Showing papers on "Lubrication theory published in 1999"

Two‐Dimensional Wafer‐Scale Chemical Mechanical Planarization Models Based on Lubrication Theory and Mass Transport

Abstract: The effects of the variation of chemical mechanical planarization (CMP) process parameters on slurry hydrodynamics and removal rate are studied using physically based models. The two models which are developed to describe and fundamentally understand the CMP process are (i) the lubrication model for slurry flow and ( ii) the mass transport model for material removal. The mass transport model is developed for copper CMP. Conditions for stable operation and reduced wafer scratching are identified from the lu brication model. The mass transport model takes into account the chemical reaction at the wafer surface, the slurry flow hydrodynam ics, and the presence of abrasive particles. The polish rates predicted by the model agree well with those measured experimental ly.

An efficient algorithm for propagating fluid-driven fractures

Abstract: This paper presents an efficient finite element algorithm for propagating fluid-driven fractures in pressure sensitive geomaterials. Fluid flow in the fracture is modelled by lubrication theory. Rock deformation is assumed to be elastoplastic and dilatent. A cohesive model based on the softening behaviour of rocks is employed as the propagation criterion. A special continuation method based on the volume of injected fluid in the fracture is used for direct coupling of the fluid-flow with rock deformation and for driving the solution during propagation. Sample results are provided for the problem of hydraulic fracturing to demonstrate the efficiency of the proposed algorithm.

Levitation of a drop over a film flow

Abstract: A vertical jet of water impinging on a horizontal surface produces a radial film flow followed by a circular hydraulic jump. We report a phenomenon where fairly large (1 ml) drops of liquid levitate just upstream of the jump on a thin air layer between the drop and the film flow. We explain the phenomenon using lubrication theory. Bearing action both in the air film and the water film seems to be necessary to support large drops. Horizontal support is given to the drop by the hydraulic jump. A variety of drop shapes is observed depending on the volume of the drop and liquid properties. We show that interaction of the forces due to gravity, surface tension, viscosity and inertia produces these various shapes.

Mixed-Film Lubrication Theory and Tension Effects on Metal Rolling Processes

Abstract: A cold rolling model, based on Wilson and Chang's asperity flattening model and von Mises homogenous deformation model, for mixed film lubrication is developed. A more rigorous average Reynolds equation is used to calculate the hydrodynamic pressure. The variations of the yield stress with strain are considered in the model. An efficient iteration procedure is developed to solve the contact area, film thickness, and hydrodynamic pressure. The model is more practical with fewer assumptions, and converges quickly. It is applicable to a wider range of rolling regimes, particularly at high rolling speed. The calculation results agree well with the literature as well as with measured data from a rolling mill.

Blade coating of a power-law fluid

Abstract: In this paper we re-examine the problem of applying a thin layer of a power-law fluid to a solid substrate by means of a simple blade coater. Specifically we use lubrication theory to examine steady plane flow of a power-law fluid in the narrow nonuniform channel formed between a fixed blade of prescribed shape and a plane substrate moving parallel to itself. The first-order asymptotic solution for the case of a weakly non-Newtonian fluid is presented. An explicit expression is obtained for the first-order pressure gradient from which the first-order contributions to several important physical quantities including the thickness of the applied fluid layer and the forces on the blade are calculated for both plane and exponentially shaped blades. In particular, we find that, depending on the shape and height ratio of the coater, the effect of weakly non-Newtonian behavior can be either to increase or to decrease both the pressure and the load from their Newtonian values. We also re-examine the approximate solutions of Hwang [Trans. ASME J. Fluids Eng. 104, 469 (1982)] and Dien and Elrod [Trans. ASME J. Lubrication Technol. 105, 385 (1983)] and make a detailed comparison between their predictions and those of the exact solution in the weakly non-Newtonian limit. We find that in this limit the Dien and Elrod approximation is usually in significantly better agreement with the exact solution than Hwang’s approximation. In the Appendix we re-examine the Dien and Elrod approximate solution for the flow of a generalized Newtonian fluid.

Gravitational Drainage of a Tangentially-Immobile Thick Film.

Abstract: We use lubrication theory to derive an evolution equation for the free surface of a draining thick free film with a zero tangential velocity component along the free surface. The films are “thick” because effects that are important in very thin films, such as intermolecular forces, do not play a role in the situation of interest. The evolution equation results from the balance of surface tension, gravity, and dynamic viscosity. Subregions of the film appear and they involve balancing these effects pairwise. Computations are performed on the full evolution equation and for various boundary conditions corresponding to different parts of the film. Matched asymptotics are developed that predict the behavior as the film enters the bath and these agree very well with the computed results. Comparison with experiment is favorable for the rate of decrease of the film thickness.

Dissipative Particle Dynamics of the Thin-Film Evolution in Mesoscale

Abstract: Computer simulation is an important tool for studying the dynamical behavior of thin films. The existing models of liquid film flows are based on the evolution equation (EE) and lubrication theory, which are approximations to the Navier-Stokes continuum equations. The validity conditions for these approximations and disadvantages of numerical schemes impose serious limitations on these continuum models. Thin liquid layers in nanoscale technology may exhibit microscale features, which cannot be described by using the EE equations. We propose new numerical models for falling film and falling sheet. They are based on the particle paradigm and the dissipative particle dynamics (DPD) method. DPD represents a system of mesoscopic-sized particles, which can interact via direct conservative, two-body potentials. The particles can exert friction and Brownian forces on each other. We consider two cases of fluid film flows for which the main driving force is the gravity. In the first case the fall of a flui...

Analysis of flux flow and the formation of oscillation marks in the continuous caster

Abstract: In the industrial process of continuous steel casting, flux added at the top of the casting mould melts and forms a lubricating layer in the gap between the steel and the oscillating mould walls. The flow of flux in the gap plays an essential role in smoothing the casting operation. The aim of the present work is to better understand the mechanics of flux flow, with an emphasis on such problems as how the flux actually moves down the mould, the physical parameters governing the consumption rate of the flux and the geometry of the lubricating layer. The problem considered is a coupled problem of liquid flow and multi-phase heat transfer. In the first part of the paper, the formation of the lubricating layer is analysed and a set of equations to describe the flux flow is derived. Then, based on an analysis of the heat transfer from the molten steel through the lubricating layer to the mould wall, a system of equations correlating the temperature field in the steel and flux with the geometry of the lubricating layer is derived. Subsequently, the equations for the flux flow are coupled with those arising from heat-transfer analysis and then a numerical scheme for the calculation of the consumption rate of flux, the geometry of the lubricating layer and the solidification surface of the steel is presented.

Oil film thickness in engine connecting-rod bearing with consideration of thermal effects : Comparison between theory and experiment

Abstract: The aim of this paper is to study the thermal ejfects on minimum oil film, thickness in a connecting-rod bearing. A comparison between the theoretical and experimental results of minimum oil film thickness in a connecting-rod bearing is presented. The transient energy equation is solved by adapting the adiahatic boundary condition for considering the thermal effects. The minimum oil film thicknesses are measured by the total capacitance method. The minimum oil film thickness over an engine cycle estimated with consideration of thermal effects is closer to that measures than that estimated by using the iso-viscous lubrication theory.

Flow phenomena in fixed-gap and gravure roll coating systems

Abstract: This thesis describes investigations into a number of coating processes using experimental, analytical and computational techniques. The first problem, considered experimentally, is that of reverse roll coating with a liquid reservoir positioned directly above horizontally aligned rollers. Measurements of the film thickness as a function of the height of fluid in the reservoir and speed ratio are presented. When the wetting line is located downstream of the nip, either a decrease in the height of the associated hydrostatic head or an increase in the speed ratio causes a reduction in the thickness of the outgoing film. However, when the wetting line is located upstream of the nip the opposite is found to be true. The bead-break instability in forward meniscus coating is considered both experimentally and analytically. Agreement between predictions from a simple mathematical model of the stable bead and experimentally determined meniscus positions is seen to be excellent. A perturbation hypothesis is used to predict the onset of the bead-break instability, at which the upstream meniscus accelerates rapidly towards the downstream one, so the two collide and the bead collapses. The results from the model compare well with experiments. An outline of a method for using the bead-break instability as a design criterion is also presented. Typically in a slot, blade or knife coater the downstream meniscus is assumed to pin at a corner of the coating device. In chapter 5, a series of experiments and a corresponding computational study, are presented which illustrate that the meniscus can advance up the face of such coating devices (in this case a roll-flat plate system). Reducing the corner angle is seen to reduce the size of the climb region and the associated recirculation at this point at the downstream meniscus. It is also shown that the meniscus can detach from the corner and retreat into the gap, which can in turn give rise to the ribbing instability. An offset gravure coating arrangement is considered in chapter 6. The coating arrangement is split into two areas of study - the offset gravure nip and the kiss coating bead. An experimental investigation of the offset nip with the two rolls vertically aligned and running at the same speed in forward mode reveals two ways in which the metered film thickness can be influenced. Either increasing the nip force by pressing the two rolls together or decreasing the roll speeds causes a reduction in the metered film thickness. At higher speeds the metered film thickness is observed to asymptote to a limiting value, the value of which depends on the gravure pattern. The reverse mode kiss coating bead operating at speed ratios greater than one is also investigated. Experiments reveal that under these conditions, all the fluid is transferred from the roll surface to the web and the two make contact due to the generation of a sub-ambient pressure field within the bead. Two models based on lubrication theory are derived, one assuming an infinitely tensioned web and a second that incorporates the effect of web flexibility. The latter is found to give much better agreement with the experimental data. Finally a perturbation hypothesis is applied to these to models in order to predict the onset of the ribbing instability, both of which are found to give reasonable agreement with the experimental data. Finally, the results of a systematic experimental investigation of reverse mode direct gravure coating is reported, where the web runs directly over a gravure roll surface. This wide ranging parametric study illustrates the effect of the operating parameters on the final film thickness. Key findings are that speed ratio, fluid properties and cell shape and size can significantly influence the final film thickness. For a fixed roll speed it is observed that as the web speed is increased the gravure bead becomes unstable. This results in streaking on the web, and gives an upper limit to the speed ratio.

Experimental Study on the Mechanism of Lubrication in Hydrodynamic Porous Thrust Bearings With a Wavy Surface

Abstract: Hydrodynamic fluid lubrication theory is applied to thrust bearings with three-dimensional, wave-shaped axial end surfaces. Optimizations of the wave height and surface porosity are experimentally determined using lubrication characteristics such as the friction coefficient and worn-out surface conditions. Lubrication characteristics such as the friction coefficient, temperature rise, thrust flotation, and oil consumption rate are evaluated for an estimation of life expectancy. In this research, the results of this theoretical application on thrust bearings clearly showed considerable improvement over conventional thrust bearings. Furthermore, this experimental research has clarified the lubrication conditions of various thrust-loaded axial end surfaces.

Material compressibility effects for the squeeze of very thin films

Abstract: The purpose of the present work is the study and clarification of the essential role played by the material compressibility of very thin solid layers such as for instance appear in surface force experiments. For the sake of simplicity, attention will be focused on an elastic film squeezed between rigid surfaces. The starting point is the classical lubrication theory reformulated within the framework of linear elasticity (Incompressible Reynolds Model). This model is then extended to include compressibility effects. This extension is based on a phenomenological analysis of the stress and strain fields obtained in some simple model cases and which are shown to correspond to an oedometric squeeze inside the contact with boundary corrections. This results in the oedometric Reynolds model which is then applied to two special cases: a uniform film of constant thickness under plane strain condition and the interfacial film occurring in the sphere/plane contact. These two problems confirm the fact that compressibility cannot be neglected for very thin films and show that the governing adimensional parameters combine compressibility and thinness.

Measurements of Compressibility Effects in Stepped Thrust Gas Film Bearings

Abstract: Hydrodynamic gas film bearings are used for supporting high-speed, lightly loaded rotating machinery. Stepped-type gas film bearings are often used for such machinery because of their simple structure, high stability and load carrying capacity. This paper describes the measurements of compressibility effects on the static and dynamic characteristics of stepped thrust gas film bearings. In the experiments, the minimum film thickness, friction torque on the bearing surface and stiffness and damping coefficients of gas films are measured for a range of rotational speed from 10,000 rpm to 20,000 rpm under a constant stator mass and a fixed step height. The measured data are compared with the theoretical results and the gas film compressibility effects on the static and dynamic characteristics of the bearings are discussed. The experimental results agree well with the predicted results based on the compressible lubrication theory. Presented at the 53rd Annual Meeting in Detroit, Michigan May 17–21, 1998

Stability of Gas Bearing Sliders for Large Bearing Number: Convective Instability of the Tapered Slider©

Abstract: The dynamics and stability of tapered air bearing sliders used for computer hard disk drive magnetic recording heads is examined using analytical methods. Lubrication theory is applied to determine the lift on the slider from the Reynolds equation in the limit of large bearing number. The dynamics of the slider are given by a nonlinear integro-differential equation. Linear stability analysis of this model yields valuable insight into the behavior of the slider. Most significantly, it is found that convective effects can not be neglected and yield either damping or instability depending on the slider configuration. This analysis is also applied to determine the response of the slider motion due to deviations in the disk surface.

Theoretical and experimental results on friction for line contacts in mixed and elastohydrodynamic lubrication regimes

Abstract: In this work the typical rectangular conjunction is studied both theoretically and experimentally. Different situations are investigated from mixed to elastohydrodynamic lubrication conditions. Experimental investigation is carried out by means of an apparatus for friction force and film thickness measurements; theoretical study is based on the numerical solution of the thermalelastohydrodynamic lubrication problem for line contacts with a finite element program. The experimental results clearly show the typical transition from mixed to elastohydrodynamic lubrication depending on the surface roughness of the specimens as well as on the lubrication parameters. The numerical program gives results in good agreement with the experimental ones for the EHL regime.

The spreading of volatile liquid droplets on heated surfaces

Abstract: A two-dimensional volatile liquid droplet on a uniformly heated horizontal surface is considered Lubrication theory is used to describe the effects of capillarity, thermocapillarity, vapor recoil, viscous spreading, contact-angle hysteresis, and mass loss on the behavior of the droplet A new contact-line condition based on mass balance is formulated and used, which represents a leading-order superposition of spreading and evaporative effects Evolution equations for steady and unsteady droplet profiles are found and solved for small and large capillary numbers In the steady evaporation case, the steady contact angle, which represents a balance between viscous spreading effects and evaporative effects, is larger than the advancing contact angle This new angle is also observed over much of the droplet lifetime during unsteady evaporation Further, in the unsteady case, effects which tend to decrease (increase) the contact angle promote (delay) evaporation In the “large” capillary number limit, matched asymptotics are used to describe the droplet profile; away from the contact line the shape is determined by initial conditions and bulk mass loss, while near the contact-line surface curvature and slip are important

多孔質動圧スラスト軸受の潤滑機構に関する実験的研究 : 第2報, スラスト受け面の各種動圧形状の検討と潤滑状態に関する実験的考察

Abstract: The application of hydrodynamic fluid lubrication theory is attempted to the porous thrust bearings with various hydrodynamic shaped axial end surfaces. The superior one within the hydrodynamic shaped axial end surfaces such as, PUMPIN, PUMPOUT, HERRINGBONE, TPDLND (Tapered Land) and HWB (Hydro Wave Bearing) are experimentally determined concerning lubrication characteristics. The measurements of lubrication characteristics such as, a friction coefficient, the temperature rise, floating height, floatation and oil consumption rate for estimation of life expectancy etc. are evaluated. In this research, the results of this application on the end surfaces of thrust bearings clearly showed considerable improvement over the conventional thrust bearings. Furthermore, this experimental study clarified the load carrying capacities and lubrication conditions of the respective shape of the axial end surfaces.

Thrust Bearings In the 2-D Thermal Elastohydrodynamic Lubrication: On the Slider Velocity Corresponding to the Maximum Load

Abstract: The thermo-elastohydrodynamic lubrication is considered for Newtonian and power-law fluids. A numerical method available in the literature is utilized in obtaining solutions, for a given set of parameters, leading to establishing the maximum carrying load in terms of the slider velocity. Comparison is made with the classical lubrication theory. It is shown that there exists a threshold of the slider velocities for which increase of the slider velocity is detrimental to the ability to support loads.

Time effect on lubricant film

Abstract: This paper discusses the time effect in thin film lubrication. Some abnormal behaviour has been found in experiments when the time effect is considered. Experimental results show that the film thickness formed at a point contact is related to the running time and history. The influence of load, velocity, and initial viscosity of lubricant on the film thickness is quite different from that of those found in hydrodynamic or elastohydrodynamic lubrication situations. The time effect of the film thickness and the mechanism of the formation of the time dependent film are discussed, based on interface physics and surface physical chemistry.

A large deformation theory for the interaction of the red cell membrane with the endothelial glycocalyx

Abstract: Develops a large deformation theory to describe the interaction of the red cell membrane with the endothelial glycocalyx. This model provides the basis for understanding the unusual lift off phenomenon observed for red cells in closely fitting capillaries. Using effective medium theory, the authors first show that the local Darcy permeability of the fiber matrix is a highly nonlinear function of compression. As a consequence, the pressure distribution on the moving cell membrane surface is three orders of magnitude greater than in classical lubrication theory. These results support the observation that if a red cell starts from rest, it will exhibit a striking popout phenomenon in which it will quickly lift off the surface and then glide near the edge of the matrix layer, which is in sharp contrast to existing models where there is a thin fluid layer between the matrix and the membrane.

Lubrication theory as a means of unravelling flow structure in thin film roll coating systems

Abstract: The aim of this paper is to demonstrate that lubrication theory provides a simple, yet powerful, means for understanding a wide variety of complex flow phenomena inside the bead of roll coating systems. Attention is focussed on the forward regime, with rollers moving in the same direction through the nip, and analytical predictions are obtained over a wide range of low flux (meniscus roll coating) situations. Although the full flow field within the coating bead is often quite complex due to the existence of eddies and transfer-jets, it is shown that the structure can be classified analytically according to the nature of the stagnation points within the flow. The analytical predictions axe compared with those from a full numerical solution of the flow field, which incorporates the effects of the upstream and downstream free surfaces. The agreement between the analytical and numerical results is extremely good in all instances, a fact which clearly demonstrates that much of this complex flow behaviour can be well understood without having to resort to complex numerical solutions.