Showing papers on "Slip ratio published in 2008"

Structured surfaces for a giant liquid slip.

Abstract: We study experimentally how two key geometric parameters (pitch and gas fraction) of textured hydrophobic surfaces affect liquid slip. The two are independently controlled on precisely fabricated microstructures of posts and grates, and the slip length of water on each sample is measured using a rheometer system. The slip length increases linearly with the pitch but dramatically with the gas fraction above 90%, the latter trend being more pronounced on posts than on grates. Once the surfaces are designed for very large slips (>20 microm), however, further increase is not obtained in regular practice because the meniscus loses its stability. By developing near-perfect samples that delay the transition from a dewetted (Cassie) to a wetted (Wenzel) state until near the theoretical limit, we achieve giant slip lengths, as large as 185 microm.

Earthquake nucleation on rate and state faults - Aging and slip laws

Abstract: We compare 2-D, quasi-static earthquake nucleation on rate-and-state faults under both “aging” and “slip” versions of the state evolution law. For both versions mature nucleation zones exhibit 2 primary regimes of growth: Well above and slightly above steady state, corresponding respectively to larger and smaller fault weakening rates. Well above steady state, aging-law nucleation takes the form of accelerating slip on a patch of fixed length. This length is proportional to b^−1 and independent of a, where a and b are the constitutive parameters relating changes in slip speed and state to frictional strength. Under the slip law the nucleation zone is smaller and continually shrinks as slip accelerates. The nucleation zone is guaranteed to remain well above steady state only for values of a/b that are low by laboratory standards. Near steady state, for both laws the nucleation zone expands. The propagating front remains well above steady state, giving rise to a simple expression for its effective fracture energy G c . This fracture energy controls the propagation style. For the aging law G c increases approximately as the square of the logarithm of the velocity jump. This causes the nucleation zone to undergo quasi-static crack-like expansion, to a size asymptotically proportional to b/(b−a)^2. For the slip law G c increases only as the logarithm of the velocity jump, and crack-like expansion is not an option. Instead, the nucleation zone grows as an accelerating unidirectional slip pulse. Under both laws the nucleation front propagates at a velocity larger than the slip speed by roughly μ′/bσ divided by the logarithm of the velocity jump, where μ′ is the effective elastic shear modulus. For this prediction to be consistent with observed propagation speeds of slow slip events in subduction zones appears to require effective normal stresses as low as 1 MPa.

A slip model for rarefied gas flows at arbitrary Knudsen number

Abstract: A slip model for wall bounded rarefied gas flows is derived from kinetic theory. A corresponding modified Reynolds lubrication equation is obtained from the slip velocity boundary conditions at walls for high Knudsen number gas flows. The slip model in a simplest form has predictions very close to the numerical solutions of linearized Boltzmann equation in the whole Knudsen number range, and is preferable to the widely applied 1st order (Maxwell slip model), 2nd order, and 1.5 order slip models.

Slip at high shear rates.

Abstract: There are contradictory published data on the behavior of fluid slip at high shear rates. Using three methodologies (molecular dynamics simulations, an analytical theory of slip, and a Navier-Stokes-based calculation) covering a range of fluids (bead-spring liquids, polymer solutions, and ideal gas flows) we show that as shear rate increases, the amount of slip, as measured by the slip length, asymptotes to a constant value. The results clarify the molecular mechanics of how slip occurs. Furthermore, they indicate that in this limit, molecular dynamics simulations must accurately account for heat transfer to the solid.

Influence of partial slip on the peristaltic flow in a porous medium

Abstract: In this paper, the slip effects are discussed on the peristaltic flow of a viscous fluid in a porous medium. A long wavelength approximation is used in the flow modelling. The solutions for stream function and axial velocity are constructed by employing the Adomian decomposition method. Numerical integration has been used for the pumping and trapping phenomena. Graphs illustrate the physical behavior. It is noted that the size of the trapped bolus decreases and its symmetry disappears for large values of the slip parameter. Further, the peristaltic pumping rate decreases by increasing the slip parameter.

Observation of Slip Flow in Thermophoresis

Abstract: Two differing theories aim to describe fluidic thermophoresis, the movement of particles along a temperature gradient. While thermodynamic approaches rely on local equilibrium, hydrodynamic descriptions assume a quasi-slip-flow boundary condition at the particle's surface. Evidence for slip flow is presented for the case of thermal gradients exceeding $(a{S}_{T}{)}^{\ensuremath{-}1}$ with particle radius $a$ and Soret coefficient ${S}_{T}$. Thermophoretic slip flow at spheres near a surface attracts or repels tracer particles perpendicular to the thermal gradient. Moreover, particles mutually attract and form colloidal crystals. Fluid dynamic slip explains the latter quantitatively.

Effect of surface slip on Stokes flow past a spherical particle in infinite fluid and near a plane wall

Abstract: The motion of a spherical particle in infinite linear flow and near a plane wall, subject to the slip boundary condition on both the particle surface and the wall, is studied in the limit of zero Reynolds number. In the case of infinite flow, an exact solution is derived using the singularity representation, and analytical expressions for the force, torque, and stresslet are derived in terms of slip coefficients generalizing the Stokes–Basset–Einstein law. The slip velocity reduces the drag force, torque, and the effective viscosity of a dilute suspension. In the case of wall-bounded flow, advantage is taken of the axial symmetry of the boundaries of the flow with respect to the axis that is normal to the wall and passes through the particle center to formulate the problem in terms of a system of one-dimensional integral equations for the first sine and cosine Fourier coefficients of the unknown traction and velocity along the boundary contour in a meridional plane. Numerical solutions furnish accurate predictions for (a) the force and torque exerted on a particle translating parallel to the wall in a quiescent fluid, (b) the force and torque exerted on a particle rotating about an axis that is parallel to the wall in a quiescent fluid, and (c) the translational and angular velocities of a freely suspended particle in simple shear flow parallel to the wall. For certain combinations of the wall and particle slip coefficients, a particle moving under the influence of a tangential force translates parallel to the wall without rotation, and a particle moving under the influence of a tangential torque rotates about an axis that is parallel to the wall without translation. For a particle convected in simple shear flow, minimum translational velocity is observed for no-slip surfaces. However, allowing for slip may either increase or decrease the particle angular velocity, and the dependence on the wall and particle slip coefficients is not necessarily monotonic.

Unsteady circular tube flow of compressible polymeric liquids subject to pressure-dependent wall slip

Abstract: A mathematical model is developed for the time-dependent circular tube flow of compressible polymeric liquids subject to pressure-dependent slip at the wall and applied to a poly (dimethyl siloxane) (PDMS). The parameters of pressure-dependent wall slip velocity and shear viscosity of the PDMS were determined using combinations of small-amplitude oscillatory shear, steady torsional and squeeze flows and were employed in the prediction of the time-dependent circular tube flow behavior of the PDMS. The numerical solutions suggest that a steady tube flow is generated when the flow boundary condition at the wall is stable, that is, either a contiguous stick (or weak slip) or a contiguous strong slip condition along the entire length of the wall. On the other hand, when the flow boundary condition changes from stick (or weak slip) to strong slip at any location along the length of the wall, undamped periodic oscillations in pressure and mean velocity are observed. The experimentally characterized and simulated tube flow curves of PDMS are similar and the simulation findings for flow stability are in general consistent with the experimentally observed flow instability behavior of PDMS.

Wall slip and spurt flow of polybutadiene

Abstract: Spurt occurs in the flow of entangled melts in a capillary rheometer in which the driving pressure is controlled. As the driving pressure increases, at a critical value there is a sudden increase in flow rate, often called spurt. This discontinuity is followed by another regime of smoothly increasing flow rate. A phenomenon that may contribute to this instability is a curve of wall shear stress versus slip velocity that has a maximum followed by a minimum, and there are models that predict such behavior. We used a sliding plate rheometer (SPR) to study wall slip for a highly entangled, linear polybutadiene at 1atm and at 46MPa. By varying the plate speed, we were able to explore the entire curve of shear stress versus slip velocity. This curve exhibited a maximum and a minimum in the stress, providing support for theories predicting this behavior and an explanation for the spurt effect in capillary rheometry. The spurt flow of the same polymer was also observed, and slip velocities were estimated and compared with those determined using the SPR. The slip velocities obtained using the two instruments were in good agreement.Spurt occurs in the flow of entangled melts in a capillary rheometer in which the driving pressure is controlled. As the driving pressure increases, at a critical value there is a sudden increase in flow rate, often called spurt. This discontinuity is followed by another regime of smoothly increasing flow rate. A phenomenon that may contribute to this instability is a curve of wall shear stress versus slip velocity that has a maximum followed by a minimum, and there are models that predict such behavior. We used a sliding plate rheometer (SPR) to study wall slip for a highly entangled, linear polybutadiene at 1atm and at 46MPa. By varying the plate speed, we were able to explore the entire curve of shear stress versus slip velocity. This curve exhibited a maximum and a minimum in the stress, providing support for theories predicting this behavior and an explanation for the spurt effect in capillary rheometry. The spurt flow of the same polymer was also observed, and slip velocities were estimated and comp...

Time-dependent tube flow of compressible suspensions subject to pressure dependent wall slip: Ramifications on development of flow instabilities

Abstract: A mathematical model developed earlier for the time-dependent circular tube flow of compressible polymer melts subject to pressure-dependent wall slip [Tang and Kalyon, J. Rheol 52, 507–525 (2008)] was applied to the tube flow of polymeric suspensions with rigid particles. The model relies on the apparent slip mechanism for suspension flow with the additional caveat that the polymeric binder slips at the wall according to a pressure-dependent wall slip condition. The numerical simulations of the tube flow of concentrated suspensions suggest that steady flow is generated when the flow boundary condition at the wall is a contiguous strong slip condition along the entire length of the tube wall. The findings of the simulations are consistent with the experimental flow curves and flow instability data collected on suspensions of a poly (dimethyl siloxane), which itself exhibits wall slip, compounded with rigid and hollow spherical particles in the 10–40% by volume range. Increasing the concentration of rigid ...

Modeling and control of adhesion force in railway rolling stocks

Abstract: In this article, two models are developed for the adhesion force in railway rolling stocks. The first model is a static model based on a beam model, which is typically used to model automobile tires. The second model is a dynamic model based on a bristle model, in which the friction interface between the rail and the wheel is modeled as contact between bristles. The validity of the beam model and bristle model is verified through an adhesion test using a brake performance test rig. We also develop wheel-slip brake control systems based on each friction model. One control system is a conventional proportional-integral (PI) control scheme, while the other is an adaptive sliding mode control (ASMC) scheme. The controller design process considers system uncertainties such as the traveling resistance, disturbance torque, and variation of the adhesion force according to the slip ratio and rail conditions. The mass of the rolling stocks is also considered as an uncertain parameter, and the adaptive law is based on Lyapunov stability theory. The performance and robustness of the PI and adaptive sliding mode wheel-slip brake control systems are evaluated through computer simulation.

Velocity profiles of water flowing past solid glass surfaces using fluorescent nanoparticles and molecules as velocity probes.

Abstract: Measurements of the velocity profile of water flowing on a glass surface using fluorescent nanoparticles and single fluorescent molecules as velocity probes show that the no slip boundary condition holds down to at least 10 nm from the surface. For water flowing on a hydrophobic solid surface, silanized glass, the no slip boundary condition fails, and a slip length of 45 nm is measured. These velocity measurements are complemented with atomic force microscopy measurements of dissipation on a small sphere oscillating near the surface with results in agreement with the velocity profiles.

Dynamics of a sphere with inhomogeneous slip boundary conditions in Stokes flow.

Abstract: The dynamic resistance of a sphere with a general inhomogeneous slip boundary condition is analyzed in Newtonian unbounded uniform flow at low Reynolds number. The boundary condition is treated as a perturbation to a homogeneous sphere, assuming that the slip length magnitude $b$ is much smaller than the sphere radius $a$. To first order, the effect of inhomogeneous slip is the same as that of a radial deformity of magnitude $b$. Full resistance tensors are presented and the dynamics of a hemispherical inhomogeneous sphere, such as a Janus particle, are explicitly calculated.

Two-Phase Flow in Porous Media with Slip Boundary Condition

Abstract: Flow in porous media described by Darcy’s law extended to two-phase flow using the concept of relative permeabilities k r naturally assumes a maximum value of 0 ≤ k r ≤ 1. Reports in literature and our own experimental data show endpoint relative permeabilities k r > 1. In the porous medium, the flux of the non-wetting phase is in many cases about 2-4 times higher when a small amount of the wetting phase is present. Here, we draw an analogy between k r > 1 and a slip-boundary condition for the pore scale flow. We use a model description assuming flow in capillary tubes with a slip boundary condition. This model predicts that the flux increase due to slip depends on the equivalent capillary radius of the flow channels. Our k r data specifically follows this dependence indicating that slip is a plausible explanation for the observation of k r > 1.

Two dimensional stagnation point flow of an elastico-viscous fluid with partial slip

Abstract: The steady, laminar flow of an elastico-viscous fluid impinging normally upon a wall has been investigated when there is a partial slip of the fluid at the wall. The governing equations of motion admit a similarity solution in terms of η, the dimensionless distance normal to the wall. The boundary value problem characterizing the flow has been solved without making any assumption on the size of either the viscoelastic fluid parameter or the partial slip parameter. The solutions are shown to exist only up to a critical value of viscoelastic fluid parameter. The effect of the partial slip is to enhance this critical value.

Interaction of Couple Stresses and Slip Flow on Peristaltic Transport in Uniform and Nonuniform Channels

Abstract: The effect of slip velocity on peristaltic flow of a couple stress fluid in uniform and nonuniform symmetric channels is studied. This problem has numerous applications. It serves as a model for the blood flow in living creatures. Using long wavelength approximation and neglecting inertial forces, a closed form solution for the axial velocity and the pressure gradient was obtained. Numerical computations were carried out to investigate the effect of couple stress parameter a and Knudsen number Kn on pressure rise, maximum pressure rise, and friction force for uniform and nonuniform channels. It is noted that the pressure rise decreases with increasing a and increasing Kn. The friction force has an opposite behavior compared with pressure rise.

Stagnation-point flow of a second-grade fluid with slip

Abstract: The steady two-dimensional stagnation-point flow of a second-grade fluid with slip is examined. The fluid impinges on the wall either orthogonally or obliquely. Numerical solutions are obtained using a quasi-linearization technique.

Frictional constitutive law at intermediate slip rates accounting for flash heating and thermally activated slip process

Abstract: [1] A constitutive law in a rate- and state-dependent framework accounting for flash heating at microscopic contacts is proposed on the basis of a simple asperity model and a thermally activated slip process thought to cause logarithmic dependency of the friction coefficient on slip rate. This law is probably applicable in an intermediate slip rate regime (about 0.001-0.1 m/s), where contact time of asperities is shorter than a cutoff time for time-dependent healing, and a phase transformation such as melting does not take place at the microscopic contacts. The steady state friction coefficient, which is constructed numerically and derived analytically, depends on slip rate and background temperature, gives a good coverage of experimental data of gabbro friction at slip rate on the order of 0.1 m/s, and explains linear dependency of the friction coefficient of Al 2 O 3 ceramics on temperature at around 0.1 m/s. Similar to the usual rate- and state-dependent friction law, the transition behavior on a sudden step in slip rate includes a positive direct effect and a following evolution effect, which are essential in considering the problems dealing with coupling of a frictional surface and surrounding elastic medium. This constitutive law illuminates the importance of the change in not only microscopic, but also macroscopic temperature; the latter, as well as the slip rate, probably changes dynamically during the nucleation of rupture and the coseismic phase.

Molecular effects on boundary condition in micro/nanoliquid flows

Abstract: We experimentally investigated molecular effects of the slip/no-slip boundary condition of Newtonian liquids in micro- and nanochannels as small as 350 nm The slip was measurable for channels smaller than approximately 2μm The amount of slip is found to be independent of the channel size, but is a function of the shear rate, the type of liquid (polar or nonpolar molecular structure), and the morphology of the solid surface (molecular-level smoothness)

Intelligent Tires Based on Measurement of Tire Deformation

Abstract: From a traffic safety point-of-view, there is an urgent need for intelligent tires as a warning system for road conditions, for optimized braking control on poor road surfaces and as a tire fault detection system. Intelligent tires, equipped with sensors for monitoring applied strain, are effective in improving reliability and control systems such as anti-lock braking systems (ABSs). In previous studies, we developed a direct tire deformation or strain measurement system with sufficiently low stiffness and high elongation for practical use, and a wireless communication system between tires and vehicle that operates without a battery. The present study investigates the application of strain data for an optimized braking control and road condition warning system. The relationships between strain sensor outputs and tire mechanical parameters, including braking torque, effective radius and contact patch length, are calculated using finite element analysis. Finally, we suggested the possibility of optimized braking control and road condition warning systems. Optimized braking control can be achieved by keeping the slip ratio constant. The road condition warning would be actuated if the recorded friction coefficient at a certain slip ratio is lower than a ‘safe’ reference value.

Effects of Corrugated Roughness on Developed Laminar Flow in Microtubes

Abstract: The effects of corrugated surface roughness on developed laminar flow in microtubes are investigated. The momentum equation is solved using a perturbation method with slip at the boundary. Novel analytical models are developed to predict friction factor and pressure drop in corrugated rough microtubes for continuum flow and slip flow. The developed model proposes an explanation on the observed phenomenon that some experimental pressure drop results for microchannel flow have shown a significant increase (15-50%) due to roughness. The developed model for slip flow illustrates the coupled effects between velocity slip and small corrugated roughness. Compressibility effect has also been examined and simple models are proposed to predict the pressure distribution and mass flow rate for slip flow in corrugated rough microtubes.

Control Device for Automatic Transmission

Abstract: A control device for an automatic transmission having a torque converter with a lock-up clutch provided between an engine and the automatic transmission, and a lock-up control device for controlling an engaged condition of the lock-up clutch. The control device includes a plurality of different target slip ratio maps each having a plurality of target slip ratio characteristic lines of the lock-up clutch predetermined according to a throttle angle, a first map selector for selecting one of the target slip ratio maps according to a running range, according to whether the running road is a level road/downhill road or an uphill road, and according to a gear position during running in the condition where an accelerator pedal is depressed, and a second map selector for selecting one of the target slip ratio maps according to a running range, according to whether the running road is a level road/uphill road or a downhill road, and according to a gear position during running in the condition where the accelerator pedal is undepressed.

Pressure-driven transient flows of Newtonian fluids through microtubes with slip boundary

Abstract: Recent advances in microscale experiments and molecular simulations confirm that slip of fluid on solid surface occurs at small scale, and thus the traditional no-slip boundary condition in fluid mechanics cannot be applied to flow in micrometer and nanometer scale tubes and channels. On the other hand, there is an urgent need to understand fluid flow in micrometer scale due to the emergence of biochemical lab-on-the-chip system and micro-electromechanical system fabrication technologies. In this paper, we study the pressure driven transient flow of an incompressible Newtonian fluid in microtubes with a Navier slip boundary condition. An exact solution is derived and is shown to include some existing known results as special cases. Through analysis of the derived solution, it is found that the influences of boundary slip on the flow behaviour are qualitatively different for different types of pressure fields driving the flow. For pressure fields with a constant pressure gradient, the boundary slip does not alter the interior material deformation and stress field; while, for pressure fields with a wave form pressure gradient, the boundary slip causes the change of interior material deformation and consequently the velocity profile and stress field. We also derive asymptotic expressions for the exact solution through which a parameter β is identified to dominate the behaviour of the flow driven by the wave form pressure gradient, and an explicit formulae for the critical slip parameter leading to the maximum transient flow rate is established.

Flow, slippage and a hydrodynamic boundary condition of polymers at surfaces

Abstract: Tailoring surface interactions or grafting of polymers onto surfaces is a versatile tool for controlling wettability, lubrication, adhesion and interactions between surfaces. Using molecular dynamics of a coarse-grained, bead-spring model and dynamic single-chain-in-mean-field simulations, we investigate how structural changes near the surface affect the flow of a polymer melt over the surface and how these changes can be parameterized by a hydrodynamic boundary condition. We study the temperature dependence of the near-surface flow of a polymer melt at a corrugated, attractive surface. At weakly attractive surfaces, lubrication layers form, the slip length is large and increases upon cooling. Close to the glass transition temperature, very large slip lengths are observed. At a more attractive surface, a 'sticky surface layer' is build up, giving rise to a small slip length. Upon cooling, the slip length decreases at high temperatures, passes through a minimum and increases upon approaching the glass transition temperature. At strongly attractive surfaces, the Navier slip condition fails to describe Couette and Poiseuille flows simultaneously. A similar failure of the Navier slip condition is observed for the flow of a polymer melt over a brush comprised of identical molecules. The wetting and flow properties of this surface are rather complex. Most notably, the cyclic motion of the grafted molecules gives rise to a reversal of the flow direction at the grafting surface. The failure of the Navier slip condition in both cases can be rationalized within a schematic, two-layer model, which demonstrates that the Navier slip condition fails to simultaneously describe Poiseuille and Couette flow if the fluid at the surface exhibits a higher viscosity than the bulk.