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Showing papers on "Lubrication theory published in 1991"


Book
01 Jan 1991
TL;DR: In this paper, the authors propose a simplified solution for deformation in dry contacts in Elastohydrodynamic Lubrication of Rectangular Conjunctions and a solution for elasthydrodynamic lubrication in ellipitcal conjunctions.
Abstract: 1: Introduction 2: Bearing Classification and Selection 3: Surface Topography 4: Lubricant Properties 5: Bearing Materials 6: Viscous Flow 7: Reynolds Equation 8: Hydrodynamic Thrust Bearings - Analytical Solutions 9: Hydrodynamic Thrust Bearings - Numerical Solutions 10: Hydrodynamic Journal Bearings - Analytical Solutions 11: Dynamically Loaded Journal Bearings 12: Hydrodynamic Journal Bearings - Numerical Solutions 13: Hydrodynamic Squeeze Film Bearings 14: Hydrostatic Lubrication 15: Hydrodynamic Bearings - Considering Fluid Inertia 16: Gas-Lubricated Thrust Bearings 17: Gas-Lubricated Journal Bearings 18: Hydrodynamic Lubrication of Nonconformal Surfaces 19: Simplified Solutions for Stresses and Deformations 20: General Solution for Stresses and Deformations in Dry Contacts 21: Elastohydrodynamic Lubrication of Rectangular Conjunctions 22: Elastohydrodynamic Lubrication of Ellipitcal Conjunctions 23: Film Thicknesses for Different Regimes of Fluid Film Lubrication 24: Rolling-Element Bearings 25: Additional Elastohydrodynamic Lubrication Applications 26: Non-Newtonian Fluid Effects in Elastohydrodynamic Lubrication 27: Thermo Elastohydrodynamic Lubrication.

1,688 citations


Journal ArticleDOI
TL;DR: In this article, the Navier-Stokes equations that govern fluid flow are reduced to the more tractable Reynolds equation, which is valid for low Reynolds numbers and under certain restrictions on the magnitude of the roughness.

319 citations


Journal ArticleDOI
TL;DR: In this article, it is found that cooling (cooling) retards (augments) the spreading process by creating flows that counteract (reinforce) those associated with isothermal spreading for both two-dimensional and axisymmetric configurations.
Abstract: A viscous-liquid drop spreads on a smooth horizontal surface, which is uniformly heated or cooled. Lubrication theory is used to study thin drops subject to capillary, thermocapillary and gravity forces, and a variety of contact-angle-versus-speed conditions. It is found for isothermal drops that gravity is very important at large times and determines the power law for unlimited spreading. Predictions compare well with the experimental data on isothermal spreading for both two-dimensional and axisymmetric configurations. It is found that heating (cooling) retards (augments) the spreading process by creating flows that counteract (reinforce) those associated with isothermal spreading. For zero advancing contact angle, heating will prevent the drop from spreading to infinity. Thus, the heat transfer serves as a sensitive control on the spreading.

292 citations


Journal ArticleDOI
TL;DR: In this article, a model for the motion of the free surface of a viscous droplet is developed by using lubrication theory, which includes both the effect of slip and the dependence of the contact angle on the slip velocity.
Abstract: The motion of the free surface of a viscous droplet is investigated. By using lubrication theory a model is developed for the motion of the free surface which includes both the effect of slip and the dependence of the contact angle on the slip velocity. We solve the resulting nonlinear partial differential equation in several ways. First we investigate the initial motion of the drop at a non-equilibrium contact angle using the method of matched asymptotics. Then we develop a pseudo-spectral method to numerically solve the full nonlinear system. The dependence of the spreading rate of the drop on the various physical parameters and for different slip models is determined.

169 citations


Journal ArticleDOI
TL;DR: In this paper, the flow of fiber suspensions in narrow gaps is examined using rheological theories for suspensions of rigid particles in a Newtonian solvent, and a dimensionless particle number Np describes the intrinsic anisotropy of the suspension order-of-magnitude estimates are developed for the velocity, stress and fiber orientation components in a narrow gap of slowly varying thickness.
Abstract: The flow of fiber suspensions in narrow gaps is examined using rheological theories for suspensions of rigid particles in a Newtonian solvent A dimensionless particle number Np describes the intrinsic anisotropy of the suspension Order-of-magnitude estimates are developed for the velocity, stress and fiber-orientation components in a narrow gap of slowly varying thickness The estimates reveal four distinct flow regimes At one extreme the flow is decoupled from fiber orientation and lubrication theory applies The other extreme exhibits a flat velocity profile with a shear boundary layer of thickness L(Np− 1 2 The key dimensionless group separating the regimes is Npδ2 Here δ describes the out-of-plane fiber orientation; it equals the greater of ϵ or CI 1 3 , where ϵ is the slenderness of the gap and CI is an interaction coefficient for fiber orientation The existence of the first regime supports the practice of decoupling the calculation of flow and fiber orientation, provided that Npδ2 is much smaller than one The fourth regime generalizes Barone and Caulk's model for compression molding flows of chopped-fiber molding compounds Limitations due to entrance effects and start-up transients are discussed, along with applications to the modeling of injection and compression molding of fiber-reinforced polymers

152 citations


Journal ArticleDOI
TL;DR: In this paper, the two-dimensional base state that ultimately exhibits a contact-line-related instability is investigated by a combination of analysis and numerical solution, where the outer solution is governed by simple kinematics and describable by lubrication theory.
Abstract: The two‐dimensional base state that ultimately exhibits a contact‐line‐related instability is investigated by a combination of analysis and numerical solution. Globally, these flows may be characterized as having a down‐slope length scale that is much greater than the length scale normal to the slope. This allows a solution by matched expansions, where the outer solution is governed by simple kinematics and describable by lubrication theory. In order to complete the solution, the flow in an inner region near the contact line must be determined. It is shown that it is not possible to model the flow in the inner region using the lubrication approximations while also requiring both that (1) the free surface meets the plane at the contact line and (2) the rate of change of the curvature of the free surface be bounded at the contact line. However, the full two‐dimensional Stokes equations allow the inner solution to be determined. A boundary integral technique is used to obtain numerical solutions to the problem in which a contact angle boundary condition is imposed. Solutions are reported for a wide range of the three relevant parameters: the capillary number, the contact angle, and the inclination angle. The computations reveal that the free surface develops a hump near the contact line as a result of a stress field that results from kinematic considerations. A scaling analysis of the numerical results verifies that, except possibly at very small contact angles, the lubrication approximations are inappropriate near the contact line.

140 citations


Journal ArticleDOI
TL;DR: In this paper, the mean thickness of a thin liquid film of deionized water with a free surface on a stationary and rotating horizontal disk has been measured with a nonobtrusive capacitance technique.
Abstract: The mean thickness of a thin liquid film of deionized water with a free surface on a stationary and rotating horizontal disk has been measured with a nonobtrusive capacitance technique. The measurements were taken when the rotational speed ranged from 0-300 rpm and the flow rate varied from 7.0-15.0 lpm. A flow visualization study of the thin film was also performed to determine the characteristics of the waves on the free surface. When the disk was stationary, a circular hydraulic jump was present on the disk. Upstream from the jump, the film thickness was determined by the inertial and frictional forces on the fluid, and the radial spreading of the film. The surface tension at the edge of the disk affected the film thickness downstream from the jump. For the rotating disk, the film thickness was dependent upon the inertial and frictional forces near the center of the disk and the centrifugal forces near the edge of the disk.

78 citations


Journal ArticleDOI
01 Jun 1991
TL;DR: Quantitative theoretical models that relate red cell mechanics to flow properties of blood in capillaries indicate that nonaxisymmetry and tank-treading do not significantly influence the flow resistance in single-file or two-file flow.
Abstract: Blood contains a high vol fraction of erythrocytes (red blood cells), which strongly influence its flow properties. Much is known about the mechanical properties of red cells, providing a basis for understanding and predicting the rheological behavior of blood in terms of the behavior of individual red cells. This review describes quantitative theoretical models that relate red cell mechanics to flow properties of blood in capillaries. Red cells often flow in single file in capillaries, and rheological parameters can then be estimated by analyzing the motion and deformation of an individual red cell and the surrounding plasma in a capillary. The analysis may be simplified by using lubrication theory to approximate the plasma flow in the narrow gaps between the cells and the vessels walls. If red cell shapes are assumed to be axisymmetric, apparent viscosities are predicted that agree with determinations in glass capillaries. Red cells flowing in microvessels typically assume nonaxisymmetric shapes, with cyclic "tank-treading" motion of the membrane around the interior. Several analyses have been carried out that take these effects into account. These analyses indicate that nonaxisymmetry and tank-treading do not significantly influence the flow resistance in single-file or two-file flow.

65 citations


Journal ArticleDOI
15 Mar 1991
TL;DR: Theoretical analyses of three previously proposed models of the aggregation-disaggregation process, with numerically calculated predictions of the corresponding viscosity vs shear rate behavior, are presented in this paper.
Abstract: Theoretical analyses are presented of three previously proposed models of the aggregation—disaggregation process, with numerically calculated predictions of the corresponding viscosity vs shear rate behavior. All the models are based on the assumption that aggregation of particles is due to surface forces of arbitrary nature and disaggregation is due to viscous stresses. The models differ from each other by the methods of taking into account hydrodynamic interaction of aggregates. Some modifications of the models are considered and different methods of the aggregates yield stress evaluation are compared. It is shown that two models (one of them is based on the mean field theory and the other utilizes the free cell theory) correspond to the diluted suspensions and the third one (based on the lubrication theory) can be applied to the suspensions of high concentration and low concentration as well.

51 citations


Journal ArticleDOI
TL;DR: In this paper, the authors used the Navier-Stokes equations to model fluid flow under a grinding wheel and compared the results with the results obtained from experiments with a smooth wheel and a one-dimensional sinusoidal roughness term.
Abstract: Fluid flow under a grinding wheel is modeled using a perturbation scheme. In this initial effort to understand the flow characteristics, we concentrate on the case of a smooth wheel with slight clearance between the wheel and workpiece. The solution at lowest order is that given by standard lubrication theory. Higher-order terms correct for inertial and two-dimensional effects. Experimental and analytical pressure profiles are compared to test the validity of the model. Lubrication theory provides good agreement with low Reynolds number flows; the perturbation scheme provides reasonable agreement with moderate Reynolds number flows but fails at high Reynolds numbers. Results from experiments demonstrate that the ignored upstream and downstream conditions significantly affect the flow characteristics, implying that only a model based on the fully two- (or three-) dimensional Navier-Stokes equations will accurately predict the flow. We make one comparison between an experiment with a grinding wheel and the model incorporating a one-dimensional sinusoidal roughness term. For this case, lubrication theory surprisingly provides good agreement with experiment.

38 citations


Journal ArticleDOI
TL;DR: In this paper, the characteristics of noncircular bearings, considering the effects of turbulence and cavitation, are numerically analyzed, and four bearing profiles are considered: circular, worn-circular, two-lobe and elliptical.
Abstract: In this paper, the characteristics of noncircular bearings, considering the effects of turbulence and cavitation, are numerically analyzed. Four bearing profiles are considered: circular, worn-circular, two-lobe and elliptical. To model the turbulence, the linearized lubrication theory of Ng and Pan is used. Reynolds' equation is suitably modified to account for both turbulence and cavitation. The equation is incorporated into the Elrod cavitation algorithm. This numerical procedure, which conserves mass throughout the bearing, implicitly incorporates the JFO boundary conditions at rupture and reformation boundaries. JFO theory is considered to accurately model cavitation in moderately to heavily loaded bearings. Performance predictions are compared to results presented in a variety of earlier papers. Presented at the 45th Annual Meeting in Denver, Colorado May 7–10, 1990

Journal ArticleDOI
TL;DR: The mass transport of diffusible substance during volume-cycled oscillatory flow in a thin-walled viscoelastic tube is studied in this paper, where a small-amplitude, long-wavelength travelling wave is generated by the oscillatory pressure gradient.
Abstract: The mass transport of a diffusible substance during volume-cycled oscillatory flow in a thin-walled viscoelastic tube is studied A small-amplitude, long-wavelength travelling wave is generated by the oscillatory pressure gradient Lubrication theory is employed for slow axial variations to derive regular perturbation solutions to the Navier–Stokes equations The convection–diffusion equation is solved in a similar manner, assuming uniform steady end concentrations and no wall flux From the velocity and concentration fields, the time-average rate of axial mass transport is calculated, and its dependence on oscillation frequency, tube stiffness, and stroke amplitude is investigated The general result is that transport is enhanced less for softer tubes than for stiffer ones and that mass flow rate as a function of frequency reaches a local maximal value The results are related to gas transport in pulmonary airways during high-frequency ventilation

Journal ArticleDOI
TL;DR: In this paper, the authors compared different nonlinear amplitude equations for long waves in core-annular flow and compared the linearization of approximate and exact theories, and found that the results of lubrication theory are not robust with respect to changes to larger gaps outside the regime of asymptotic validity.
Abstract: Different nonlinear amplitude equations for long waves in core‐annular flow are compared. Each equation has its own limits of validity that can be critically assessed by comparing the linearization of approximate and exact theories. Long wave theory gets the dispersion relation for the longest waves correctly but cannot accommodate cases like capillary instability, in which the most dangerous wave is not surpassingly long. Small gap lubrication based theories accommodate shorter waves of the size of the core when various extra conditions are satisfied, but various stabilizing mechanisms associated with inertia may not be well represented. One theory in which lubrication theory is used in the water film but not in the core captures the shear stabilization of inertia when the gap is small enough. The criterion for small enough is not uniform in the viscosity ratio and surpassingly small films are required for validity when the oil viscosity is large. The results of lubrication theory are not robust with respect to changes to larger gaps outside the regime of asymptotic validity; for example, the stabilizing effects of the inertia of the core and annulus may reverse for larger, but still small thicknesses.

Journal ArticleDOI
TL;DR: In this article, the motion of a rigid disk-shaped particle with rounded edges, which fits closely in the space between two parallel flat plates, and which is suspended in a viscous fluid subject to an imposed pressure gradient, is analyzed.
Abstract: The motion of a rigid disk-shaped particle with rounded edges, which fits closely in the space between two parallel flat plates, and which is suspended in a viscous fluid subject to an imposed pressure gradient, is analysed. This problem is relevant to the squeezing of red blood cells through narrow slot-like channels which are found in certain tissues. Mammalian red cells, although highly flexible, conserve volume and surface area as they deform. Consequently, a red cell cannot pass intact through a channel which is narrower than some minimum width. In channels that are just wide enough to permit cell passage, the cell is deformed into its ‘critical’ shape: a disk with rounded edges. In this paper, the fluid mechanical aspects of such motions are considered, and the particle is assumed to be rigid with the critical shape. The channel cross-section is assumed to be rectangular. The flow of the suspending fluid is described using lubrication theory. Use of lubrication theory is justified by considering the motion of a circular cylinder between parallel plates. For disk-shaped particles, approximate solutions are obtained by applying lubrication equations throughout the flow domain. In the region beyond the particle, this is equivalent to assuming a Hele-Shaw flow. More accurate solutions are obtained by including effects of boundary layers around the particle and at the sides of the channel. Pressure distributions and particle velocities are computed as functions of geometrical parameters, and it is shown that the particle may move faster or slower than the mean velocity of the surrounding fluid, depending on the channel dimensions.

Journal ArticleDOI
TL;DR: In this paper, a three-dimensional spectral algorithm for the solution of Stokes flow between eccentrically rotating cylinders is described, where pressure boundary conditions at the two ends of the finite length cylinders and the effect of a fluid line source on the inner cylinder are considered.
Abstract: A three-dimensional spectral algorithm for the solution of Stokes flow between eccentrically rotating cylinders is described. Included in the model are pressure boundary conditions at the two ends of the finite length cylinders and the effect of a fluid line source on the inner cylinder. A comparison of results for the load and couple on the inner cylinder is made with those available from lubrication theory in the absence of a line source. Good agreement is shown for long, short and finite journal bearings when the various geometrical assumptions inherent in the lubrication analysis are satisfied.

Journal ArticleDOI
TL;DR: A description of the flow of blood cells in the capillary blood vessels is presented, using the lubrication theory approach first suggested by Lighthill as well as taking into account a wider range of elastic deformations which affect the cell.

Journal ArticleDOI
TL;DR: In this article, the leveling of a thin-liquid film on a substrate having a mesa-like feature is analyzed by finite element analysis and lubrication theory applied to the free surface viscous flow problem.
Abstract: The leveling of a thin‐liquid film on a substrate having a mesa‐like feature is analyzed by finite element analysis and lubrication theory applied to the free‐surface viscous flow problem. The height of the mesa is on the order of 1 μm and has a width on the order of 100 μm; the thin‐liquid film is initially conformal to the substrate and has a thickness on the order of 1 μm. Capillarity is found to be the primary driving force for flow. The predicted leveling times from the numerical simulations compare favorably with an analytical solution developed from lubrication theory for the leveling of a thin film on a smooth substrate.

Journal ArticleDOI
TL;DR: In this paper, the problems of fluid film lubrication for non-Newtonian lubricants are reviewed by classifying the studies by rheology models, and the results of these studies are presented.
Abstract: This review describes the recent studies of fluid film lubrication by non-Newtonian lubricants. Present-day lubricating oils contain a large quantity of high-molecular-weight polymers as a viscosity index improver and a viscosity thickener. Greases have been widely used in various types of equipment and machinery to simplify the lubricating system. These lubricants exhibit a non-Newtonian behavior. However, the classical theory of fluid film lubrication deals with the lubricants whose behavior is Newtonian. In recent years, several investigators have studied the fluid film lubrication characteristics of non-Newtonian lubricants in various bearings by considering different rheology models. In this paper, the problems of fluid film lubrication for such lubricants are reviewed by classifying the studies by rheology models.

Journal ArticleDOI
TL;DR: In this paper, the stresslets of two deforming spheres in a low Reynolds number flow are calculated asymptotically for the case in which the imposed flow field tends, far from the spheres, to a two-dimensional pure-straining motion perpendicular to the line of centers.
Abstract: The stresslets of two spheres in a low Reynolds number flow are calculated asymptotically for the case in which the imposed flow field tends, far from the spheres, to a two‐dimensional pure‐straining motion perpendicular to the line of centers. The spheres are assumed to be nearly touching. The analysis is based on a complementary problem in which lubrication theory is used to calculate the flow between two deforming spheres. As well as providing asymptotic estimates of the singular nature of the stresslets, the solution shows an unexpected feature for a lubrication flow, this being the fact that, for one special case, the pressure in the flow field is zero.

Journal ArticleDOI
TL;DR: In this paper, an analytical solution for two-dimensional incompressible film flow between a sinusoidally grooved (or rough) surface and a flat surface is presented for Navier-Stokes equations.
Abstract: An analytical solution is presented for two-dimensional, incompressible film flow between a sinusoidally grooved (or rough) surface and a flat-surface. The upper grooved surface is stationary whereas the lower, smooth surface moves with a constant speed. The Navier-Stokes equations were solved employing both mapping techniques and perturbation expansions. Due to the inclusion of the inertia effects, a different pressure distribution is obtained than predicted by the classical lubrication theory. In particular, the amplitude of the pressure distribution of the classical lubrication theory is found to be in error by over 100 perent (for modified Reynolds number of 3-4).

Book ChapterDOI
TL;DR: In this article, the use of fluid film lubrication theory as a design tool, alongside traditional tribological approaches, has much merit, and the situation is reviewed and it is concluded that use of lubrication theories as a tool for design has much value.
Abstract: Synopsis The durability of the cam and follower contact of the valve train of automobile engines has proved to be suspect in recent times. The received wisdom as to the mechanism of operation is that boundary lubrication pertains during the loading cycle. This view may well have delayed the application of fluid film lubrication theory in the study of the device. Modern thinking would lead to the view that some element of elastohydrodynamic lubrication must be occurring and that the mode of lubrication would be better described as ‘mixed’. The situation is reviewed and it is concluded that the use of lubrication theory as a design tool, alongside traditional tribological approaches, has much merit.

01 Jan 1991
TL;DR: In this paper, the degradation of shear strength of soils due to prolonged contamination of soils is an emerging problem and a theoretical explanation is provided for the above observations with the aid of a microscopic model for soils.
Abstract: The degradation of shear strength of soils due to prolonged contamination of soils is an emerging problem. The experiments conducted at New Jersey institute of Technology showed a gradual reduction of the unconfined compressive strength and the modulus of the contaminated soils with the increase in the amount of contamination. It was also found that the pore fluid viscosity was responsible for the degradation of the shear strength and the change in stress-strain behavior. In this paper a theoretical explanation is provided for the above observations with the aid of a microscopic model for soils. The microscopic model TRUBAL (Strack & Cundall, 1984), a computer program which was developed to model dry granular assemblies of spheres in three dimension, was modified and used in this study. To adopt the above model for this research, the computer program was first modified to accommodate the pore pressure changes. In order to model the degradation of shear strength of soils due to chemical contamination, the pore fluid in the granular assembly was replaced with fluids of different pore fluid viscosities. The influence of pore fluid viscosities on the granular assembly was modeled by introducing the theory on converging-diverging wedges in basic lubrication theory. The results show that the modified microscopic model is capable of explaining the experimental observations.

01 Jan 1991
TL;DR: In this paper, the authors used the Navier-Stokes equations to model fluid flow under a grinding wheel and compared the results with the results obtained from experiments with a smooth wheel and a one-dimensional sinusoidal roughness term.
Abstract: Fluid flow under a grinding wheel is modeled using a perturbation scheme. In this initial effort to understand the flow characteristics, we concentrate on the case of a smooth wheel with slight clearance between the wheel and workpiece. The solution at lowest order is that given by standard lubrication theory. Higher-order terms correct for inertial and two-dimensional effects. Experimental and analytical pressure profiles are compared to test the validity of the model. Lubrication theory provides good agreement with low Reynolds number flows; the perturbation scheme provides reasonable agreement with moderate Reynolds number flows but fails at high Reynolds numbers. Results from experiments demonstrate that the ignored upstream and downstream conditions significantly affect the flow characteristics, implying that only a model based on the fully two- (or three-) dimensional Navier-Stokes equations will accurately predict the flow. We make one comparison between an experiment with a grinding wheel and the model incorporating a one-dimensional sinusoidal roughness term. For this case, lubrication theory surprisingly provides good agreement with experiment.

Book ChapterDOI
TL;DR: In this article, it is shown that under periodic excitation circumferentially nonuniform clearances develop due to viscous seal material behaviour, and calculated values of film thickness and friction are in agreement with experimental data.
Abstract: In practice rotary shaft seals will experience a small-amplitude dynamic excitation. It is shown that under periodic excitation circumferentially nonuniform clearances develop due to viscous seal material behaviour. The nearby fluid will fill these gaps, so entrainment and squeeze effects can develop fluid pressures which are sufficiently high to overcome the radial preload. Viscous seal properties are essential in this type of EHD lubrication. Hence it is designated viscoelastohydrodynamic (VEHD) lubrication. At present, this lubrication concept is the only macrohydrodynamic theory that explains the existence of a consistent circumferentially nonuniform film geometry of appreciable dimensions. Moreover, calculated values of film thickness and friction are in agreement with experimental data.

Journal ArticleDOI
01 Mar 1991-Wear
TL;DR: In this article, the authors measured the lift force of a hydrodynamic sector bearing during simultaneous transverse oscillation and translation and compared it with predictions from lubrication theory for several conditions of bearing orientation and vibration amplitude and frequency.


Journal Article
TL;DR: In this article, the authors studied two idealized models of a fracture, in which the roughness follows a sinusoidal or a sawtooth variation, and concluded that the validity of the lubrication approximation requires the fracture walls to be smooth over lengths on the order of one standard deviation of the aperture.
Abstract: Lubrication theory is used to study the permeability of rough-walled rock fractures. Two idealized models of a fracture, in which the roughness follows a sinusoidal or a sawtooth variation, are studied in detail. The results are similar to those found previously from numerical analysis of fractures with random aperture distributions, in that the ratio of the hydraulic aperture depends mainly on the mean and the standard deviation of the aperture distribution. Higher-order approximations to the Navier-Stokes equations are then studied, and it is concluded that the validity of the lubrication approximation requires the fracture walls to be smooth over lengths on the order of one standard deviation of the aperture.

Journal ArticleDOI
TL;DR: In this paper, a physical model is developed to describe the phenomenon of bouncing which was observed in a previous two-body collision experiment for hydrocarbon liquid droplets, where the repulsive forces acting between the colliding droplets are caused by the intervening air flow, which is analyzed on the basis of the lubrication theory taking into account the deformation of the droplets.
Abstract: A physical model is developed to describe the phenomenon of bouncing which was observed in our previous two-body collision experiment for hydrocarbon liquid droplets. The repulsive forces acting between the colliding droplets are caused by the intervening air flow, which is analyzed on the basis of the lubrication theory taking into account the deformation of the droplets. The droplet bouncing takes place for a restricted range of the collision Weber number which depends on the droplet size and rheological properties. Its bounderies are identified in terms of the underlying elementary physics. In particular, the upper limit is proportional to the liquid viscosity, while the lower has little dependence, consistent with the experimental result.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the transient properties of a lightly loaded cylindrical slider with normal motion and found that the sliding motion as well as the normal motion are started impulsively from rest.
Abstract: The transient properties of a lightly loaded cylindrical slider with normal motion is investigated in the present paper. The sliding motion as well as the normal motion are started impulsively from rest. The method of separation of variables is used to solve for the velocity field in the unsteady momentum equation for the thin film lubrication. A pressure dependent equation in integral‐differential form is obtained through the use of mass continuity. The Coyne‐Elrod rupture model is used when cavitation occurs. The computational results show that the steady state solution after a long period of time agrees satisfactorily with that predicted using classical lubrication theory.