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Showing papers on "Lubrication theory published in 1994"


Journal ArticleDOI
TL;DR: In this article, an experimental study on the onset and evolution of centrifugally driven rivulets is presented, which aims to investigate the influence on the instability of various experimental conditions (drop volume and rotational frequency), the wetting properties of the liquid (surface tension and contact angle), and fluid viscoelasticity.
Abstract: An experimental study on the onset and evolution of centrifugally driven rivulets is presented, which aims to investigate the influence on the instability of various experimental conditions (drop volume and rotational frequency), the wetting properties of the liquid (surface tension and contact angle), and fluid viscoelasticity. The apparatus allows continuous observation of the drop shapes following an impulsive spin‐up of the substrate, and these are analyzed by digital image analysis. The flows exhibit an onset time, or, equivalently, a critical radius, before which the drop spreads axisymmetrically. Data on drop spreading are compared with simple predictions of lubrication theory. The measured azimuthal wave number and growth rate of the instability are in good agreement with the linear stability analysis of Troian et al. [Europhys. Lett. 10, 25 (1989)], as long as the critical radius is taken from the experiment itself. The most unstable wavelength is found to be independent of both drop size and rotation speed in the range of parameters investigated, as observed previously by Melo et al. [Phys. Rev. Lett. 63, 1958 (1989)]. On the other hand, a change in the wetting properties of the liquid significantly modifies the critical radius, which, in turn, affects the number of fingers, with the nonwetting fluid exhibiting a smaller critical radius. This trend is in agreement with the mechanism of instability that is linked to the presence of a capillary ridge near the edge of the drop. No qualitative nor quantitative difference in behavior has been observed between a Boger fluid having a relaxation time of about 1 s, and its Newtonian solvent, in the experimental conditions considered.

125 citations


Journal ArticleDOI
TL;DR: In this paper, the authors describe the behavior of a droplet modeled as an infinitely long strip of finite width and arbitrary height profile, subject to a uniform temperature gradient imposed along the base.
Abstract: Migration of a small drop of liquid, initially at rest on a level, solid surface, can be induced by means of thermocapillary forces. If a temperature gradient is imposed across the solid, it has the effect of diminishing the surface tension on the warmer side of the droplet. Consequently, migration manifests itself as the difference in surface tension preferentially draws the droplet toward the cooler region of the solid. The study describes the behavior of a droplet modeled as an infinitely long strip of finite width and arbitrary height profile, subject to a uniform temperature gradient imposed along the base. Lubrication theory is employed to determine the velocity and pressure fields within the drop, as well as the net migration velocity of the droplet as a whole. The role of the dynamic boundary condition in the vicinity of the contact lines (including the allowance for slip) on the migration velocity is highlighted.

96 citations


Journal ArticleDOI
TL;DR: In this article, the authors examined the lubrication theory in more detail by a comparison with equilibrium stress analysis for rigid-plastic solids, and the results were consistent with the theory, suggesting that it is a useful first approximation.
Abstract: Lubrication theory is commonly employed to analyse the squeeze-film flow of plastic fluids under no-slip wall boundary conditions. Solutions exist for both Bingham and Herschel-Bulkley fluids but they infer that there exists a rigid or unyielded core and flow zones adjacent to the platens; it has been recognised previously that such a velocity field is kinematically inconsistent. Furthermore, the pressure boundary condition at the edge of the platens is conventionally set to zero which is inconsistent with experimental data presented here for a model Herschel-Bulkley fluid (Plasticine). An attempt has been made to examine the lubrication theory in more detail by a comparison with equilibrium stress analysis for rigid-plastic solids. Squeeze-film measurements were carried out using a model Herschel-Bulkley fluid and the results were consistent with the theory, suggesting that it is a useful first approximation. Nevertheless, the approach does not resolve the kinematic inconsistency resulting in lubrication theory.

92 citations


Journal ArticleDOI
TL;DR: In this paper, the authors extend lubrication theory for spreading of thin drops in the presence of gravity and thermocapillarity to include mass transport and solutocapiliarity.
Abstract: Solder drops spreading on metallic substrates are a reactive form of the wetting problem. A metallic component may diffuse in the liquid toward a metal substrate, where it is consumed by a reaction that forms a solid intermetallic phase. The resulting spatial variation in the composition of the drop may cause composition gradients along the free surface of the drop. Together with any thermal gradients along the free surface, Marangoni effects may, in turn, modify the bulk transport in the spreading drop. Motivated by this situation, we extend lubrication theory for the spreading of thin drops in the presence of gravity and thermocapillarity to include mass transport and solutocapillarity. We use an approximate solute profile in the drop to derive coupled evolution equations for the free surface shape and concentration field. Numerical solutions for the nonreactive (single component) drop agree well with previous theory. In the reactive case, we are only able to compute results for parameters outside of th...

61 citations


Journal ArticleDOI
TL;DR: In this article, a more general class of similarity solutions is considered, and a transformation is identified reducing the governing partial differential equations to a set of nonlinear ordinary differential equations, the solutions of which correspond to integral curves in a two-dimensional phase plane.
Abstract: Consider a dilute, insoluble surfactant monolayer on the free surface of a thin viscous film. A gradient in surfactant concentration generates a gradient in surface tension, driving a flow that redistributes the surfactant so that these gradients decay. The nonlinear evolution equations governing such flows, derived using lubrication theory, have previously been shown to admit a set of simple similarity solutions representing the spreading of a monolayer over an uncontaminated interface. Here, a much more general class of similarity solutions is considered, and a transformation is identified reducing the governing partial differential equations to a set of nonlinear ordinary differential equations, the solutions of which correspond to integral curves in a two‐dimensional phase plane. This allows the construction of solutions to a wide range of problems. Many new solutions are revealed, including one that cannot be determined by simpler techniques, namely the closing of an axisymmetric hole in a monolayer,...

60 citations


Journal ArticleDOI
TL;DR: In this paper, an existing model of surfactant-driven flows, based on lubrication theory, is extended to incorporate the transport of a passive solute and absorption of the solute at the wall beneath the liquid layer.

47 citations


Journal ArticleDOI
TL;DR: In this article, the effect of elasticity on the spreading of a spinning drop of fluid is investigated in the context of lubrication theory, and it is shown that the Oldroyd-B constitutive equation permits a solution in which the free surface of the central part of the drop thins uniformly in space.
Abstract: The effect of elasticity on the spreading of a spinning drop of fluid is investigated in the context of lubrication theory. It is shown that the Oldroyd-B constitutive equation permits a solution in which the free surface of the central part of the drop thins uniformly in space. Perturbation results for small effects of elasticity indicate an increased thinning rate of the free surface compared to Newtonian results for the central part of the spinning drop, and that this enhanced thinning rate persists only over a few characteristic relaxation times. Elastic effects in the capillary region near the moving contact line are also investigated by perturbation theory for small elasticity. Two methods for resolving the contact line singularity are chosen: matching the free surface profile to a precursor film of thickness b, and introducing slip at the spinning plate. For the precursor film model, the free surface correction changes character from a net enhancement of the capillary ridge near the contact line for large b, to a negative correction over most of the profile for small b. With the slip model, the free surface correction gives a net enhancement of the capillary ridge for all values of the slip parameter α. The difference between the models for thin precursor films or slight slip is explained by examining the manner in which the stress relaxes near the contact line. The results suggest that viscoelastic contact line dynamics may be more sensitive to the local molecular physics than the Newtonian counterparts.

32 citations


Journal ArticleDOI
TL;DR: The model developed in Part 1 (Lister 1994) for the solidification of hot fluid flowing in a thin buoyancy-driven layer between cold solid but freely deformable boundaries is extended to study the case of continual release of fluid.
Abstract: The model developed in Part 1 (Lister 1994) for the solidification of hot fluid flowing in a thin buoyancy-driven layer between cold solid but freely deformable boundaries is extended to study the case of continual release of fluid. In this model lubrication theory was applied to reduce the equations of mass and heat conservation to a kinematic-wave equation and an advection-diffusion equation, which were coupled by the rate of solidification. The equations allow the source flux to be specified, and the cases of constant input and of flux proportional to a power of time are considered here. The structure of the flow differs significantly from the case of constant-volume release considered in Part 1. The advective resupply of heat prevents the flow from solidifying completely at the source and, if the initial fluid temperature is greater than the melting temperature of the solid, will in fact lead to rapid melting near the source. A perturbation expansion is used to describe the development of thermal boundary layers at the flow margins and the initial self-similar extension of the zone of melting. As the flow propagates beyond its thermal entry length, the fluid temperature falls to the liquidus value and melting gives way to solidification. At large times nearly all of the fluid supplied solidifies against the margins of the flow but, provided the source flux decreases less rapidly than t−½, sufficient reaches the nose of the flow that the flow continues to increase in length indefinitely. Analytic solutions are given for this long-time regime showing, for example, that the length increases asymptotically like t1/2 for constant-flux input. The theoretical solutions, which are calculated by a combination of analytic and numerical methods, may be used to describe the propagation of a dyke fed by a large body of magma through the Earth's lithosphere or the flow of lava down the flanks of a volcano during an extensive period of eruption.

30 citations


Proceedings ArticleDOI
01 Dec 1994
TL;DR: In this article, an apparatus for measuring dynamic friction in a lubricated journal bearing is described, which has been designed, constructed and used to measure friction in the presence of sinusoidally-varying velocity at various frequencies.
Abstract: An apparatus for measuring dynamic friction in a lubricated journal bearing is described. This apparatus has been designed, constructed and used to measure friction in the presence of sinusoidally-varying velocity at various frequencies. Experimental results tend to confirm theoretical predictions which are based on the hydrodynamic lubrication theory.

22 citations


Journal ArticleDOI
TL;DR: In this article, the authors outline the theory behind a computer simulation of solder paste flowing out of a stencil aperture during printing for surface-mount technology (SMT) assembly.
Abstract: In this paper we outline the theory behind a computer simulation of solder paste flowing out of a stencil aperture during printing for surface-mount technology (SMT) assembly. Although developed to deal with solder pastes, the techniques are applicable for any dense suspension satisfying certain conditions. The simulation is based on lubrication theory, and hence is valid when the gaps between particles are small. The motion of each particle in the paste is calculated from the forces exerted by nearest-neighbour particles and the walls, and the movement of each individual particle is tracked. We present here the theory, methods, assumptions, limitations and general applicability of the model. In Part II, we present the results of the model for the special case of solder paste withdrawing from a stencil aperture.

21 citations


Journal ArticleDOI
TL;DR: In this paper, film thickness and pressure distribution of EHL in line contacts for four kinds of greases and one type of oil are calculated under a series of rolling velocities by using an inverse solution method.
Abstract: In this paper, film thickness and pressure distribution of EHL in line contacts for four kinds of greases and one type of oil are calculated under a series of rolling velocities by using an inverse solution method. The Herschel-Bulkley model is used for the rheological characteristics of the grease. Based on the theoretical analysis and numerical calculation, the following influences on film thickness and pressure distribution in EHL of grease are analyzed: the effects of starvation, yield stress, presheared grease and fresh grease, and approach and separation between two cylinders. The effect of different rheological characteristics of grease on film thickness is also investigated. Presented as a Society of Tribologists and Lubrication Engineers paper at the ASME/STLE Tribology Conference in San Diego, California, October 19-21, 1992

Journal ArticleDOI
TL;DR: In this article, the modified Reynolds equation for the hydrodynamic lubrication theory under the slip condition is used to describe the compressible fluid flow within the gas bearing, and a factored implicit finite difference (FIFD) scheme is applied for pressure calculations.
Abstract: This paper suggests a method to predict the static solution for gas-lubricated slider bearings in a hard disk drive (HDD) by using an optimization technique. The modified Reynolds equation for the hydrodynamic lubrication theory under the slip condition is used to describe the compressible fluid flow within the gas bearing, and a factored implicit finite difference (FIFD) scheme is applied for pressure calculations. An optimization technique is employed to find the solution at which the forces and moments acting on the gas bearing are in a state of equilibrium


Journal ArticleDOI
TL;DR: In this article, three perturbation approaches that apply for regular hydrodynamic lubrication problems are discussed: a cross-film coordinate perturbant, an iterative scheme, and a regular perturbance in terms of the film aspect ratio.
Abstract: Three perturbation approaches that apply for regular hydrodynamic lubrication problems are discussed: a cross-film coordinate perturbation, an iterative scheme, and a regular perturbation in terms of the film aspect ratio. The methods are used to derive higher order terms for a driven corner flow with a Newtonian lubricant of constant properties. Reasons for preferring the regular perturbation scheme are presented, and this method is used to obtain the correct curvature correction in an infinitely long journal bearing. Criteria for identifying singular geometries in hydrodynamic lubrication are set fourth

Journal ArticleDOI
TL;DR: In this article, the stability characteristics of hybrid porous journal bearings with a turbulent fluid film have been investigated theoretically following Constantinescu's turbulent lubrication theory, and the stability curves have been drawn for different Re, eccentricity ratios, slenderness ratios and bearing speed parameters.

Journal ArticleDOI
TL;DR: In this article, a model of Reynolds stress in turbulent lubrication theory was proposed by Tieu and Kosasih (1992) based on a modified Van Driest mixing length,formula.
Abstract: Recently a model of Reynolds stress in turbulent lubrication theory was proposed by Tieu and Kosasih (1992) based on a modified Van Driest mixing length,formula. It was developed,from a study of Poiseuille, flow velocities in narrow gaps. As a continuation of that study, the paper describes an investigation into fluid velocities in fluid film bearings. Experimental velocity profiles of planar flows in various film geometries are compared with the pro,files calculated using the mixing length model in the transition-turbulent regime. Excellent agreements have been attained, confirming the validity of the formula in the superlaminar theory

Journal Article
TL;DR: In this article, the static and dynamic performances of a floating ring journal bearing with central circumferential grooves at the inner and outer films are obtained numerically using the isothermal lubrication theory.
Abstract: The static and dynamic performances of a floating ring journal bearing with central circumferential grooves at the inner and outer films are obtained numerically using the isothermal lubrication theory. The Elrod algorithm implementing the Jakobsson-Floberg-Olsson cavitation boundary condition is adopted to predict cavitation regions in the inner and outer films more accurately than conventional analyses which use the half-Sommerfeld or Reynolds condition. The supply pressure drop in the circumferential groove of the inner film due to the rotation of the journal and ring is taken into account. It is shown that lubricant supply pressure has a significant influence on the static and dynamic performances of the bearing since it is closely related to the extent of the cavitation region. When the supply pressure is low and the journal speed is high, the supply pressure drop results in severe starvation of the lubricant in the inner film and affects the overall performance of the bearing remarkably.

Journal ArticleDOI
TL;DR: In this article, the transient freezing of water impinging vertically on a subzero disk through a circular jet is studied experimentally to determine the interaction of the fluid flow and the solidification process.
Abstract: The transient freezing of water impinging vertically on a subzero disk through a circular jet is studied experimentally to determine the interaction of the fluid flow and the solidification process. Experiments are performed over a range of the jet Reynolds number (1600

Journal ArticleDOI
01 Dec 1994
TL;DR: In this paper, the fluid force generated in a squeeze film damper undergoing large amplitude radial motion is described in terms of non-linear hydrodynamic inertial and damping coefficients, together with afluid static force.
Abstract: The fluid force generated in a squeeze film damper undergoing large amplitude radial motion is described in terms of non-linear hydrodynamic inertial and damping coefficients, together with afluid static force. Linear-in-the-parameter polynomial forms are introduced to represent the variation of these contributions with radial position. A generalized state variable filter identification method is developed which enables all the parameters in the non-linear model to be estimated from experimental data. The method is validated by processing simulated data and then applied to some new experimental data. Experimental results, relating to the influence of the supply pressure and the operating frequency on the coefficients, are presented and discussed. Comparisons are made with corresponding predictions derived from existing lubrication theory. The parametric non-linear model is found to give a good fit to experimental data over a significant region within the vicinity of the initial static equilibrium position...

Journal ArticleDOI
TL;DR: In this article, the bearing load of a plane inclined sector-shaped hydrodynamic thrust bearing, under simultaneous translation and transverse vibration, was measured experimentally and the results were used to evaluate the lubrication theory solutions.
Abstract: The bearing load of a plane inclined sector-shaped hydrodynamic thrust bearing, undersimultaneous translation and transverse vibration, is measured experimentally. The results are used to evaluate the lubrication theory solutions. Consequently, both the influences of the unsteady film inertia, measured by the squeeze Reynolds number Re s , and the convectiue film inertia, measured by the modified Reynolds number Re * , on load amplitude and phase are investigated

Journal ArticleDOI
TL;DR: In this article, the effects of journal surface shear stress on the stability of rigid rotor supported by hydrodynamic journal bearings operated in the turbulent flow regime are examined theoretically for a wide range of bearing length-to-diameter ratios.
Abstract: In this second report, the effects of journal surface shear stress on the stability of rigid rotor supported by hydrodynamic journal bearings operated in the turbulent flow regime are examined theoretically for a wide range of bearing length-to-diameter ratios. Based on the finite width turbulent lubrication theory considering the fluid shear stress acting on the journal surface, the numerical solutions for the whirl onset velocities and journal center trajectories are obtained. It is clarified from the numerical results that the rate of decrease of whirl onset velocities due to the effects of journal surface shear stress under the constant Sommerfeld number decreases with an increase of bearing length-to-diameter ratio.

Journal ArticleDOI
TL;DR: In this paper, a non-Newtonian turbulent lubrication theory based on the friction law of fluid was formulated and applied to the inclined long slider bearing, and the bearing performance such as pressure distribution, load capacity and friction force was analyzed.
Abstract: This paper describes a new theoretical approach to formulate the non-Newtonian turbulent lubrication theory based on the friction law of fluid. Combining the concept of equivalent pressure flow and resistance formula for pressure flow in the lubrication films, the one-dimensional generalized turbulent lubrication equation considering the non-Newtonian effect of lubrication fluid is derived, in which the equation for non-Newtonian turbulence coefficient is greatly simplified under the assumption of strong shear flow. The non-Newtonian turbulent lubrication equation obtained is applied to the inclined long slider bearing, and the bearing performance such as pressure distribution, load capacity and friction force is analyzed. From the results, the effect of non-Newtonian characteristics on the turbulent lubrication behaviour of long slider bearing is clarified.

Journal ArticleDOI
TL;DR: In this paper, the static and dynamic performances of a floating ring journal bearing with central circumferential grooves at the inner and outer films are obtained numerically using the isothermal lubrication theory.
Abstract: The static and dynamic performances of a floating ring journal bearing with central circumferential grooves at the inner and outer films are obtained numerically using the isothermal lubrication theory. The Elrod algorithm implementing the Jakobsson-Floberg-Olsson cavitation boundary condition is adopted to predict cavitation regions in the inner and outer films more accurately than conventional analyses which use the half-Sommerfeld or Reynolds condition. The supply pressure drop in the circumferential groove of the inner film due to the rotation of the journal and ring is taken into account. It is shown that lubricant supply pressure has a significant influence on the static and dynamic performances of the bearing since it is closely related to the extent of the cavitation region. When the supply pressure is low and the journal speed is high, the supply pressure drop results in severe starvation of the lubricant in the inner film and affects the overall performance of the bearing remarkably.

Journal ArticleDOI
TL;DR: In this paper, a computer program was developed to analyze piston-skirt lubrication under conditions close to those in an actually operating engine, taking into account boundary lubrication and effects on the oil film pressure due to surface characteristics.
Abstract: A computer program has been developed to analyze piston-skirt lubrication under conditions close to those in an actually operating engine. The program takes into account boundary lubrication and effects on the oil film pressure due to surface characteristics. It also considers the original profile, thermal expansion and elastic deformation of the piston-skirt, and can generate realistic results in this manner. The variation of piston-skirt lubrication conditions, such as boundary lubrication area and friction force, during an engine cycle has been analyzed in relation to such parameters as surface waviness, oil temperature, engine load and speed ; thus, a good understanding of piston-skirt lubrication has been obtained.