Lubrication Approach Research Articles

Peristaltic Motion of a non-Newtonian Nanofluid in an Asymmetric Channel

The peristaltic transport of a Carreau-Yasuda fluid in an asymmetric channel is studied. Problem formulation is given in the presence of nanoparticles and contributions of Brownian motion and thermophoresis are taken into account. Lubrication approach is employed. The resulting nonlinear system of equations is solved numerically, and the effects of sundry parameters on the velocity, temperature, and concentration are analyzed. Heat and mass transfer rates are computed and examined. The results show that the impact of the non-Newtonian parameters on flow quantities get reversed when we move from shear thinning to shear thickening fluids. The temperature of the nanofluid in presence of Brownian motion increases, furthermore the influence of Brownian motion parameter on temperature and concentration distributions is opposite

Quantitative characterization of solid lubricant transfer film quality

Solid lubricant materials have become necessary in applications for which traditional lubrication approaches become impractical. These materials are often mated against a harder metallic counter surface (counterface) of higher surface energy. During sliding, wear fragments from the solid lubricant transfer to the counterface to form a protective barrier known as the transfer film. Historically, the coverage attributes of these transfer films have correlated strongly to the tribological performance of the solid lubricant. Although transfer film quality is often identified as a critical contributor to the success of a candidate solid lubricant, the community lacks a quantitative means to measure quality. Transfer film cohesion and adhesion are likely very important but they are also difficult to measure and not necessarily related to the visual features that have motivated the use of adjectives like ‘quality’, ‘thin’, ‘uniform’, and ‘tenacious’. Area fraction and film thickness are more easily quantified, but to date, they have not proven to be robust predictors of tribological success. A recent visual study of transfer film evolution for a successful alumina–PTFE nanocomposite suggests that the characteristic size of domains of exposed counterface may correlate more closely with wear performance. This paper presents a method for quantifying transfer film quality based on this metric, which we call the free-space length (Lf). To illustrate the application of the method, we study the connection between the wear rate and free-space length for the transfer film of a well-studied alumina–PTFE system. The correlation to wear was best for the free-space length and worst for area fraction.

Influence of Lateral Walls on Peristaltic Flow of a Couple Stress Fluid in a Non-Uniform Rectangular Duct

In the present investigation we have studied the peristaltic flow of a couple str ess fluid in a non-uniform 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 side walls of a non-uniform 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 couple stress fluid.

An extended Bretherton model for long Taylor bubbles at moderate capillary numbers

When (long) bubbles are transported in tubes containing a fluid, the presence of a thin film of fluid along the tube walls causes the velocity of the bubble to be different from the average fluid velocity. Bretherton [“The motion of long bubbles in tubes,” J. Fluid Mech. 10, 166 (1961)] derived a model to describe this phenomenon for pressure driven flows based on a lubrication approach coupled with surface deformation of the bubble. Bretherton found that the parameter governing the physics involved is the capillary number (Ca) which expresses the relationship between speed of the bubble, surface tension, and viscosity of the liquid. The results of Bretherton are here re-derived and analyzed in a slightly more perspicuous manner. Incorporating the condition that the bubble-film combination should fit inside the tube results in an expression very similar to the one found empirically by Aussillous and Quéré [“Quick deposition of a fluid on the wall of a tube,” Phys. Fluids 12, 2367 (2000)] of the Taylor [“Deposition of a viscous fluid on the wall of a tube,” J. Fluid Mech. 10, 161 (1961)] experimental data. Our expression is valid for Ca values up to Ca = 2.0, but approaches Bretherton's result for low values of Ca. The analysis is done in terms of the pressure buildup which originates from the interplay between surface tension and lubrication due to the thin layer of fluid near the tube wall.

Consequence of nanofluid on peristaltic transport of a hyperbolic tangent fluid model in the occurrence of apt (tending) magnetic field

In the current study, sway of nanofluid on peristaltic transport of a hyperbolic tangent fluid model in the incidence of tending magnetic field has been argued. The governing equations of a nanofluid are first modeled and then simplified under lubrication approach. The coupled nonlinear equations of temperature and nano particle volume fraction are solved analytically using a homotopy perturbation technique. The analytical solution of the stream function and pressure gradient are carried out using perturbation technique. The graphical results of the problem under discussion are also being brought under consideration to see the behavior of various physical parameters.

Effect of Slip on Peristaltic Flow of Powell-Eyring Fluid in a Symmetric Channel

Peristaltic flow of non-Newtonian fluid in a symmetric channel with partial slip effect is examined. The non-Newtonian behavior of fluid is characterized by the constitutive equations of Powell-Eyring fluid. The motion is induced by a sinusoidal wave traveling along the flexible walls of channel. The flow is analyzed in a wave frame of reference moving with the velocity of wave. The equations governing the flow are solved by adopting lubrication approach. Series solutions for the stream function and axial pressure gradient are obtained. Impact of slip and other emerging flow parameters is plotted and analyzed graphically.

Effect of Slip on Peristaltic Flow of Powell-Eyring Fluid in a Symmetric Channel

Peristaltic flow of non-Newtonian fluid in a symmetric channel with partial slip effect is examined. The non-Newtonian behavior of fluid is characterized by the constitutive equations of Powell-Eyring fluid. The motion is induced by a sinusoidal wave traveling along the flexible walls of channel. The flow is analyzed in a wave frame of reference moving with the velocity of wave. The equations governing the flow are solved by adopting lubrication approach. Series solutions for the stream function and axial pressure gradient are obtained. Impact of slip and other emerging flow parameters is plotted and analyzed graphically.

On the mathematical paradoxes for the flow of a viscoplastic film down an inclined surface

In this paper we consider the motion of thin visco-plastic Bingham layer over an inclined surface whose profile is not flat. We assume that the ratio between the thickness and the length of the layer is small, so that the lubrication approach is suitable. Under specific hypotheses (e.g. creeping flow) we analyze two cases: finite tilt angle and small tilt angle. In both cases we prove that the physical model generates two mathematical problems which do not admit non-trivial solutions. We show that, though the relevant physical quantities (e.g. stress, velocity, shear rate, etc.) are well defined and bounded, the mathematical problem is inherently ill posed. In particular, exploiting a limit procedure in which the Bingham model is retrieved from a linear bi-viscous model we eventually prove that the underlying reason of the inconsistency has to be sought in the hypothesis of perfect stiffness of the unyielded part. We therefore conclude that: either the Bingham model is inappropriate to describe the lubrication motion over a non-flat surface, or the lubrication technique fails in approximating thin Bingham films.

On the mechanism of wetting failure during fluid displacement along a moving substrate

This work investigates the onset of wetting failure for displacement of Newtonian fluids in parallel channels. A hydrodynamic model is developed for planar geometries where an advancing fluid displaces a receding fluid along a moving substrate. The model is evaluated with three distinct approaches: (i) the low-speed asymptotic theory of Cox [J. Fluid Mech. 168, 169–194 (1986)], (ii) a one-dimensional (1D) lubrication approach, and (iii) a two-dimensional (2D) flow model solved with the Galerkin finite element method (FEM). Approaches (ii) and (iii) predict the onset of wetting failure at a critical capillary number Cacrit, which coincides with a turning point in the steady-state solution family for a given set of system parameters. The 1D model fails to accurately describe interface shapes near the three-phase contact line when air is the receding fluid, producing large errors in estimates of Cacrit for these systems. Analysis of the 2D flow solution reveals that strong pressure gradients are needed to pump the receding fluid away from the contact line. A mechanism is proposed in which wetting failure results when capillary forces can no longer support the pressure gradients necessary to steadily displace the receding fluid. The effects of viscosity ratio, substrate wettability, and fluid inertia are then investigated through comparisons of Cacrit values and characteristics of the interface shape. Surprisingly, the low-speed asymptotic theory (i) matches trends computed from (iii) throughout the entire investigated parameter space. Furthermore, predictions of Cacrit from the 2D flow model compare favorably to values measured in experimental air-entrainment studies, supporting the proposed wetting-failure mechanism.

Simulation of Heat and Chemical Reactions on Peristaltic Flow of a Williamson Fluid in an Inclined Asymmetric Channel

This work concerns the peristaltic flow of a Williamson fluid model in an inclined asymmetric channel under combined effects of heat and mass transfer. The governing nonlinear partial differential equations are simplified under the lubrication approach and then solved analytically and numerically. The analytical results are computed with the help of regular perturbation and the numerical results are found by using shooting method.

On the wetting dynamics in a Couette flow

AbstractThe dynamics of moving contact lines in a two-phase Couette flow is investigated by using a matched asymptotic procedure. The walls are assumed to be partially wetting, and the microscopic contact angle is finite but sufficiently small so that the lubrication approach can be used. Explicit formulas are derived to characterize the shear-induced interface deformation and the critical capillary number for the onset of wetting transition. It is found that the apparent contact angle vanishes for liquid–air systems and remains finite for liquid–liquid systems when the wetting transition occurs.

Hydration lubrication

AbstractThe hydration lubrication paradigm, whereby hydration layers are both strongly held by the charges they surround, and so can support large pressures without being squeezed out, and at the same time remain very rapidly relaxing and so have a fluid response to shear, provides a framework for understanding, controlling, and designing very efficient boundary lubrication systems in aqueous and biological media. This review discusses the properties of confined water, which—unlike organic solvents—retains its fluidity down to molecularly thin films. It then describes lubrication by hydrated ions trapped between charged surfaces, and by other hydrated boundary species including charged and zwitterionic polymer brushes, surfactant monolayers, liposomes, and biological macromolecules implicated in synovial joint lubrication. Finally, challenges and prospects for future development of this new boundary lubrication approach are considered.

Modeling and Numerical Simulation of the Grinding Temperature Field with Nanoparticle Jet of MQL

In this research, the heat transfer model of surface grinding temperature field with nanoparticle jet flow of MQL as well as the proportionality coefficient model of energy input workpiece was established, respectively. The numerical simulation of surface grinding temperature field of three workpiece materials was conducted. The results present that, in the workpiece, the surface temperature was significantly higher than the subsurface temperature, presenting relatively large temperature gradient along the direction of workpiece thickness. The impact of the grinding depth on grinding temperature was significant. With the increase of the cut depth, peak values of the grinding temperature rocketed. Distribution rules of the temperature field of 2Cr13 in four cooling and lubrication approaches were the same. Based on the excellent heat transfer property of nanofluids, the output heat through the grinding medium acquired an increasingly high proportion, leading to the drop of the temperature in the grinding zone. For the same cooling and lubrication conditions, grinding temperature presented insignificant changes along the direction of grinding width. Yet, under different cooling conditions, the temperature variation was significant. MQL grinding conditions with additive nanoparticles demonstrated great impact on the weakening of temperature effect on the grinding zone.

A Fast, Experimentally validated, Particle Augmented Mixed Lubrication Framework to Predict CMP

ABSTRACTFabrication of integrated circuits is a multi-step process that involves chemical mechanical polishing (CMP) for planarizing the deposited layers. Although dependent on the consumables and machine operating conditions, most CMP researchers assume that the polishing occurs in the mixedlubrication regime, where the applied load on the wafer is supported by the hydrodynamic slurry pressure and the contact stress generated during the pad-wafer contact. The particle augmented mixed lubrication (PAML) approach has been employed by Terrell and Higgs (2009) as a high-fidelity asperity-scale mixed-lubrication CMP model. The current work introduces a more computationally efficient wafer-scale PAML model, called PAML-lite, which employs a two-dimensional average flow Reynold's Equation incorporating spatial dependence of entrainment velocities to model the hydrodynamic pressure. The contact mechanics are modeled using a Winkler elastic foundation in cylindrical polar coordinates. The resulting slurry hydrodynamic pressure distribution and contact stress are used to determine the equilibrium configuration of the system in the form of a nominal clearance and rolling and pitch angles. Local and wafer scale material removal rate (MRR) is predicted by assuming a uniform distribution of particle sizes. The prediction of PAML-lite were then benchmarked against experimental results. Upon verification, parametric studies were conducted to understand the effect of some unexplored CMP parameters.

The Thermal Effects of CMP as a Particle Augmented Mixed Lubrication Tribosystem

ABSTRACTMost chemical mechanical polishing (CMP) researchers assume that the polishing occurs in the mixed-lubrication regime, where the applied load on the wafer is supported by the hydrodynamic slurry pressure and the contact stress generated during the pad-wafer contact. Consequently, the particle augmented mixed lubrication (PAML) approach has been employed as an extremely high-fidelity asperity-scale mixed-lubrication CMP model in the past. Recently, a more computationally efficient PAML approach, PAML-lite, which considers the slurry’s fluid and particle dynamics, the pad/wafer contact mechanics, and the resulting material removal, was introduced. The current work presents the PAML-lite framework with the isothermal assumption relaxed. As a result, wafer-scale interfacial temperatures during CMP can be predicted by considering asperity heating and dissipation of the heat into the solid and fluid media in the sliding contact.

Dynamic Spreading of Nanofluids on Solids Part II: Modeling

Recent studies on the spreading phenomena of liquid dispersions of nanoparticles (nanofluids) have revealed that the self-layering and two-dimensional structuring of nanoparticles in the three-phase contact region exert structural disjoining pressure, which drives the spreading of nanofluids by forming a continuous wedge film between the liquid (e.g., oil) and solid surface. Motivated by the practical applications of the phenomenon and experimental results reported in Part I of this two-part series, we thoroughly investigated the spreading dynamics of nanofluids against an oil drop on a solid surface. With the Laplace equation as a starting point, the spreading process is modeled by Navier-Stokes equations through the lubrication approach, which considers the structural disjoining pressure, gravity, and van der Waals force. The temporal interface profile and advancing inner contact line velocity of nanofluidic films are analyzed through varying the effective nanoparticle concentration, the outer contact angle, the effective nanoparticle size, and capillary pressure. It is found that a fast and spontaneous advance of the inner contact line movement can be obtained by increasing the nanoparticle concentration, decreasing the nanoparticle size, and/or decreasing the interfacial tension. Once the nanofluidic film is formed, the advancing inner contact line movement reaches a constant velocity, which is independent of the outer contact angle if the interfacial tension is held constant.

Peristaltic Flow of a Carreau Fluid in a Rectangular Duct

In the present investigation we have studied the peristaltic flow of a Carreau fluid in a rectangular duct. The flow is investigated in the wave frame of reference moving with the velocity c away from the fixed frame. The peristaltic wave propagating on the horizontal side walls of a rectangular duct is studied under long wave length and low Reynolds number approximation. The analytical solutions of velocity and pressure gradient have been found under lubrication approach with the help of Homotopy perturbation method. Graphical results are displayed to see the behavior of various emerging parameters of Carreau fluid. The comparison of the present work is also made with the existing literature.

First-order energy-integral model for thin Newtonian liquids falling along sinusoidal furrows

An average modeling methodology under the lubrication approach is used to formulate a set of three coupled nonlinear partial differential equations based on the Nusselt scales. This system, known as the energy-integral method in literature, simplifies the Navier-Stokes equation at the first order and analyzes the dynamics of a thin sheet of fluid flowing over a topography with sinusoidally varying longitudinal furrows. Limiting cases of the linear stability results are mathematically discussed and the complete linear system is numerically handled by means of finite differences to approximate the eigenfunctions and their derivatives in a periodic domain. In a geometry which resembles a vertical shift of a topography, with the amplitude being equal to the shift length, it is found that such a geometry stabilizes the flow compared to its counterpart with no shift, such that the wave characteristics get affected. To confirm the stability results, a numerical investigation is performed.

Simulation of heat and mass transfer on peristaltic flow of hyperbolic tangent fluid in an asymmetric channel

SUMMARYIn the present analysis, the influence of heat and mass transfer on the peristaltic flow of a hyperbolic tangent fluid in an asymmetric channel has been discussed. The highly nonlinear equations are simplified under lubrication approach. The perturbation and numerical solutions of the problem are not only discussed but the validity of the results is also being checked. The graphical results of the problem under discussion are also being brought under consideration to see the behavior of various physical parameters. Copyright © 2012 John Wiley & Sons, Ltd.

A lubrication approach to friction in thermoplastic composites forming processes

Friction is an important phenomenon that can dominate the resulting product geometry of thermoplastic composites upon forming. A model was developed that predicts the friction between a thermoplastic laminate and a rigid tool. The model is based on the Reynolds equation for thin film lubrication and assumes hydrodynamic lubrication on a meso-mechanical level. The frictional properties are calculated, solely based on the rheological properties of the matrix constituent and the fabric weave geometry. The results have been validated against pull-out experiments of a 2 × 2 twill polypropylene (Twintex) weave at melt temperatures.