Lubrication Approach Research Articles

Microelastohydrodynamics of Swimming Organisms Near Solid Boundaries in Complex Fluids

Microorganisms such as sperm routinely swim close to solid boundaries and within non-Newtonian fluids. In this paper, we exploit the lubrication approximation to model the motion of a flexible sheet near a rigid wall and immersed in a complex fluid. This allows us to specify an internally generated force density on the sheet and allow its shape and velocity to be determined by the interplay between the forcing and the fluid motion. We obtain results for Newtonian and complex fluids, focusing specifically on the influence of shear thinning/thickening and of yield stress. In the latter case, we characterise the threshold forcing that is required for successful swimming to occur. Our results highlight the usefulness of the lubrication approach in modelling micro-scale fluid-structure interactions.

Peristaltic flow of a Jeffrey fluid in a rectangular duct

In the present investigation we have studied the peristaltic flow of a Jeffrey fluid in a rectangular duct. The flow is investigated in a wave frame of reference moving with the velocity c away from the fixed frame. The peristaltic waves propagating on the horizontal sidewalls of a rectangular duct is studied under lubrication approach. The exact solutions of velocity and pressure gradient have been found under lubrication approach. The pumping characteristics, axial pressure gradient, velocity field and trapping phenomena have been discussed to highlight the physical features of emerging parameters of the Jeffrey fluid. The comparison is also made with the existing literature.

Attraction between two similar particles in an electrolyte: effects of Stern layer absorption

When Debye length is comparable or larger than the distance between two identical particles, the overlapping among the particles double-layers can play an important role in their interactions. This paper presents a theoretical analysis of the interaction among two identical particles with overlapped double-layers. We particularly focus on the effect of a Stern electro static condition from linearization of the adsorption isotherm near the isoelectric (neutrality) point in order to capture how polyvalent ion condensation affect sand reverses the surface charge. The stationary potential problem is solved within the framework of an asymptotic lubrication approach for a mean-field Poisson-Boltzmann model. Both spherical and cylindrical particles are analyzed. The results are finally discussed in the context of Debye-Hückel (D-H) limit and beyond it.

Influence of inclined magnetic field on peristaltic flow of a Williamson fluid model in an inclined symmetric or asymmetric channel

In this paper the influence of inclined magnetic field on the peristaltic flow of a Williamson fluid in an inclined symmetric or asymmetric channel has been investigated initially in the wave frame of reference. The highly nonlinear equations are simplified under lubrication approach. The analytical and numerical solutions of the proposed problem have been computed and analyzed. The graphical results are displayed to see the effects of various physical parameters of interest.

Application of the Amplitude Reduction Technique Within Probabilistic Rough EHL Models

Over the years, the deterministic elastohydrodynamic lubrication (EHL) approach has been widely used. This technique is very powerful in capturing details of asperity deformation and interaction. The probabilistic EHL methodology is still used when the main interest of the engineer is directed toward computations of bulk properties. During recent years, the results of many deterministic analyses have been published. The reduction of the waviness amplitude in EHL contacts under rolling-sliding was systematically studied and it was shown that the amplitude reduction is completely described by a single parameter that includes relative wavelength and the operating conditions. This approach, usually referred to as the amplitude reduction technique, has opened the way for developing improved probabilistic EHL models by incorporating the effects of fluid-induced roughness deformation, which is calculated using the fast fourier transform. In this paper we provide a review of the latest developments in the amplitude reduction technique and we present a probabilistic EHL algorithm for the computation of the load supported by the fluid, the elastically deformed asperities and the plastically deformed asperities, in a mixed EHL contact with either isotropic on nonisotropic roughness. The fluid-induced roughness deformation is incorporated into the probabilistic model via the use of the amplitude reduction technique.

Droplet migration: Quantitative comparisons with experiment

An important practical feature of simulating droplet migration computationally, using the lubrication approach coupled to a disjoining pressure term, is the need to specify the thickness, H*, of a thin energetically stable wetting layer, or precursor film, over the entire substrate. The necessity that H* be small in order to improve the accuracy of predicted droplet migration speeds, allied to the need for mesh resolution of the same order as H* near wetting lines, increases the computational demands significantly. To date no systematic investigation of these requirements on the quantitative agreement between prediction and experimental observation has been reported. Accordingly, this paper combines highly efficient Multigrid methods for solving the associated lubrication equations with a parallel computing framework, to explore the effect of H* and mesh resolution. The solutions generated are compared with recent experimentally determined migration speeds for droplet flows down an inclined plane.

Particles Driven Up the Wall by Bursting Bubbles

The phenomenon of particles being "driven up the wall" of a vessel by bursting bubbles at an air-water interface covered with hydrophobic nanoparticles is reported. Experiments have shown that the bubbles bursting at the interface give rise to the local surface pressure gradient, which pushes the particles to climb and coat the walls of the vessel. A theoretical model based on the lubrication approach to estimate the height and speed at which the particle layers climb up the walls yields values that are in fair agreement with the experimental measurements. The effects of the liquid viscosity, electrolyte strength, and particle wettability are also examined.

Peristaltic Flow of a Two-Layer System in a Poroflexible Tube

Peristaltic transport in an axisymmetric tube, with a layer of porous material in the peripheral region and a Newtonian fluid in the core region, is investigated under the lubrication approach. The wall of the tube is considered to be poroflexible, and a slip boundary condition of Saffman type is used. The fluid flow is studied in a wave frame of reference moving with constant velocity c of the peristaltic wave propagating on the wall of the tube. The interface is determined as a part of the solution using the conservation of mass in both regions of the porous medium and fluid medium separately. A shear stress jump condition is used at the interface between the peripheral and core regions. Pumping characteristics, trapping, and reflux phenomena are discussed for various parameters of interest governing the flow like wall slip constant kk and an increase in Β. Copyright © 2007 Begell House, Inc.

Formation and mobility of droplets on composite layered substrates

A mesoscale fluid film placed on a solid support may break up and form droplets. In addition, droplets may exhibit spontaneous translation by modifying the wetting properties of the substrate, resulting in asymmetry in the contact angles. We examine mechanisms for droplet formation and motion on uniform and terraced landscapes, i.e., composite substrates. The fluid film stability, droplet formation and velocity are studied theoretically in the isothermal case using a lubrication approach in one spatial dimension. The droplet properties are found to involve contributions from both the terraced layer thickness and molecular interactions via the disjoining potential.

On a Particle-Augmented Mixed Lubrication Approach to Predicting CMP

ABSTRACTChemical mechanical polishing (CMP) is a process commonly used to planarize or polish thin film surfaces to enable stacking of additional levels to enhance lithographic patterning of wafers. It is used to make surfaces atomically smooth and is also an interim step in integrated circuit (IC) manufacturing. CMP is an example of a tribological regime called Particle-Augmented Mixed Lubrication (PAML) as named by the authors. PAML occurs when two surfaces in relative motion under load are partially separated by an intervening fluid-particle mixture. The load is supported by both asperities and fluid, and the interface is further complicated by the addition of nanoparticles. PAML involves four core components that must be modeled integrally—fluid mechanics, particle dynamics, contact mechanics, and material removal (wear). This work introduces the fundamental tenets of PAML, and describes how it is an effective first principle multi-physics approach to modeling CMP. By inputting the artificial random topographies for the pad and wafer with their actual mechanical properties, the PAML modeling simulation results predict the instantaneous material removal as the wear volume caused by particle-induced wear. These discrete instantaneous material removal events lead to the cumulative wear seen during CMP over a short time. Although only a small fraction of the time of the actual CMP process, tests of 120μs show that the cumulative material removal occurring over the entire simulation is approximately 0.012μm3. This work suggests that a generalized multi-physics modeling simulation of the CMP process is plausible.

Dynamic stretching of a planar liquid bridge

A thin incompressible viscous planar free liquid film in a void and under zero gravity is analyzed by means of a reduced-dimension (lubrication) approach. Linear analysis focuses on films with harmonic modulations in the axial film velocity enforced at the ends of the planar bridge. Effects of changes in the problem parameters on the overall distortion characteristics of the film are discussed. Nonlinear film distortion and break-up are investigated for the case of temporally increasing velocity at the end of the film resulting in continuous film stretching eventually leading to film rupture. Implementation of the employed numerical model is validated for the linear limit by comparison with the analytical linear solutions and for harmonically modulated film-end velocities. Within the nonlinear analysis of the continuously stretched film bridge, several distinct film topologies are identified depending on liquid Weber number and Reynolds number, i.e., the magnitude of the stretching rate (end velocity) compared to signal propagation rates through the liquid via capillary waves and viscous action. That is, the Weber number is the square of the ratio of stretching rate to capillary wave velocity while the Reynolds number is the ratio of stretching rate to the characteristic viscous velocity. Here, film topology is typically characterized by three distinct regions, i.e., a film wedge forming at the pulling end(s), the film center region and a transition region. The size and shape of these regions greatly depend on the particular case under investigation. Film distortion characteristics observed for continuously compressed planar films conform with observations made by other authors for the similar case of contracting free liquid films.

New condensation-type monomer combinations as ashless antiwear compositions

Environmentally acceptable antiwear additives should preferably not contain more elements than carbon, hydrogen, oxygen, nitrogen; compounds composed of these elements can be selected or designed to be biodegradable. Most recently, lactam compounds were found to be very effective antiwear additives towards ceramic materials as well as metals. Lactam compounds are referred to as cycloamides. This paper aims at (i) describing compounds of a new antiwear additive group of lactams; particular emphasis is on caprolactam, the monomer used to synthesize Nylon 6; (ii) demonstrating the large synergistic antiwear effect observed when caprolactam is mixed with another condensation-type monomer, i.e. C 36 dimer acid/glycol monoester; and (iii) showing one example of possible practical applications of such mixtures as specific running-in lubricants. Tribological tests carried out on a high-speed/high-load pin-on-disk machine demonstrated that caprolactam is an extremely effective antiwear additive for alumina-on-alumina as well as steel-on-steel systems. Similar antiwear effectiveness was also achieved for higher molecular weight cycloamides, e.g. laurolactam. Compositions of the monoester and caprolactam were tested using the T-11 pin-on-disk tester developed by the Institute for Terotechnology in Radom, Poland. This apparatus allows one to run tests at elevated temperatures up to around 300°C. It also continuously records the coefficient of friction and linear displacement due to wear. Combinations of the monoester and caprolactam showed a striking synergistic antiwear effect and reduced friction coefficient. A new small engine running-in lubrication approach is also described. This approach not only provides excellent and most impressive running-in performance but also results in substantial economic savings in labor and materials.

Transverse squeeze flow of concentrated aligned fibers in viscous fluids

This paper examines the effect that aligned long fiber reinforcement has on the processing characteristics of thermoplastic composites. More specifically, the influence of fiber volume fraction on the transverse shear viscosity of unidirectional composites is explored. Through both experimental evaluation and theoretical modeling, the study focuses on the flow behavior of a model material consisting of unidirectional nylon or glass fibers algned in a clay matrix. The flow behavior of a commercially produced material (APC-2) composed of unidirectional carbon fibers aligned in a thermoplastic polyether ether ketone (PEEK) matrix is also examined. An experimental technique has been employed that characterizes both the bulk transverse shearing viscosity and the fluid mechanics of such highly filled fiber-resin systems in squeeze flow. Squeeze flow experiments were performed for the model material containing various fiber volume fractions and, with specially designed hot platens, for the carbon fiber-PEEK composites. Flow visualization techniques have been developed to measure the velocity profile of the material during flow. A cell model is proposed to calculate the effect of fiber volume fraction on the transverse shear viscosity of aligned fiber composites and, hence, the squeeze force requirements of such materials. The cell model, which calculates individual fiber interactions based on the lubrication approach with a viscous Newtonian or Carreau fluid, demonstrates the effects of varying the fiber volume fraction, fiber diameter and the shear thinning nature of the matrix fluid on the force requirement under constant squeeze rates. Comparisons are made between the experimenttally measured squeeze force and the cell model predictions. Good agreement is found at high fiber volume fractions as the lubrication flow assumptions become more accurate.

Inertia Effects in a Hybrid Bearing With a 45 Degree Entrance Region

An investigation is presented that illustrates the effects of inertia on the flow and pressure field throughout a hybrid hearing with a 45 degree entrance region. This type of bearing has been previously shown to offer better performance over the hybrid bearing with a normal entry region. A two-dimensional planar approach is adopted and the resulting flow governing equations are solved using the Galerkin Weighted Residual finite element method. This algorithm incorporates an advanced streamline upwinding method to evaluate the nonlinear effects of the convection terms. The results demonstrate the complex nature of the velocity field and its subsequent impact on the pressure field. This comprehensive parametric study also shows why traditional lubrication approaches that typically exclude convection effects will become unreliable at high operating speeds of turbomachinery. A set of loss coefficients modeling the pressure ‘ram’ effects are provided to illustrate the inertia effects in the entrance region of the film lands. In a hybrid bearing, these effects have to be characterized according to the operating parameters of the bearing and the journal direction of rotation.

A unified lubrication approach for the design of a coat‐hanger die

AbstractA simple unified lubrication approach has been proposed to design a coat‐hanger die that can deliver wide and uniform liquid sheets. This approach requires that the wall stress in the manifold be constant. With this constraint, any inelastic non‐Newtonian fluid model can be used to describe the liquid motion inside the die. Fluid models that can represent the pseudoplastic or viscoplastic behavior of polymeric liquids have been selected for illustration. A general equation that can be solved to determine the effect of production variations on flow uniformity inside the die has also been derived.

Flow of generalized Newtonian fluids across a periodic array of cylinders

Traditionally, the capillary model has been used to describe the permeability–porosity relationship for porous media. Although this approach works reasonably well in flow through granular media, it fails to model the flow across aligned fibrous media, due to its inherent assumptions. A more realistic approach is chosen, using flow across regular arrays of cylinders. A closed form solution is developed by matching the analytic solution using the lubrication approach for low porosities and the analytic cell model solution for high porosities. This closed form solution is extended to generalized Newtonian fluids by linearizing the cell model solution about the Newtonian point, and extending the lubrication approach to power‐law fluids. The results of the closed form solutions agree well with the numerical solution obtained by solving the Stokes equations in square and hexagonal arrangements of cylinders for Newtonian and mildly shear‐thinning fluids. A scaling is suggested which allows one to separate the effect of the fluid rheology and the porosity on the resistance to flow.

Higher-order corrections to the axisymmetric interactions of nearly touching spheres

Two unequal spheres are immersed in an axisymmetric low-Reynolds-number flow and are separated by a small nondimensional distance ε. The forces and stresslets exerted by the spheres on the fluid are calculated asymptotically to O(ε ln ε), in order to improve the convergence of numerical calculations of the same quantities. The main obstacle to the extension to O(ε ln ε) was the breakdown of the usual lubrication approach at higher orders in ε. The method adopted here obtains expressions for the functions of immediate interest, but does so by postponing the resolution of the fundamental difficulties until a higher order in ε.

On Stokes flow of a Newtonian fluid through a pipe with stationary random surface roughness

The problems of Stokes’ flow through corrugated pipes are considered. The corrugations are of small amplitude e and are modeled by stationary random noises. A perturbation solution [up to O(e2)] is developed showing that the pressure drop enhancement is an order O(e2) effect and is always positive. Furthermore, for slowly varying corrugations, the pressure drop enhancement depends on the statistics of the corrugations em(z) only through its mean square e2<m2≳ and can be predicted by the simpler lubrication approach.