liquid. We focus mainly on cases where the ratio of the film thickness, δ, to the sphere diameter, D, is in the range 0.03 < δ/D < 0.09 and the Stokes number, St, a measure of the sphere inertia to viscous forces, is below a critical level Stc so that the spheres do not rebound and escape from the liquid layer. This provides us with the scope to verify the force acting on the sphere, derived from lubrication theory. Using high-speed video imaging we show, for the first time, that the equations of motion based on the lubrication approximation correctly describe the deceleration of the sphere when St < Stc. Furthermore, we show that the penetration depth at which the sphere motion is first arrested by the viscous force, which decreases with increasing Stokes number, matches well with theoretical predictions. An example for a shear-thinning liquid is also presented, showing that this simple set-up may be used to deduce the short-time dynamical behaviour of non-Newtonian liquids.

A new lubrication theory to derive far-field axial pressure difference due to force singularities in cylindrical or annular vessels

Abstract: In simulations of creeping flow, the effect of suspended particles on a fluid is often represented by force singularities responsible for singular Stokesian solutions, which are infinite at the sphere center and decay far from the particle. In this article, we consider such singular fields centered at a point inside a cylindrical or annular conduit containing highly viscous medium. Across an unbounded infinite domain, these singular flows cannot produce a finite pressure difference as they decay to zero far from the center. However, in the presence of bounding cylindrical surfaces, the reflected flow from the walls creates a finite pressure difference between the far fields across the force singularity along the axial direction. To quantify the effect of the reflected flow, we present a new lubrication analysis, which, on the one hand, identifies the specific singular fields capable of producing axial pressure difference and, on the other hand, provides explicit expressions for the far-field pressure. Tho...

Application of Lubrication Theory and Study of Roughness Pitch During Laminar, Transition, and Low Reynolds Number Turbulent Flow at Microscale

Abstract: This work aims to experimentally examine the effects of different roughness structures on internal flows in high-aspect-ratio rectangular microchannels. Additionally, a model based on lubrication theory is compared to these results. In total, four experiments were designed to test samples with different relative roughness and pitch placed on the opposite sides forming the long faces of a rectangular channel. The experiments were conducted to study (i) sawtooth roughness effects in laminar flow, (ii) uniform roughness effects in laminar flow, (iii) sawtooth roughness effects in turbulent flow, and (iv) varying-pitch sawtooth roughness effects in laminar flow. The Reynolds number was varied from 30 to 15,000 with degassed, deionized water as the working fluid. An estimate of the experimental uncertainty in the experimental data is 7.6% for friction factor and 2.7% for Reynolds number. Roughness structures varied from a lapped smooth surface with 0.2 μ m roughness height to sawtooth ridges of height 117 μ m....

Thin-film rupture for large slip

Abstract: The rupture of thin liquid films on hydrophobic substrates, assuming large slip at the liquid-solid interface, is studied using a recently developed strong slip lubrication model, it is shown that the rupture passes through up to three self-similar regimes with different dominant balances and different scaling exponents. For one of these regimes the similarity is of second kind, and the similarity exponent is determined by solving a boundary-value problem for a nonlinear ODE. Furthermore, finite-time rupture is proved for this regime.

Solution agreement between dry contacts and lubrication system at ultra-low speed

Abstract: The Reynolds equation has been widely applied in lubrication analyses, but the extent and limit of its application have not been fully explored. Great efforts have been made so that the solution convergence speed and accuracy are significantly improved. However, while the working conditions are severe, such as extremely heavy load, low speed, and low viscosity due to temperature increase, the lubricant film thickness becomes very thin and surface contact may occur. As a consequence, the lubrication solution becomes difficult. Contact and thin-film or mixed lubrication under severe conditions are of great importance, as many components operate in such regimes. This article investigates the solution evolution of the Reynolds equation as the entraining velocity decreases, using the unified mixed elastohydrodynamic lubrication (EHL) model presented by Hu and Zhu. By comparing the ultra-low speed solution of the Reynolds equation with that of dry contact analysis, it is found that the solution of the R...

Thin film lubrication dynamics of a binary mixture: Example of an oscillatory instability

Abstract: We study thin film instabilities in liquid films with deformable surface using the lubrication theory. An externally applied vertical temperature gradient may give cause to an instability (Marangoni instability) of the flat motionless film. Contrary to the earlier work where mostly pure fluids were discussed, the focus of the present paper lays on instabilities in mixtures of two completely miscible liquids. We show that the normally found monotonic long-wave instability may turn into an oscillatory one if the two components have a different surface tension and if the Soret coefficient establishes a stabilizing vertical concentration gradient. A systematic derivation of the basic equations in long-wave approximation is given. The character of instabilities is studied using linear stability analysis. Finally, a real system consisting of a water-isopropanol mixture is discussed in some detail.

On the lateral migration of a slightly deformed bubble rising near a vertical plane wall

Abstract: Deformation-induced lateral migration of a bubble slowly rising near a vertical plane wall in a stagnant liquid is numerically and theoretically investigated. In particular, our focus is set on a situation with a short clearance c between the bubble interface and the wall. Motivated by the fact that numerically and experimentally measured migration velocities are considerably higher than the velocity estimated by the available analytical solution using the Faxen mirror image technique for a/(a + c) ≪ 1 (here a is the bubble radius), when the clearance parameter ϵ(=c/a) is comparable to or smaller than unity, the numerical analysis based on the boundary-fitted finite-difference approach solving the Stokes equation is performed to complement the experiment. The migration velocity is found to be more affected by the high-order deformation modes with decreasing ϵ. The numerical simulations are compared with a theoretical migration velocity obtained from a lubrication study of a nearly spherical drop, which describes the role of the squeezing flow within the bubble–wall gap. The numerical and lubrication analyses consistently demonstrate that when ϵ ≤ 1, the lubrication effect makes the migration velocity asymptotically μVB12/(25ϵγ) (here, VB1, μ and γ denote the rising velocity, the dynamic viscosity of liquid and the surface tension, respectively).

Dynamics of elastocapillary rise

Abstract: We present the results of a combined experimental and theoretical investigation of the surface-tension-driven coalescence of flexible structures. Specifically, we consider the dynamics of the rise of a wetting liquid between flexible sheets that are clamped at their upper ends. As the elasticity of the sheets is progressively increased, we observe a systematic deviation from the classical diffusive-like behaviour: the time to reach equilibrium increases dramatically and the departure from classical rise occurs sooner, trends that we elucidate via scaling analyses. Three distinct temporal regimes are identified and subsequently explored by developing a theoretical model based on lubrication theory and the linear theory of plates. The resulting free-boundary problem is solved numerically and good agreement is obtained with experiments.

Comparisons of Slip-Corrected Reynolds Lubrication Equations for the Air Bearing Film in the Head-Disk Interface of Hard Disk Drives

Abstract: Slip-corrected Reynolds equations have not been widely used in the air bearing simulations for the head-disk interface in hard disk drives since Fukui and Kaneko [Trans ASME J Tribol 110:253–262, 1988] published a more accurate generalized lubrication equation (FK model) based on the linearized Boltzmann equation for molecular gas lubrication. However, new slip models and slip-corrected Reynolds equations continue to be proposed with certain improvements or with the more physical basis of kinetic theory. Here, we reanalyze those slip models and lubrication equations developed after the FK model was published. It is found that all of the slip-corrected Reynolds equations are of limited use in the air bearing simulations, and that these new slip-corrected Reynolds equations cannot replace the FK model for calculating an accurate pressure distribution of molecular gas lubrication.

Shock-wave solutions in two-layer channel flow. I. One-dimensional flows

Abstract: We study the dynamics of an interface separating two immiscible layers in an inclined channel. Lubrication theory is used to derive an evolution equation for the interface position that models the two-dimensional flow in both co- and countercurrent configurations. This equation is parameterized by viscosity and density ratios, and a total dimensionless flow rate; the system is further characterized by the height of the interface at the channel inlet and outlet, which are treated as additional parameters. In the present work, which corresponds to part I of a two-part paper, we focus on one-dimensional flows. We use an entropy-flux analysis to delineate the existence of various types of shocklike solutions, which include compressive Lax shocks, pairs of Lax and under-compressive shocks, and rarefaction waves. Flows characterized by unstably stratified layers are accompanied by the formation of propagating, large-amplitude interfacial waves, which are not shocklike in nature. The results of our transient num...

Effect of gravity on the dynamics of non-isothermic ultra-thin two-layer films

Abstract: The effect of gravity on the dynamics of non-isothermic ultra-thin two-layer films is studied in this paper. The joint action of disjoining pressure and thermocapillary forces is taken into account. The problem is considered in a long-wave approximation. The linear stability of a quiescent state and thermocapillary flows is investigated. It has been found that the influence of the upper fluid density is significantly stronger than that of the difference of fluid densities. Nonlinear flow regimes are studied by means of numerical simulations. The gravity can lead to the formation of stripes or holes instead of droplets. The two-dimensional wavy patterns are replaced by one-dimensional waves with the fronts inclined or transverse to the direction of the horizontal temperature gradient.