Showing papers on "Lubrication theory published in 2008"

Experimental validation of the tip asymptotics for a fluid-driven crack

Abstract: This paper provides experimental confirmation of the opening asymptotes that have been predicted to develop at the tip of fluid-driven cracks propagating in impermeable brittle elastic media. During propagation of such cracks, energy is dissipated not only by breaking of material bonds ahead of the tip but also by flow of viscous fluid. Theoretical analysis based on linear elastic fracture mechanics and lubrication theory predicts a complex multiscale asymptotic behavior of the opening in the tip region, which simplifies either as 1 2 or as 2 3 power law of the distance from the tip depending on whether the dominant mechanism of energy dissipation is bond breaking or viscous flow. The laboratory experiments entail the propagation of penny-shaped cracks by injection of glycerin or glucose based solutions in polymethyl methacrylate (PMMA) and glass specimens subjected to confining stresses. The full-field opening is measured from analysis of the loss of intensity as light passes through the dye-laden fluid that fills the crack. The experimental near-tip opening gives excellent agreement with theory and therefore confirms the predicted multi-scale tip asymptotics.

An axisymmetric hydrodynamic interface element for finite-element computations of mixed lubrication in rubber seals

Abstract: This paper presents an elegant way to compute hydrodynamic lubrication in machine parts, especially in highly deformable dynamic seals. In such tribologic systems, the sealing and frictional behaviour is highly related to the interaction between the hydrodynamic lubrication and the structural deformation of the seal. In this work, a hydrodynamic interface element is developed in order to achieve a strong coupling of the fluid dynamics and the deformation of the solid structure. The fluid flow is represented by the two-dimensional steady-state Reynolds equation, the structural deformation by standard finite-element procedures. This method enables the application of arbitrary, non-linear material models provided by finite-element programs. Furthermore, a model for mixed lubrication, including frictional effects, is presented.

Wetting failure and contact line dynamics in a Couette flow

Abstract: Liquid-liquid wetting failure is investigated in a two-dimensional Couette system with two immiscible fluids of arbitrary viscosity. The problem is solved exactly using a sharp interface treatment of hydrodynamics (lubrication theory) as a function of the control parameters - capillary number, viscosity ratio and separation of scale - i.e. the slip length versus the macroscopic size of the system. The transition at a critical capillary number, from a stationary to a non-stationary interface, is studied while changing the control parameters. Comparisons with similar existing analyses for other geometries, such as the Landau-Levich problem, are also carried out. A numerical method of analysis is also presented, based on diffuse interface models obtained from multiphase extensions of the lattice Boltzmann equation. Sharp interface and diffuse interface models are quantitatively compared, indicating the correct limit of applicability of the diffuse interface models.

Wetting failure and contact line dynamics in a Couette flow

Abstract: Liquid-liquid wetting failure is investigated in a two-dimensional Couette system with two immiscible fluids of arbitrary viscosity. The problem is solved exactly using a sharp interface treatment of hydrodynamics (lubrication theory) as a function of the capillary number, viscous ratio and separation of scale, i.e. slip length versus macroscopic scale of the system. The existence of critical velocities, above which no stationary solutions are found, is analyzed in detail in terms of the relevant parameters of the system. Comparisons with existing analysis for other geometries are also carried out. A numerical method of analysis is also presented, based on diffuse interface models obtained from multiphase extensions of the lattice Boltzmann equation (LBE). Sharp interface and diffuse interface models are quantitatively compared face to face indicating the correct limit of applicability of the diffuse interface models.

Squeeze Film Lubrication in Silicone Oil: Experimental Test of the No-Slip Boundary Condition at Solid−Liquid Interfaces

Abstract: The hydrodynamic force between a spherical glass particle (radius ∼ 10 μm) and a smooth, flat glass plate in Newtonian silicone oil (viscosity, η ∼ 95 mPa s) was measured using the atomic force microscopy (AFM) colloidal probe technique and was compared to Reynolds lubrication theory. When the particle and plate were coated with a hydrophobic silane, the measured forces were consistent with Reynolds lubrication theory without the need to introduce the concept of a slip length. When the particle was hydrophilic, the results were more variable, sometimes being consistent with the no-slip boundary condition and sometimes being better fitted by invoking a constant slip length (up to 33 nm). The hydrophilic system was not well characterized because the hydrophilic solid may have entrained or attracted a layer of water (η = 0.001 Pa s) of unknown thickness, which would lubricate the flow and explain the apparent slip length. In addition, all AFM force measurements suffer from the problem that the solids occasio...

Application of Lubrication Theory to Near-Dry Green Grinding – Feasibility Analysis

Abstract: This paper describes an investigation about the grinding fluid optimization supply based on lubrication theory. The models for three-dimensional hydrodynamic flow pressure in contact zone between wheel and work are presented based on Navier-Stokes equation and continuous formulae. It is well known that hydrodynamic fluid pressure generates due to this fluid flux, and that it affects overall grinding resistance and machining accuracy. Moreover, conventional methods of delivering grinding fluid, i.e. flood delivery via a shoe or jet delivery tangential to the wheel via a nozzle, have been proved that they can not fully penetrate this boundary layer and thus, the majority of the cutting fluid is deflected away from the grinding zone. Therefore, in this paper, a new delivery method of grinding fluid, the minimum quantity lubricant (MQL)-near-dry green grinding is presented and analyzed for it not only reduces hydrodynamic lift force but also reduces grinding fluid cost to achieve green manufacturing. Experiments have been carried out to validate the performance of the MQL supply compared with conventional flood cooling. The experimental results have shown that the theoretical model is in agreement with experimental results and the model can well forecast hydrodynamic pressure distribution at contact zone between and workpiece and the MQL supply in grinding is feasible. Experiments have also been carried out to evaluate the performance of the MQL technology compared with conventional flood cooling. Experimental data indicate that the proposed method does not negatively affect to the surface integrity and the process validity has been verified.

Electroosmotic flow and particle transport in micro/nano nozzles and diffusers.

Abstract: Micro/nano nozzles and diffusers have been used for ionic transport, drug and gene delivery. In this paper, a mathematical model is developed to simulate the electroosmotic flow (EOF) and particle transport in micro/nano nozzles/diffusers. The electrical potential and the flow field are investigated using the lubrication and the Debye–Huckel approximations specially for nanonozzles (overlapped electric double layers) and microdiffusers (thin EDLs) for which experimental results exist. The results show that a pressure field is induced by the presence of EDLs and the magnitude of this induced pressure is proportional to the ratio of the Debye length to the channel half-height. Embedded particles are often employed to illustrate the flow field and thus measure the local fluid velocity. The direction of particle motion is found to be dependent primarily on the particle charge and the wall charge. The calculated particle velocities compare well with experimental data.

Influence of Multiscale Roughness Patterns in Cavitated Flows: Applications to Journal Bearings

Abstract: This paper deals with the coupling of two major problems in lubrication theory: cavitation phenomena and roughness of the surfaces in relative motion. Cavitation is defined as the rupture of the continuous film due to the formation of air bubbles, leading to the presence of a liquid-gas mixture. For this, the Elrod-Adams model (which is a pressure-saturation model) is classically used to describe the behavior of a cavitated thin film flow. In addition, in practical situations, the surfaces of the devices are rough, due to manufacturing processes which induce defaults. Thus, we study the behavior of the solution, when highly oscillating roughness effects on the rigid surfaces occur. In particular, we deal with the reiterated homogenization of this Elrod-Adams problem, using periodic unfolding methods. A numerical simulation illustrates the behavior of the solution. Although the pressure tends to a smooth one, the saturation oscillations are not damped. This does not prevent us from defining an equivalent homogenized saturation and highlights the anisotropic effects on the saturation function in cavitated areas.

Coarsening of unstable thin films subject to gravity.

Abstract: Thin films of viscous fluids coating hydrophobic substrates are unstable to dewetting instabilities, and long-time evolution leads to the formation of an array of near-equilibrium droplets connected by ultrathin fluid layers. In the absence of gravity, previous use of lubrication theory has shown that coarsening dynamics will ensue-the system will evolve by successively eliminating small drops to yield fewer larger drops. While gravity has only a weak influence on the initial thin film, we show that it has a significant influence on the later stages of the coarsening dynamics, dramatically slowing the rate of coarsening for large drops. Small drops are relatively unaffected, but as coarsening progresses, these aggregate into larger drops whose shape and dynamics are dominated by gravity. The change in the mean drop shape causes a corresponding gradual transition from power-law coarsening to a logarithmic behavior.

Wetting failure and contact line dynamics in a Couette flow

Abstract: Liquid–liquid wetting failure is investigated in a two-dimensional Couette system with two immiscible fluids of arbitrary viscosity. The problem is solved exactly using a sharp interface treatment of hydrodynamics (lubrication theory) as a function of the control parameters – capillary number, viscosity ratio and separation of scale – i.e. the slip length versus the macroscopic size of the system. The transition at a critical capillary number, from a stationary to a non-stationary interface, is studied while changing the control parameters. Comparisons with similar existing analyses for other geometries, such as the Landau–Levich problem, are also carried out. A numerical method of analysis is also presented, based on diffuse interface models obtained from multiphase extensions of the lattice Boltzmann equation. Sharp interface and diffuse interface models are quantitatively compared, indicating the correct limit of applicability of the diffuse interface models.

Effect of small particles on the near-wall dynamics of a large particle in a highly bidisperse colloidal solution.

Abstract: We consider the hydrodynamic effect of small particles on the dynamics of a much larger particle moving normal to a planar wall in a highly bidisperse dilute colloidal suspension of spheres. The gap h0 between the large particle and the wall is assumed to be comparable to the diameter 2a of the smaller particles so there is a length-scale separation between the gap width h0 and the radius of the large particle b⪢h0. We use this length-scale separation to develop a new lubrication theory which takes into account the presence of the smaller particles in the space between the larger particle and the wall. The hydrodynamic effect of the small particles on the motion of the large particle is characterized by the short time (or high frequency) resistance coefficient. We find that for small particle-wall separations h0, the resistance coefficient tends to the asymptotic value corresponding to the large particle moving in a clear suspending fluid. For h0⪢a, the resistance coefficient approaches the lubrication va...

Transition of frictional states and surface roughness effects in lubricated contacts

Abstract: In order to investigate frictional performances in different lubrication regimes and effects of surface roughness, the friction on engineering surfaces with different roughness patterns and amplitudes were measured. Results show a smooth transition of lubrication states from full-film hydrodynamic lubrication to mixed and boundary lubrication. Data from the tests also suggest that the transition of friction regimes is affected by roughness amplitude. It is observed that not only the smoother surfaces give rise to the lower critical velocities of transition from full-film to mixed lubrication, but also the friction coefficients at the point of the transition are much smaller for the smoother surfaces. For the transition from mixed to boundary lubrication, however, effects of roughness amplitude are insignificant. As a result, it is concluded that under the same contact conditions, different features in roughness cause the system to transit in different routines from one lubrication regime to another. Furth...

Lubrication analysis of the viscous micro/nano pump with slip

Abstract: A viscous pump is a device such that a cylindrical rotor is eccentrically placed in a channel, so that the viscous resistance between the small and large gaps between the cylinder and the channel walls generate a net flow along the channel. Assuming that the gaps between the cylinder and the channel walls are small compared to the radius of the rotor, the hydrodynamic theory of lubrication may be utilized to study the viscous pump. Here lubrication theory is used to obtain an analytical solution which relates the flowrate, rotation rate, pressure drop and applied torque as functions of two geometric parameters for a viscous pump. This analysis differs from a previous similar study in two ways. Firstly, certain integrals are evaluated explicitly, and secondly the standard no-slip boundary condition of fluid mechanics has been replaced with the Navier boundary condition which allows a degree of tangential velocity slip on all solid boundaries. Comparison with the prior known solution shows that the solution obtained in this study predicts a slightly improved pump performance for the case of no-slip. For the case of slip, our results demonstrate that the performance of the pump is significantly improved.

Lubrication approximation for micro-particles moving along parallel walls

Abstract: Lubrication expressions for the friction coefficients of a spherical particle moving in a fluid between and along two parallel solid walls are explicitly evaluated in the low-Reynolds-number regime. They are used to determine lubrication expression for the particle free motion under an ambient Poiseuille flow. The range of validity and the accuracy of the lubrication approximation is determined by comparing with the corresponding results of the accurate multipole procedure. The results are applicable for thin, wide and long microchannels, or quasi-two-dimensional systems.

Effects of electrokinetic slip flow on lubrication theory

Abstract: A lubrication theory that includes the coupled effects of electric double layer (EDL) and boundary slip is developed. The consideration of EDL (electro-viscous effect) and boundary slip near the solid surface increases and decreases apparent viscosity, respectively. Both effects are important for flow within microscales and lubrication problems. Under the usual assumptions of lubrication and Debye—Huckel approximation for low surface potential, the Navier—Stokes equation with body force due to the electrical potential, as well as the Navier slip boundary conditions, is utilized to derive the velocity distributions, apparent viscosity, and modified Reynolds equation. The apparent viscosity is expressed explicitly as functions of the Debye length, the electro-viscosity, and the slip length. The coupled effects of EDL and boundary slip on the apparent viscosity and one-dimensional slider-bearing performance are analysed and discussed. Results show that the load capacity increases as a decrease in inverse Deb...

Studies on tribology

Abstract: In high speed rotating machines such as turbines and generators, vibrations of a rotating shaft often hinder the smooth operation of the machine or even cause failure. Oil whip is one of such vibrations due to oil film action of journal bearing. Its mechanism and preventive method is explained and proposed in this paper. Further theoretical and experimental analyses are made for considering heat generation and temperature rise in hydrodynamic lubrication. The usefulness of the lubrication theory based on the k–e model is also shown for bearings with high eccentricity ratios. In the latter half of this paper, water lubrication, nitrogen gas lubrication and tribo-coated indium lubrication are shown as new promising methods, and their mechanisms are discussed and the importance of tribo-layer is explained. Some mechanisms of wear are introduced for better understanding of tribo-layer. In the last part of this paper, the mechanisms of generating static friction are shown for the cases of plastic contact and elastic contact, which is the base for understanding the mechanism of initiation of macroscopic sliding.(Communicated by Hidesato ITO , M.J.A.)

A Potential Elastohydrodynamic Origin of Load-Support and Coulomb-Like Friction in Lung∕Chest Wall Lubrication

Abstract: BACKGROUND: During normal breathing, the mesothelial surfaces of the lung and chest wall slide relative to one another Experimentally, the shear stresses induced by such reciprocal sliding motion are very small, consistent with hydrodynamic lubrication, and relatively insensitive to sliding velocity, similar to Coulomb-type dry friction Here we explore the possibility that shear-induced deformation of surface roughness in such tissues could result in bidirectional load supporting behavior, in the absence of solid-solid contact, with shear stresses relatively insensitive to sliding velocity METHOD OF APPROACH: We consider a lubrication problem with elastic blocks (including the rigid limit) over a planar surface sliding with velocity U , where the normal force is fixed (hence the channel thickness is a dependent variable) One block shape is continuous piecewise linear (V block), the other continuous piecewise smoothly quadratic (Q block) The undeformed elastic blocks are spatially symmetric; their elastic deformation is simplified by taking it to be affine, with the degree of shape asymmetry linearly increasing with shear stress RESULTS: We find that the V block exhibits nonzero Coulomb-type starting friction in both the rigid and elastic case, and that the smooth Q block exhibits approximate Coulomb friction in the sense that the rate of change of shear force with U is unbounded as U → 0 ; shear force ∝U(1/ 2) in the rigid asymmetric case and ∝U(1/ 3) in the (symmetric when undeformed) elastic case Shear-induced deformation of the elastic blocks results in load supporting behavior for both directions of sliding CONCLUSIONS: This mechanism could explain load-supporting behavior of deformable surfaces that are symmetrical when undeformed, and may be the source of the weak velocity dependence of friction seen in the sliding of lubricated, but rough, surfaces of elastic media such as the visceral and parietal pleural surfaces of the lung and chest wall

Ultrasonic measurement of rolling element bearing lubrication using piezoelectric thin film transducers

Abstract: This paper describes the measurement of lubricant layer thickness using ultrasound. High frequency (20–200 MHz) ultrasound is excited using a piezoelectric AlN film deposited onto the outer raceway of a rolling element bearing. This sensor allows the interrogation of the small lubricated region between the ball and raceway. The reflection coefficient from the lubricant layer is then measured and the layer thickness extracted via a quasi‐static spring model. Good agreement is shown with known lubrication theory.

Electrohydrostatically driven flow and instability in a vertical hele-shaw cell.

Abstract: The electrohydrostatic capillary-driven flow of a viscous poorly conducting Newtonian fluid rising between conducting parallel plates is studied both theoretically and experimentally. By scaling the problem with a pressure and time derived by considering Maxwell stresses along the interface, it is determined that the dimensionless parameters governing the flow are the hydrostatic bond (Bo(H)), electrostatic bond (Bo(E)) and electrostatic Reynolds (Re(E)) numbers. A lubrication theory analysis, in the limit Re(E) --> 0, of the momentum balance leads to an analytical solution for the elapsed time versus interface position that is analogous to one derived by Washburn (1921) for the capillary pressure-driven flow of a fluid in cylindrical capillaries (Washburn, E. W. Phys. Rev. 1921, 17 (3), 273-283). Experiments are performed using silicone and castor oil at gap spacing less than the capillary length for two ranges of electrostatic Reynolds numbers 0.001 1), a convective instability is observed in plots of the interface position as a function of time. The propagating front also reveals an interfacial instability for large electrostatic Reynolds numbers coupled with large fluid displacements. The theory and experiments for the static rise height show good agreement with theory while the flow dynamics show good qualitative agreement in the applicable limits at low electrostatic Reynolds numbers.

Galerkin method for feedback controlled Rayleigh–Bénard convection*

Abstract: The problem of feedback controlled Rayleigh–Benard convection is considered. For this problem with the simple flow structure in the vertical direction, a Galerkin method that uses only a few basis functions in this direction is presented. This approximation yields considerable simplification of the problem, explicitly incorporates the non-classical boundary conditions at the horizontal boundaries of the fluid layer resulting from feedback control and reduces the dimension of the original problem by one. This method is in spirit very similar to lubrication theory, where the simple laminar flow in the vertical direction is integrated out across the height of the fluid layer.Using a minimal set of appropriate basis functions to capture the nonlinear behaviour of the flow, we investigate the effects of feedback control on amplitude, wavelength and selection of patterns via weakly nonlinear analysis and numerical simulations of the resulting dimension-reduced problems in two and three dimensions.In the second part of this study we discuss the derivation of the appropriate basis functions and prove convergence of the Galerkin scheme.

Spreading of thin liquid droplets on rotating disks

Abstract: In many industrial processes solids are coated to obtain specific surface properties, as e.g. corrosion resistance, mechanical, optical, or electrical properties. Even today many of such coating processes are not fully understood and the choice of parameters is mainly based on experience. Hence, a prediction of the complete hydrodynamic process in its dependency on the parameters appears highly desirable. This would e.g. allow for a precise prediction of the (liquid) layer thickness and shape and help to optimize the quality of the coating. A common coating technique is the so–called spin coating. The coating agent is dissolved or suspended in a liquid, brought onto the solid, spread by rotation, and the carrier liquid is finally removed by evaporation or by chemical reactions. In this article an evolution equation is derived from lubrication theory, valid for thin liquid layers. The model involves a dynamic contact angle, centrifugal, capillary, gravitational, and molecular (London–van–der–Waals) forces. The evolution equation without molecular forces can even be solved analytically, provided the capillary number is small. Otherwise a numerical integration of the governing equations is engaged. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Characteristics of Multistage Viscous Micropumps Using Cylindrical Rotors

Abstract: The present paper describes the flow fields and pressure characteristics for viscous micropumps with 2 through 5 cylindrical rotors, respectively, in a rectangular duct. The experiment, the numerical simulation and the theoretical analysis are performed. In the experiments, centimeter-scale (not micrometer-scale) pump models are used and the low Reynolds number corresponding to micrometer-scale flow is realized by using glycerin as working fluid. In the numerical simulations, the commercial software, STAR-CD, is used. With respect to the flow fields and the performances, qualitative agreements between experimental and numerical results are obtained. In the theoretical analysis, the 2D lubrication theory is adopted and a new pressure performance formula is proposed. The performance curves derived from the formula show qualitatively and quantitatively good agreements with the numerical ones.

二重円筒流れを用いた新型粘性マイクロポンプの圧力特性に関する理論的，実験的，数値的研究

Abstract: In the present paper, a new viscous micropump using double-circular flows is proposed. Its pressure characteristics are investigated by using a theoretical analysis, a model experiment and a numerical simulation. In the theoretical analysis, the two-dimensional lubrication theory for a journal bearing with infinite length is adopted. In the model experiment, the low Reynolds number flow in practical micropumps is realized by using glycerin as working fluid, and a centimeter-scale (not micrometer-scale) model pump is examined. In the numerical simulation, the SIMPLE method is used to obtain steady-state solutions. With respect to the pressure characteristics, the theoretical results show good agreements with the experimental and the numerical ones quantitatively. The pressure at zero flow rate obtained is quite larger than that of an existing viscous micropump.