Showing papers on "Lubrication theory published in 1996"
367 citations
TL;DR: In this paper, a semi-analytical model based on lubrication analysis is derived to predict the effect of tow shape and intra-tow permeability on the overall bed permeability for flow through rectangular arrays of porous elliptical cylinders.
Abstract: The permeability of preform materials used in liquid moulding processes such as resin transfer moulding and structural reaction injection moulding is a complex function of weave pattern, packing characteristics, tow structure and intra-tow properties. The development of tools for predicting permeability as a function of these parameters is of great practical importance because such capability would speed process design and optimization, and provide a step towards establishing processing-performance relations. In this study, transverse flow in aligned fibrous porous media has been investigated. A semi-analytical model based on lubrication analysis is derived to predict the effect of tow shape and intra-tow permeability on the overall bed permeability for flow through rectangular arrays of porous elliptical cylinders. The Brinkman equation is used to model flow inside the porous structures, and the Stokes equation to model flow in the open media between the structures. The model predictions are verified by comparing with rigorous finite element calculations. The model shows that the influence of the intra-tow permeability on the overall bed permeability increases with inter-tow packing, and increasing degree of tow ellipticity. The influence is particularly critical for ‘stacked’ geometries for which previous models predict a zero permeability. A method for predicting intra-tow permeability is also proposed and investigated by comparing the model predictions for overall bed permeability with some experimental data for flow in a model porous medium. The comparison shows that use of the method enables the experimentally measured permeability value to be properly bounded.
118 citations
TL;DR: In this paper, the authors describe laboratory experiments on millimeter-sized drops of liquid in air which indicate that both thermocapillary and isothermal shear flows are able to prevent the coalescence of bodies of liquid which would occur readily in the absence of such flows.
Abstract: We describe laboratory experiments on millimeter‐sized drops of liquid in air which indicate that both thermocapillary and isothermal shear flows are able to prevent the coalescence of bodies of liquid which would occur readily in the absence of such flows. We have also carried out molecular dynamics computer simulations of nanometer‐sized drops, which show the same qualitative behavior in the case of an applied shear. At the other extreme, persistent non‐coalescence of larger drops was observed in microgravity conditions in a space shuttle experiment. We give an explanation of the experimental observations based upon lubrication theory and simple continuum hydrodynamics arguments, along with complementary microscopic insight obtained from the molecular simulations.
102 citations
TL;DR: A finite element analysis of Taylor flow in a cylindrical capillary was performed using a commercial FEM program (FIDAP) to solve the fundamental fluid dynamics equations together with the capillary forces at the gas-liquid interface as mentioned in this paper.
Abstract: A finite-element analysis of Taylor flow in a cylindrical capillary was performed using a commercial FEM program (FIDAP) to solve the fundamental fluid dynamics equations together with the capillary forces at the gas–liquid interface. A moving-surface formulation was used to calculate the bubble shape. The thickness of the liquid film surrounding the gas bubble, the degree of mixing in the liquid phase, and the slip velocity between the two phases were calculated. These parameters influence the performance of monolith reactors operating in the Taylor flow regime. On comparison with experimental results it was found that the FEM calculation generally predicts a thinner liquid film, which can possibly be explained in terms of a peripheral variation in surface tension. Moreover, the wavelength of the wiggles predicted in the liquid film near the tail end of the bubble was compared to those arising from a simplified mathematical analysis available in the literature. Good agreement was found for Ca < 0.005, while for higher Ca the FEM predicts significantly shorter wavelengths, indicating that the lubrication theory is not valid here.
90 citations
TL;DR: This paper considers locally symmetric or even singularities in the (LE) and in the modified lubrication equation (MLE), both of which have the property that entropy bounds forbid finite-time singularities when n is sufficiently large.
Abstract: Fourth-order degenerate diffusion equations arise in a “lubrication approximation” of a thin film or neck driven by surface tension. Numerical studies of the lubrication equation (LE) $h_t + ( h^n h_{xxx} )_x = 0$ with various boundary conditions indicate that singularity formation in which $h( x( t ),t ) \to 0$ occurs for small enough n with “anomalous” or “second type” scaling inconsistent with usual dimensional analysis.This paper considers locally symmetric or even singularities in the (LE) and in the modified lubrication equation (MLE) $h_t + h^n h_{xxxx} = 0$. Both equations have the property that entropy bounds forbid finite-time singularities when n is sufficiently large. Power series expansions for local symmetric similarity solutions are proposed for equation (LE) with $n < 1$ and (MLE) for all $n \in \mathbb{R}$. In the latter case, special boundary conditions that force singularity formation are required to produce singularities when n is large. Matching conditions at higher-order terms in the...
78 citations
TL;DR: In this article, the authors examined the post-buckling deformations of cylindrical shells conveying viscous fluid and found that if the pressure drop through the tube is kept constant during the buckling, the fluid-solid coupling slowed down the collapse.
61 citations
TL;DR: In this paper, the effects of geometric change due to wear on stability of hydrodynamic turbulent journal bearings have been investigated numerically, following Constantinescu's turbulent lubrication theory.
56 citations
TL;DR: In this paper, the translational and rotational motion of a sphere in a viscous Lennard-Jones liquid using molecular dynamics simulations was studied, and it was found that the drag and torque on a sphere were consistent with hydrodynamics results even when the size of the sphere is comparable to that of the fluid molecules.
Abstract: We have studied the translational and rotational motion of a sphere in a viscous Lennard-Jones liquid using molecular dynamics simulations. The drag and torque on a sphere in an effectively unbounded fluid are found to agree with continuum hydrodynamics results even when the size of the sphere is comparable to that of the fluid molecules. The diffusivity of a spherical tracer particle is in accord with the Stokes-Einstein relation, and the corresponding Brownian motion is determined by its interaction with the layers formed by fluid molecules around it. When a sphere moves near a solid wall, we find that the drag and torque agree with lubrication theory down to molecular scales, but the predicted divergence is regularized at very short distances due to depletion of fluid molecules near the wall and the appearance of slip at high shear stress.
46 citations
01 Jan 1996
TL;DR: In this article, the authors examined the post-buckling deformations of cylindrical shells conveying viscous fluid and found that the fluid-solid interaction leads to a violent collapse of the tube such that immediate opposite wall contact occurs after the buckling if the volume flux is kept constant during buckling.
Abstract: This paper examines the post-buckling deformations of cylindrical shells conveying viscous fluid . The wall deformation is modelled using geometrically nonlinear shell theory , and lubrication theory is used to model the fluid flow . The coupled fluid ‐ solid problem is solved using a parallelized FEM technique . It is found that the fluid ‐ solid interaction leads to a violent collapse of the tube such that immediate opposite-wall contact occurs after the buckling if the volume flux is kept constant during buckling . If the pressure drop through the tube is kept constant during the buckling , the fluid ‐ solid coupling slows down the collapse (compared to buckling under a dead load) . The ef fects of various parameters (upstream pressure , axial pre-stretch and the geometry of the tube) on the post-buckling behaviour are examined and the exact geometrically nonlinear shell theory is compared to Sanders’ (1963) moderate rotation theory . Finally , the implications of the results for previous models which described the wall deformation using so called ‘‘tube laws’’ are discussed .
36 citations
TL;DR: A theoretical model is used to simulate single-file motion of red cells though capillaries with variable cross-sections, assuming axisymmetric geometry, and effects of cell membrane shear viscosity and elasticity are included, but bending resistance is neglected.
Abstract: Red blood cells undergo continual deformation when traversing microvessels in living tissues. This may contribute to higher resistance to blood flow observed in living microvessels, compared with that in corresponding uniform glass tubes. We use a theoretical model to simulate single-file motion of red cells though capillaries with variable cross-sections, assuming axisymmetric geometry. Effects of cell membrane shear viscosity and elasticity are included, but bending resistance is neglected. Lubrication theory is used to describe the flow of surrounding plasma. When a red cell encounters a region of capillary narrowing, additional energy is dissipated, due to membrane viscosity, and due to narrowing of the lubrication layer, increasing the flow resistance. Predicted resistance to cell motion in a vessel with periodic constrictions (diameter varying between 5 microns and 4 microns) is roughly twice that in a uniform vessel with diameter 4.5 microns. Effects of transient red cell deformations may contribute significantly to blood flow resistance in living microvessels.
35 citations
TL;DR: In this article, the stability of cylindrical shells conveying viscous flow is examined and the most unstable circumferential buckling wavenumber and the buckling modes are determined for an experimental procedure in which the upstream pressure is held at a constant value while the volume flux is increased until buckling occurs.
TL;DR: In this article, the steady state behavior of non-circular worn journal bearings is analyzed for various wear depth parameters (δ 0), following Constantinescu's turbulent lubrication theory.
TL;DR: In this paper, an ultrathin fluid lubrication film thickness between mica surfaces is measured using this apparatus, and it is found that when the film thickness is more than about 10 nm (ten times as large as the molecular diameter of OMCTS), there is good agreement with the conventional continuum fluid lubrications theory (EHL theory).
Abstract: A new apparatus which can measure force and separation between surfaces accurately is developed. Ultrathin fluid lubrication film thickness between mica surfaces is measured using this apparatus. Octamethylcyclotetrasiloxane (OMCTS) is used as a lubricant. As a result of the experiment, it is found that when the film thickness is more than about 10 nm (ten times as large as the molecular diameter of OMCTS), there is good agreement with the conventional continuum fluid lubrication theory (EHL theory). In case of film thickness less than 10 nm, however, it deviates from the theoretical prediction and discretization of film thickness is observed. It is considered that this phenomenon is due to the solvation force (structural force), and that the molecular effect cannot be neglected in such an ultrathin lubrication phenomenon as in this experiment.
TL;DR: In this article, the theoretical and practical significance of thin-film lubrication is elaborated, and the characteristics describing thin-layer lubrication and its main research directions are suggested, and a new lubrication regime, thin film lubrication has been discussed.
Abstract: Various phenomena are revealed under EHL and micro-EHL conditions, such as the properties of the lubricant under high pressure, traction, and the load-bearing capacity of the lubricant film, and are discussed in the present paper. A new lubrication regime, thin film lubrication, has been discussed. The theoretical and practical significance of research on thin film lubrication is elaborated. Finally, the characteristics describing thin film lubrication and its main research directions are suggested.
TL;DR: In this paper, a moving spectral element method is described for solving the dynamically loaded journal bearing problem, where the inner cylinder rotates and is also free to move under a time-dependent load, while the outer cylinder (the bearing) is stationary.
TL;DR: In this article, the authors present an analysis of the performance characteristics of a journal bearing with three-dimensional asperities operating in a turbulent regime, based on the linearized lubrication theory.
TL;DR: In this article, a heat transfer correlation for the steady-state natural convection in a meniscus-shaped cavity was established and a closed-form exact conduction solution was also presented for the cylindrical case.
TL;DR: In this article, the authors extend hydrodynamic lubrication theory to lubrication with liquid-liquid and liquid-gas mixtures, and apply it to journal bearings, roller bearings and to cold rolling.
TL;DR: In this paper, the authors investigate the hydrodynamic stability of a thin surfactant-coated liquid film spreading strictly by Marangoni stresses and show that such a film is linearly stable to small perturbations of all wavenumbers.
Abstract: Within lubrication theory, we investigate the hydrodynamic stability of a thin surfactant coated liquid film spreading strictly by Marangoni stresses. These stresses are generated along the air-liquid interface because of local variations in surfactant concentration. The evolution equations governing the unperturbed film thickness and surface surfactant concentration admit simple self-similar solutions for rectilinear geometry and global conservation of insoluble surfactant. A linear stability analysis of these self-similar flows within a quasi steady-state approximation (QSSA) yields an eigenvalue problem for a single third-order nonlinear differential equation. The analysis indicates that a thin film driven purely by Marangoni stresses is linearly stable to small perturbations of all wavenumbers. The insights gained from this calculation suggest a flow mechanism that can potentially destabilize the spreading process.
01 Jan 1996
TL;DR: In this paper, a physical model of thin film lubrication with the fluid layer, the ordered liquid layer and the adsorbed layer is proposed and the functions of these different layers are discussed.
Abstract: Thin film lubrication is a transition region between elastohydrodynamic lubrication and boundary lubrication, A technique of relative optical interference intensity with the resolution of 0.5 nm in the vertical direction and 1.5 nm in the horizontal direction is used in a pure rolling process to measure the film thickness with different lubricants, speeds, loads and substrate surface energy. Experimental data show that the characteristics of thin film lubrication are different from those of elastohydrodynamic lubrication and boundary lubrication. As the rolling speed decreases, a critical film thickness can be found to distinguish thin film lubrication from elastohydrodynamic lubrication. Such thickness is related to the substrate surface energy, atmospheric viscosity of lubricant, etc. A physical model of thin film lubrication with the fluid layer, the ordered liquid layer and the adsorbed layer is proposed and the functions of these different layers are discussed.
TL;DR: In this article, the authors simulate the flow of a Newtonian fluid in a tangential counter-rotating twin screw extruder using a cylindrical coordinate lubrication theory model.
Abstract: In this paper we simulate the flow of a Newtonian fluid in a tangential counter-rotating twin screw extruder using a cylindrical coordinate lubrication theory model. Special attention is given to the material flows leading to mixing specially to inter-screw and backward leakage between the screws, and how they vary with process conditions.
TL;DR: In this paper, a molecular dynamics computer simulation of boundary lubrication, in which the lubricant and sliding solid surfaces are represented at an atomistic level, has given new insights into the mechanism of boundary liveness.
01 Sep 1996
TL;DR: In this paper, the performance characteristics of two types of journal bearings, tilting-pad and offset halves, operating under high-speed conditions where the journal peripheral speed is in excess of 100 m/s.
Abstract: This paper describes the performance characteristics of two types of journal bearings, tilting-pad and offset halves, operating under high-speed conditions where the journal peripheral speed is in excess of 100 m/s. Experimental investigations into bearing eccentricity, temperatures and dynamic coefficients were carried out with a specially designed test rig. These results are compared with theoretical data which are obtained from thermohydrodynamic lubrication theory. The agreement is satisfactory. However, further improvements are necessary to predict more accurate thermal performance of the unloaded pads.
TL;DR: In this article, a general view of non-laminar hydrodynamic lubrication is presented and the effects of inertia forces in laminar and in turbulent flows are shown.
Abstract: The classical theory of hydrodynamic lubrication assumes that the flow regime is laminar and the inertia forces in the fluid film are negligible. For large bearings using low viscosity lubricant or for high speed, the inertia forces could be important and non laminar flow occurs. In that presentation a general view of non laminar lubrication is presented. The different flow regimes which occur in bearings are shown. The transition criteria between laminar and Taylor vortices and turbulence are given. The theories to obtain the characteristics of bearings operating in turbulent flow regime are presented. The effects of inertia forces in laminar and in turbulent flows are shown.
01 Jan 1996
TL;DR: In this article, a hydrodynamic lubrication theory was applied to the oil film at the vane sides in a vane compressor and analyzed vane behavior and contact forces under steady-state operating condition.
Abstract: In order to utilize HFC refrigerant, which is said to make lubricating condition worse, as a working fluid in a refrigeration cycle, it is needed to evaluate the lubricating condition at sliding parts accurately. In this study, we analyzed oil film at vane sides in a vane compressor vvith a hydrodynamic lubrication theory_ We also analyzed the vane behavior, frictional loss on the vane side and leakage flow through these clearances under steady-state operating condition. It is clarified that the inclination of the vane in a vane slot of a rotor changes with rotor rotation and the vane is pressed strongly on its trailing side against an edge of the vane slot when pressure of working fluid in compression chamber approaches discharge pressure. The calculated results of vane behavior and contact forces are influenced by method of modeling of the oil film pressure under the condition that the vane comes into contact with the rotor_ INTRODUCTION In order to utilize HFC refrigerant, which is said to make lubricating condition worse, as a working fluid in a refrigeration cycle, many studies conceming lubrication and wear have been done. Most of the studies discussed about compatibility and wear of materials and elasto-hydrodynamic lubrication (EHL) conditions, but a hydrodynamic lubrication theory is also useful due to its simplicity as the first step to evaluate influences of clearance, oil viscosity and operating condition on the lubricating condition. In this study, we analyzed oil film at vane sides in a vane compressor with the hydrodynan1ic lubrication theory. We also analyzed vane behavior, frictional loss on the vane side and leakage flow through these clearances under steady-state operating condition. At that time, three models of oil film pressure under the condition that the vane comes into contact \:vith a vane slot of a rotor are proposed and the results with these models are compared with each other. THEORETICAL ANALYSIS In this study, we applied the hydrodynamic lubrication theory to the oil film at the vane sides in the vane compressor and analyzed the vane behavior and contact forces under steady-state operating condition. Lubrication Model of Oil Film at Vane Side Figure 1 shows a schematic view of the vane compressor for an automotive air conditioner and Fig. 2 shows a lubrication model of oil film at the vane side. The followings are assumed for simplicity. (!)Sliding portion has infinite width. (2)Lubricant is incompressible and its viscosity is constant. (3 )Inertial force oflubricant is negligible. (4)Deformations of the vane and the vane slot of rotor are negligible. (5)Rotational speed ofthe rotor is constant. Relationship between pressure, P, of oil film and clearance height, h, on coordinates system shown in Fig. 2, which move with the vane, is expressed by the Re:ynolds equation as follows. a{h (aP;a)}jex = -617u az;ex + 12 17ja = dhofdt +xdkjdt ( 3) Integrating Eq. (I) under the following boundary conditions,
TL;DR: In this paper, the elastohydrodynamic force on two slightly deformable bodies approaching one another head on is calculated in the limit of small gap sizes and small deformations by combining Hertz's theory of deformation and lubrication theory.
Abstract: The elastohydrodynamic force on two slightly deformable bodies approaching one another head on is calculated in the limit of small gap sizes and small deformations by combining Hertz's theory of deformation and lubrication theory. An expression for the lubrication force analytical in the deformation and gap size is obtained. The effect of the gap size, the elasticity and the velocity of approach on the lubrication force is demonstrated. Further, the lubrication force with a pressure dependent viscosity is calculated.
TL;DR: In this paper, the transition from fluid to mixed lubrication was defined by looking for the first contact point between the two surfaces, and the transition was shown to change with the number of asperities on the contacting surfaces.
Abstract: Fluid lubrication and mixed lubrication can both be phenomena in the study of the lubrication of rough surfaces. In this paper, we take the surface as random process and, by studying the contact of surfaces which present roughness, we can put forward a method which defines the transition from fluid lubrication to mixed lubrication, by looking for the first contact point between the two surfaces. This study suggests that the transition between fluid and mixed lubrication relates to the number of asperities on the contacting surfaces, an advance on former methods. We also apply this method to piston ring/cylinder lubrication research. The results show that the transition changes with time.
TL;DR: In this article, the authors developed and applied both in the incompressible and compressible case, and showed that compressibility effects are essential for very thin layers, which finally leads to an oedometric thin film model to be applied for analysing the experimental results.
Abstract: The rheological analysis of surface force apparatus experiments, usually based on lubrication theory, requires a refined modelisation taking into account the heterogeneity resulting from confinement effects. Such a model is developed and applied both in the incompressible and compressible case. It is shown that compressibility effects are essential for very thin layers. This finally leads to an oedometric thin film model to be applied for analysing the experimental results.
TL;DR: In this paper, an analytical solution for a two-dimensional arbitrarily shaped guide bearing under finite amplitude transverse vibration and translation of a plate is presented, which uses the method of averaged inertia and a perturbation method on the Navier-Stokes equations to predict the bearing load and phase.