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Showing papers on "Lubrication theory published in 1993"


Journal ArticleDOI
TL;DR: In this article, the spreading of a localized distribution of surfactant on a thin viscous film is considered, in the situation in which the surfactants is soluble in the bulk layer and the boundary beneath the fluid is impermeable to the material.
Abstract: The spreading of a localized distribution of surfactant on a thin viscous film is considered, in the situation in which the surfactant is soluble in the bulk layer and the boundary beneath the fluid is impermeable to surfactant. The surfactant distribution is controlled by advection and diffusion both at the surface of the film, where the surfactant forms a monolayer, and in the bulk. The bulk and surface surfactant concentrations are related by linearized sorption kinetics. The surfactant diffuses rapidly across the thin fluid layer, and lubrication theory is used to derive evolution equations for the film height and the surface and cross‐sectionally averaged bulk surfactant concentrations. A special case of the governing equations describes the Marangoni flow induced by a locally hot region of the layer. It is shown that in comparison to the spreading of insoluble surfactant, transient desorption of surfactant from the monolayer to the bulk causes the spreading rate to diminish, although once the bulk and surface concentrations are locally in equilibrium, film deformations are more severe, with a sharp pulse in the film height created just upstream of the leading edge of the surfactant distribution.

223 citations


Journal ArticleDOI
TL;DR: A theoretical analysis is presented predicting the closure of small airways in the region of the terminal and respiratory bronchioles by a coupled capillary-elastic instability leading to liquid bridge formation, wall collapse or a combination of both.
Abstract: A theoretical analysis is presented predicting the closure of small airways in the region of the terminal and respiratory bronchioles. The airways are modelled as thin elastic tubes, coated on the inside with a thin viscous liquid lining. This model produces closure by a coupled capillary-elastic instability leading to liquid bridge formation, wall collapse or a combination of both. Nonlinear evolution equations for the film thickness, wall position and surfactant concentration are derived using an extended version of lubrication theory for thin liquid films. The positions of the air-liquid and wall-liquid interfaces and the surfactant concentration are perturbed about uniform states and the stability of these perturbations is examined by solving the governing equations numerically. Solutions show that there is a critical film thickness, dependent on fluid, wall and surfactant properties above which liquid bridges form. The critical film thickness, epsilon c, decreases with increasing mean surface-tension or wall compliance. Surfactant increases epsilon c by as much as 60 percent for physiological conditions, consistent with physiological observations. Airway closure occurs more rapidly with increasing film thickness and wall flexibility. The closure time for a surfactant rich interface can be approximately five times greater than an interface free of surfactant.

164 citations


Journal ArticleDOI
TL;DR: In this article, a Faxen law for the pressure moment of one rigid particle in a general low-Reynolds number flow is found in terms of the ambient pressure, and the pressure moments of two rigid spheres immersed in a linear ambient flow are calculated using multipole expansions and lubrication theory.
Abstract: The pressure moment of a rigid particle is defined to be the trace of the first moment of the surface stress acting on the particle. A Faxen law for the pressure moment of one spherical particle in a general low‐Reynolds‐number flow is found in terms of the ambient pressure, and the pressure moments of two rigid spheres immersed in a linear ambient flow are calculated using multipole expansions and lubrication theory. The results are expressed in terms of resistance functions, following the practice established in other interaction studies. The osmotic pressure in a dilute colloidal suspension at small Peclet number is then calculated, to second order in particle volume fraction, using these resistance functions. In a second application of the pressure moment, the suspension or particle‐phase pressure, used in two‐phase flow modeling, is calculated using Stokesian dynamics and results for the suspension pressure for a sheared cubic lattice are reported.

73 citations


Journal ArticleDOI
TL;DR: In this article, the effects of the surface roughness, eccentric or moment loads, supply pressure and speed of rotation on the friction, flow rate, and power losses were studied numerically.
Abstract: On mixed and fluid film lubrication the characteristics of hydrostatic bearings for hydraulic equipment are studied numerically. By applying a mixed lubrication model derived in a previous paper to the bearings, we clarify the effects of the surface roughness, eccentric or moment loads, supply pressure and speed of rotation on the friction, flow rate, and power losses. Introducing the concept of a ratio of hydrostatic balance, we show that the minimum power loss is given as the ratio becomes close to unity

59 citations


Journal ArticleDOI
TL;DR: In this paper, the importance of different non-linear mechanisms, such as plastic yielding, rock dilation, cohesive zone and fluid-lag on a hydraulic fracture propagating in a low permeability formation was examined.

56 citations


Journal ArticleDOI
TL;DR: In this paper, the authors extend hydrodynamic lubrication theory to lubrication with mixtures of a Newtonian liquid and an ideal gas, and derive two coupled non-linear equations in component densities.
Abstract: Mixtures do not exhibit Newtonian behavior even when their individual components themselves are Newtonian, and thus classical lubrication theory is not applicable to bearings lubricated with mixtures. Our objective is to extend hydrodynamic lubrication theory to lubrication with mixtures of a Newtonian liquid and an ideal gas. To this end, we make use of the theory of interacting continua and derive two coupled non-linear equations in component densities. The extended theory is tested on finite journal bearings: our results of pressure distribution show good qualitative agreement with the experimental data of Braun et al

42 citations


Journal ArticleDOI
TL;DR: In this paper, a lubrication theory for the power law fluid is developed and analyzed, where flow between rigid walls of arbitrary shape under combined Couette and squeezing motion with a pressure gradient is considered.
Abstract: A lubrication theory for the power law fluid is developed and analyzed. Only the infinite width gap is considered. Considered is flow between rigid walls of arbitrary shape under combined Couette and squeezing motion with a pressure gradient. equations appropriate to a thin film are derived by asymptotic integration of the three-dimensional equations of fluid mechanics. Further integration of these equations yields an algebraic equation for the pressure gradient. Working out the details of the structure of the equation enables us to develop a numerical algorithm for its solution

37 citations


Book ChapterDOI
C. M. Taylor1
TL;DR: In this paper, the authors highlight the significance of a lubricant as an engineering design material and highlight the physical and chemical actions associated with the modes of lubrication known as hydrodynamic, elastohydrodynamics, mixed, and boundary.
Abstract: Publisher Summary This chapter highlights the significance of a lubricant as an engineering design material. If the lubricant film is sufficiently thick to prevent the opposing solids from coming into contact, the condition is referred to as “fluid film lubrication.” This condition is often considered as the ideal form of lubrication since it provides low friction and a high resistance to wear. The behavior of the contact is governed by the bulk physical properties of the lubricant, and the frictional characteristics arise purely from the shearing of the viscous lubricant. Different modes of lubrication are significant in the alternative tribological components of the engine and a component may undergo a wide range of lubrication regimes during a cycle. The physical and chemical actions associated with the modes of lubrication known as hydrodynamic, elastohydrodynamic, mixed, and boundary are discussed in the chapter.

28 citations


Journal ArticleDOI
TL;DR: In this paper, pyroclastic flows are modeled as laminar debris flows moving on an inclined plane, and their physics is discussed within the classical framework of lubrication theory.
Abstract: In this note I investigate some theoretical characteristics of pyroclastic flow deposits, assuming that these flows are Bingham fluids, probably the simplest non-Newtonian fluids. Pyroclastic flows are modeled as laminar debris flows moving on an inclined plane, and their physics is discussed within the classical framework of lubrication theory. Using general hydrodynamics methods, I show that the arrestment and emplacement of pyroclastic flows may be seen as the time-asymptotic limit of their equations of motion. This limit is found to be a nonlinear ordinary differential equation, whose solution gives the shape of pyroclastic flow deposits. The model suggests that these flows stop when the supply of material from the source is depleted; deposit thickness is controlled principally by the flow yield stress τz, a parameter characteristic of Bingham fluids, while deposit length, a measure of flow mobility, depends on τz, on the source flux q0, and on the slope θ of the solid substrate. Even in this simple model, theoretical analysis shows a complex correlation between flow parameters and deposit profiles.

28 citations


Journal ArticleDOI
TL;DR: In this article, the extended Reynolds equations of Al-Sharif et al, derived for binary mixture lubricants, were employed to study strip-rolling with oil-in-water emulsion.
Abstract: Petroleum oil-in-water emulsion, where water is the continuous phase, is often employed under circumstances where the high heat capacity of water is beneficial while the poor lubricating properties of an oil-in-water emulsion can be tolerated Usage includes cold-rolling but also some hot rolling applications However, emulsions do not exhibit Newtonian behavior even when their individual components themselves are Newtonian, thus classical lubrication theory is not valid for these applications In this paper we employ the extended Reynolds equations of Al-Sharif et al, derived for binary mixture lubricants, to study strip-rolling lubricated with oil-in-water emulsion We are able to predict several experimentally observed phenomena such as oil-pooling, enhancement of oil-pooling with increased strip yield stress and with increased roller speed

23 citations


Journal ArticleDOI
TL;DR: In this article, the authors applied Lubrication theory to solve flow problems in profile extrusion dies without flow separations, for Newtonian and power law type fluids, based on velocity calculation within cross sections perpendicular to the flow.
Abstract: Lubrication theory has been applied to solve flow problems in profile extrusion dies without flow separations, for Newtonian and power law type fluids. The method is based on velocity calculation within cross sections perpendicular to the flow. Pressure drop can also be obtained from a macroscopic balance, if the flow rate is known. Comparison of pressure drops in 2-D and 3-D geometries has been made with numerical simulation obtained by a finite element method. Results show a good accuracy of the proposed method.

Journal ArticleDOI
TL;DR: The evaporation and contraction of a droplet wetting a flat metallic surface is monitored using photoacoustic detection and the results are interpreted in terms of an effective backing model together with the lubrication theory for droplet dynamics.
Abstract: The evaporation and contraction of a droplet wetting a flat metallic surface is monitored using photoacoustic detection. The results are interpreted in terms of an effective backing model together with the lubrication theory for droplet dynamics

Journal ArticleDOI
TL;DR: In this article, the governing continuity, momentum and energy equations for a Newtonian fluid, which are coupled, via temperature dependent density and viscosity are solved simultaneously using the finite difference method, to yield various bearing characteristics.
Abstract: Parallel sliding load support has been a subject og numerous theoretical and experimental investigations. Postulated mathematical models suffer from restricting assumptions. The present analysis evaluates thre several models that have appeared and provides an orderly analysis which elaborates on the mechanism that may be responsible for the fluid generated lifting force. The governing continuity, momentum and energy equations for a Newtonian fluid, which are coupled, via temperature dependent density and viscosity are solved simultaneously using the finite difference method, to yield various bearing characteristics

Book ChapterDOI
01 Jan 1993
TL;DR: In this paper, the processes which lead to topological reconfiguration of fluid interfaces are studied in Hele-Shaw flow and an asymptotic theory for the local thickness of thin fluid layers is developed.
Abstract: The processes which lead to topological reconfiguration of fluid interfaces are studied in Hele-Shaw flow. This is motivated by recent experiments of droplet forma tion through the osculation of two interfaces separating immiscible fluids. In the Hele-Shaw approximation, such a configuration reduces to interface dynamics through their representation as vortex sheets. To begin, we focus on thin fluid layers and develop an asymptotic theory which yields simplified, nonlinear equations for the local thickness. As particular examples, we consider the dynamics of gravity driven fluid jets, as well as the motion of unstably stratified fluid layers. In both cases, the bounding interfaces collide at a finite time, with an associated singularity in the fluid velocity. Some comparison is made with simulations of the full Hele-Shaw equations, and connections with experiments are discussed.

Journal ArticleDOI
02 Aug 1993-Wear
TL;DR: In this article, the steady state performance of finite hydrodynamic porous journal bearings in turbulent regimes was investigated, following Constantinescu's turbulent lubrication theory, and a numerical method was employed to solve the governing differential equations for a wide range of bearing parameters.

Journal ArticleDOI
TL;DR: In this article, the flow of a suspension of rigid rods in a wedge of small angle is considered and the small scale structure within these zones is determined, and matched asymptotic expansions are used to provide jump conditions across them.
Abstract: The flow of a suspension of rigid rods in a wedge of small angle is considered. In the lubrication limit when the angular width of the channel is small but the rod concentration is high it is found that wedges of fluid (here called stagnant zones ) in the interior of the channel become asymptotically static. The small scale structure within these zones is determined, and matched asymptotic expansions are used to provide jump conditions across them. These results are found to show good agreement with exact solutions for wedge flows even when the angular half-width of the wedge is not small (up to 30°, say). Analogous jump conditions are devised for stagnant zones in general planar lubrication flows of rigid rod suspensions.

Journal ArticleDOI
TL;DR: In this paper, the authors considered non-axisymmetric motion of a rigid particle in a cylindrical fluid-filled tube, with negligible inertial effects, and showed that the particle's motion along the tube axis is stable or unstable depending on its shape.
Abstract: We consider non-axisymmetric motion of a rigid particle in a cylindrical fluid-filled tube, with negligible inertial effects. The particle is assumed to fit closely in the tube, and lubrication theory is used to describe the fluid flow in the narrow gap between the particle and the tube wall. The solution to the Reynolds lubrication equation and the components of the resistance matrix are expressed in terms of a Green's function. For the case in which the gap is almost uniform, the Green's function is expanded as a power series in a small parameter δ, characteristic of the variations in gap width, and the first two terms are obtained. The velocity of a freely suspended axisymmetric particle driven by a pressure difference along the tube is deduced from the resistance matrix. According to the results at first order in δ, in general the particle moves transversely with a constant velocity. In the absence of higher-order effects, it would eventually collide with the wall. Motion along the tube axis is a neutrally stable solution to the equations of motion at first order. However, if effects at second order in δ are included, motion of an axisymmetric particle along the tube axis is stable or unstable depending on its shape. Generally, if the particle is narrower near the front than near the rear, and the width near the middle is at least as large as the mean of the widths near the front and rear, then its motion is stable. Numerical calculations (not restricted to small δ) confirm these results for axisymmetric particles, and show that a non-axisymmetric shape similar to a red blood cell has a stable equilibrium position in the tube.

Journal ArticleDOI
TL;DR: In this article, a model of the coupling of the mass transfer of surfactants and the fluid flows in emulsion systems is presented, based on the surface Peclet number Pes.

Journal ArticleDOI
TL;DR: In this paper, the authors measured the transport of aerosol through the airways of a hollow cast of a canine tracheobronchial tree, and found that the aerosol particles were fastest in the gas of highest kinematic viscosity (helium), and slowest in a gas of lowest kinematics viscoelasticity (sulfur hexafluoride).
Abstract: Transport of aerosol through the airways of a hollow cast of a canine tracheobronchial tree was measured for steady flow in different gas mixtures. A small bolus of 0.5-μm aerosol particles was inserted as a tracer of convective motion in the flow at the entrance of the trachea, and particles were collected and counted as they arrived at a flow-balanced sampling bag at a peripheral segment of the cast. Transport was fastest in the gas of highest kinematic viscosity (helium), and slowest in the gas of lowest kinematic viscosity (sulfur hexafluoride). This is consistent with the lubrication theory that describes an axial core in the divergent flow field of the bronchial tree. The finer core in helium transports the particles at a greater velocity to distal airways. Transport of gases through the in vivo respiratory tract should also be influenced by these fluid mechanics of convection resembling Poiseuille flow that is substantially modified according to lubrication theory. As predicted by some other invest...

Journal ArticleDOI
TL;DR: In this paper, the authors describe the thin-film melting of a block of solid phase-change material (the bearing) around a rotating cylinder (the shaft) and determine the relation between the force applied on the shaft and the speed with which the shaft migrates into the bearing.

Journal ArticleDOI
01 Feb 1993-Wear
TL;DR: In this article, a modified mixing length expression of Reynolds stress in transition and turbulent lubrication theory was introduced to determine the performance characteristics of sector-shaped thrust bearings when operated in the transition regime taking into account the inertia effects.

Book ChapterDOI
TL;DR: In this paper, an attempt is made to delineate regimes of lubrication where one or the other of the mechanisms is predominant, where measurements of friction are carried out for several perfluoropolyether lubricants in a thickness range of 0 to 80 nm and at sliding speeds of 0.25 to 250 mm/s.
Abstract: Historically, the lubrication of solid surfaces has been characterized as comprising four major regimes: boundary lubrication, mixed lubrication, EHD, and hydrodynamic lubrication. One generally expects that the presence of the lubricant serves to reduce the friction of the interface. However, for very smooth surfaces, the introduction of lubricant can cause a substantial increase in friction over that of unlubricated sliding. While this increase in friction has been attributed to adhesive and/or viscous effects, it has been difficult to predict which of these contributions is most important to a given sliding regime. In the present work, an attempt is made to delineate regimes of lubrication where one or the other of the mechanisms is predominant. Measurements of friction are carried out for several perfluoropolyether lubricants in a thickness range of 0 to 80 nm and at sliding speeds of 0.25 to 250 mm/s. Three distinct regimes of lubrication are observed. The first, an “adhesion” regime, is characterized by large friction at low speeds and a decreasing friction with increasing sliding speed. The second, a hydrodynamic regime, is well described by classical lubrication theory and exists at higher sliding velocities than the first regime. The third regime, identified by an abrupt change in the dependence of friction on velocity, exists at relatively large sliding speeds and indicates substantial shear-thinning of the lubricant. The onset of the third regime is predicted from consideration of the tensile stresses in the lubricant film. It is also found modelling the lubricant as a continuum is valid at least down to 23 nm for the materials studied.


Journal ArticleDOI
TL;DR: In this paper, the authors apply the recently introduced Reynolds stress expression (Tieu and Kosasih, 1992) in the transition-turbulent lubrication analysis, which can be extended to apply in the transilion regime.
Abstract: This paper applies the recently introduced Reynolds stress expression (Tieu and Kosasih, 1992) in the transition-turbulent lubrication analysis. The Reynolds stress is modeled using the mixing length expression which is able to account for the effect of local shear stress gradient, and it can be extended to apply in the transilion regime. This theory is then used to determine three-dimensional velocity distributions between parallel plates. From the results, a set of coefficients covering transition-turbulent regime used in conjunction with the modified Reynolds equation is presented

Journal ArticleDOI
TL;DR: In this paper, an analysis procedure is presented which determines the rotordynamic stiffness, damping, and added mass coefficients for circumferentially-grooved annular seals with turbulent incompressible flow.
Abstract: An analysis procedure is presented which determines the rotordynamic stiffness, damping, and added mass coefficients for circumferentially-grooved annular seals with turbulent incompressible flow. Hirs' turbulent lubrication theory is used as the basis for the governing equations. Friction factors in the groove are based on theory for a turbulent shear layer and an entrance loss model is applied at the inlet and land regions of the seal. The governing equations are expanded into zeroth and first order equations for small rotor displacements about a centered position. The zeroth order solution determines the velocity distribution and seal leakage. The first order solution determines the dynamic pressure distribution which is integrated to yield the fluid force reactions. Comparison to published experimental results shows moderate quantitative agreement and good qualitative agreement with seal test data. Presented at the 47th Annual Meeting In Philadelphia, Pennsylvania May 4–7, 1992

Patent
21 Dec 1993
TL;DR: In this article, the difference between the supply flow rate qA of a paint supplied to a strip from an applicator roll obtained by using the gap between the applicator and pickup roll, obtained by applying the elastodynamic lubrication theory and the leak flow ratio qL left on the applicators roll 16 and a steel strip S is used to prepare a film thickness control equation, and the film thickness is controlled according to the equation.
Abstract: PURPOSE: To highly precisely control the thickness of a film formed on a strip even when a paint having a non-Newtonian viscosity behavior is used. CONSTITUTION: The difference between the supply flow rate qA of a paint supplied to a strip from an applicator roll obtained by using the gap between the applicator roll and pickup roll obtained by applying the elastodynamic lubrication theory and the leak flow rate qL left on the applicator roll 16 obtained by using a gap between the applicator roll 16 and a steel strip S is used to prepare a film thickness control equation, and the film thickness is controlled according to the equation. Further, the relation between the shear rate and the measured apparent viscosity is previously obtained, the equation of the measured apparent viscosity and gap is allied with the equation of the shear rate to obtain the true apparent viscosity, and both gaps are respectively obtained by using the true apparent viscosity. COPYRIGHT: (C)1995,JPO

Journal ArticleDOI
TL;DR: In this paper, the authors considered the high-velocity penetration of a melting solid by a thermally insulated slender body and provided a closed solution of the problem of the fusion zone around a moving slender body.
Abstract: The high-velocity penetration of a melting solid by a thermally insulated slender body is considered. Under certain constraints on the dimensionless melting parameters the flow in the molten layer can be described within the framework of lubrication theory. The local angle of inclination of the body and the surfaces of the molten layer with respect to the velocity is assumed to be small and is taken into account in the linear approximation. The heat flow into the solid is found by simulating the body and the molten layer by means of a segment with distributed heat sources. Within the framework of this simple formulation a closed solution of the problem of the fusion zone around a moving slender body is constructed. The dependence of the shape of the molten layer and the structure of the temperature and longitudinal velocity fields in the layer on the shape of the body and the other governing parameters of the problem is investigated. The results obtained also give a solution of the problem of the melting of a solid rubbing at high velocity against a thermally insulated rough substrate, when the characteristic height of the roughness is of the order of the thickness of the layer and the characteristic length of the order of the contact length.

Journal ArticleDOI
TL;DR: In this paper, the authors measured the frictional force and leakage flow rate under a lubrication range from mixed to fluid film and found that the minimum power losses are given by the ratio of hydrostatic balance being close to unity independent of the surface roughness, the loads, the speed of rotation and the restrictors.
Abstract: It is strongly desired to clarify performances of hydrostatic bearings under mixed lubrication conditions because seldom there is information available on them. Therefore, in a previous paper, we calculated the performances of friction, leakage flow rate and power losses under conditions ranging from mixed to fluid film lubrication and clarified numerically the effects of surface roughness, the eccentric loads (moment loads), the supply pressure and the speed of rotation. In this paper, by the use of an apparatus featuring circular hydrostatic thrust bearings acting on concentric loads, we measure the frictional force and leakage flow rate under a lubrication range from mixed to fluid film. The surface roughness, the supply pressure, the loads, the speed of rotation and the restrictors are selected as main experimental parameters. We evaluate the coefficient of friction, the leakage flow rate and power losses for the bearing-modulus and the ratios of hydrostatic balance. Furthermore, these experimental results are compared with the theoretical ones. The conclusions are as follows : 1) the minimum power losses are given by the ratio of hydrostatic balance being close to unity independent of the surface roughness, the loads, and the speed of rotation; 2) the coefficient of friction of hydrostatic bearings can be clarified generally versus a bearing-modulus by use of the load carrying capacity due to asperities; 3) a larger surface roughness, causes a larger leakage flow rate in mixed lubrication; 4) the larger the supply pressure, the larger the power losses in fluid film and under mixed lubrication; 5) the larger the speed of rotation, the larger are the proportional power losses under mixed lubrication; 6) the size of restrictors seldom have any effects under mixed lubrication conditions.

Book ChapterDOI
D.A. Jones1
TL;DR: In this article, the Reynolds equation of viscous flow is used to estimate the effective temperature of the fluid within the film, of its viscosity, and of the viscous friction in the bearing.
Abstract: Publisher Summary This chapter discusses the basic concepts of viscous flow and develops the governing equation of fluid film lubrication, the “Reynolds equation.” It presents a model for various operating parameters bearing specifically the “narrow journal bearing theory.” An ideally elastic material obeys the Hooke's law—that is, under stress an equilibrium strain develops, the two being proportional to one another. The plain journal bearings associated with reciprocating internal combustion engines tend to be narrow in relation to their diameters. The bearing's load capacity may be estimated from an integration routine. The mean temperature rise in the fluid expelled from a bearing provides a reliable means of estimating the effective temperature of the fluid within the film, of its viscosity, and of the viscous friction in the bearing.