A thin-film model for corotational Jeffreys fluids under strong slip

We derive a thin-film model for viscoelastic liquids under strong slip which obey the stress tensor dynamics of corotational Jeffreys fluids.     

Effects of partial slip on axisymmetric flow of an electrically conducting viscoelastic fluid past a stretching sheet

The entrained flow of an electrically conducting non-Newtonian, viscoelastic second grade fluid due to an axisymmetric stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equation into an ordinary differential equation. The issue of paucity of boundary conditions is addressed, and an effective numerical scheme has been adopted to solve the obtained differential equation even without augmenting the boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and skin friction coefficient. It is observed that in presence of slip, the velocity decreases with an increase in the magnetic parameter. That is, the Lorentz force which opposes the flow leads to enhanced deceleration of the flow. Moreover, it is interesting to find that as slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid.     

Comparative study on electroosmosis modulated flow of MHD viscoelastic fluid in the presence of modified Darcy’s law

Magnetic field plays an important role in numerous fields such as biological, chemical, mechanical and medical research. In clinical and medical research the high field magnets are extremely important to create 3D images of anatomical and diagnostic importance from nuclear magnetic resonance signals. In view of these applications, the purpose of present work is to explore the impact of an external magnetic field on the viscoelastic fluid flow in the existence of electroosmosis, porous medium and slip boundary conditions. The governing equation is modified under the suitable dimensionless quantities. The resulting non-dimensional differential equation is evaluated by analytical as well as numerical (finite difference and cubic B-spline) methods. The convergence analysis is also presented for the numerical methods. The variations of sundry parameters on velocity, volume flow rate and skin friction are presented through graphical representations. The current analysis depicts that, the higher velocities are noticed in viscoelastic fluid as compared with Newtonian fluid. The velocity enhances with rising of slip and Darcy parameters. Volume flow rate rises with the slip and viscoelastic parameters. Skin friction is a decreasing function of zeta potential, Darcy number and Hall current parameter. The limiting solutions can be captured for the Newtonian fluid model by setting the viscoelastic parameter to zero.     

Axisymmetric convection flow of fractional Maxwell fluid past a vertical cylinder with velocity slip and temperature jump

A novel finite volume method is developed to investigate the axisymmetric convection flow and heat transfer of fractional viscoelastic fluid past a vertical cylinder. Fractional cylindrical governing equations are formulated by fractional Maxwell model and generalized Fourier's law. The velocity slip and temperature jump boundary conditions are considered across the fluid-solid interface. Numerical results are validated by exact solutions of special case with source terms. The effects of fractional derivative parameter and boundary condition parameters on flow and heat transfer characteristics are discussed. The viscoelastic fluid performs evident shear thickening property in the fractional Maxwell constitutive relation. Moreover, the boundary condition parameters have remarkable influence on velocity and temperature distributions.     

Polymer thin films and surfaces: Possible effects of capillary waves

It is discussed how the proximity of a free surface or mobile interface may affect the strain relaxation behavior in a viscoelastic material, such as a polymer melt. The eigenmodes of a viscoelastic film are thus derived, and applied in an attempt to explain the experimentally observed substantial shift of the glass transition temperature of sufficiently thin polymer films with respect to the bulk. Based on the idea that the polymer freezes due to memory effects in the material, and exploiting results from mode-coupling theory, the experimental findings of several independent groups can be accounted for quantitatively, with the elastic modulus at the glass transition temperature as the only fitting parameter. The model is finally applied discussing the possibility of polymer surface melting. A surface molten layer is predicted to exist, with a thickness diverging as the inverse of the reduced temperature. A simple model of thin polymer film freezing emerges which accounts for all features observed experimentally so far. Received 8 August 2001     

Dynamic instability of supercritical driveshafts mounted on dissipative supports—Effects of viscous and hysteretic internal damping

The case of a rotating shaft with internal damping mounted either on elastic dissipative bearings or on infinitely rigid bearings with viscoelastic suspensions is investigated in order to obtain the stability region. A Euler-Bernoulli shaft model is adopted, in which the transverse shear effects are neglected and the effects of translational and rotatory inertia, gyroscopic moments, and internal viscous or hysteretic damping are taken into account. The hysteretic damping is incorporated with an equivalent viscous damping coefficient. Free motion analysis yields critical speeds and threshold speeds for each damping model in analytical form. In the case of elastic dissipative bearings, the present results are compared with the results of previous studies on finite element models. In the case of infinitely rigid bearings with viscoelastic suspensions, it is established that viscoelastic supports increase the stability of long shafts, thus compensating for the loss of efficiency which occurs with classical bearings. The instability criteria also show that the effect of the coupling which occured between rigid modes introducing external damping and shaft modes are almost more important than damping factor. Lastly, comparisons between viscous and hysteretic damping conditions lead to the conclusion that an appropriate material damping model is essential to be able to assess these instabilities.     

Nonlinear vibration of viscoelastic embedded-DWCNTs integrated with piezoelectric layers-conveying viscous fluid considering surface effects

This article studies the nonlinear vibration of viscoelastic embedded nano-sandwich structures containing of a double walled carbon nanotube (DWCNT) integrated with two piezoelectric Zinc oxide (ZnO) layers. DWCNT and ZnO layers are subjected to magnetic and electric fields, respectively. This system is conveying viscous fluid and the related force is calculated by modified Navier–Stokes relation considering slip boundary condition and Knudsen number. Visco–Pasternak model with three parameters of the Winkler modulus, shear modulus, and damp coefficient is used for simulation of viscoelastic medium. The nano-structure is simulated as an orthotropic Timoshenko beam (TB) and the effects of small scale, structural damping and surface stress are considered based on Eringen's, Kelvin-voigt and Gurtin–Murdoch theories. Energy method and Hamilton's principle are employed to derive motion equations which are then solved using differential quadrature method (DQM). The detailed parametric study is conducted, focusing on the combined effects of small scale effect, fluid velocity, thickness of piezoelectric layer, boundary condition, surface effects, van der Waals (vdW) force on the frequency and critical velocity of nano-structure. Results indicate that the frequency and critical velocity increases with assume of surface effects.     

Slip Boundary Conditions for the Compressible Navier–Stokes Equations

The slip boundary conditions for the compressible Navier–Stokes equations are derived systematically from the Boltzmann equation on the basis of the Chapman–Enskog solution of the Boltzmann equation and the analysis of the Knudsen layer adjacent to the boundary. The resulting formulas of the slip boundary conditions are summarized with explicit values of the slip coefficients for hard-sphere molecules as well as the Bhatnagar–Gross–Krook model. These formulas, which can be applied to specific problems immediately, help to prevent the use of often used slip boundary conditions that are either incorrect or without theoretical basis.     

A thin-film equation for viscoelastic liquids of Jeffreys type

We derive a novel thin-film equation for linear viscoelastic media describable by generalized Maxwell or Jeffreys models. As a first application of this equation we discuss the shape of a liquid rim near a dewetting front. Although the dynamics of the liquid is equivalent to that of a phenomenological model recently proposed by Herminghaus et al. (S. Herminghaus, R. Seemann, K. Jacobs, Phys. Rev. Lett. 89, 056101 (2002)), the liquid rim profile in our model always shows oscillatory behaviour, contrary to that obtained in the former. This difference in behaviour is attributed to a different treatment of slip in both models.     

Various kinds of two-dimensional rheological models

Two-dimensional rheological models consisting of two-dimensional elastic, viscous, and plastic elements are introduced in order to represent more closely the real rheological behavior of various isotropic and orthotropic viscoelastic, elastoplastic, viscoplastic, and elastoviscoplastic bodies in the plane-stress or plane-strain state, respectively. These models represent schematically the unit area of a body and consist of plane elastic, viscous, and plastic regions with rectangular straight boundaries lying in the principal direction of orthotropy.

The two-dimensional rheological models may be considered either from the phenomenological or from the structural point of view. They may also represent rheological structures with variously oriented multiphase systems having elastic, viscous, and plastic properties. The configuration of such models may correspond to the rheological nonhomogeneity of bodies and to both kinds of orthotropy arising either from the orthotropic properties of elastic, plastic, and viscous phases or from various configurations of phases. These models may also represent nonsymmetrical shear effects which are analogous to those arising in elastic Cosserat media.

The main differences between the presented two-dimensional models and the usual rheological models, which are one-dimensional, consist of the possibilities of representing directly two-dimensional rheological behavior, the anisotropy of rheological processes, and nonsymmetrical shear effects in rheological bodies.     

Ultrasonic scattering cross sections of shell-encapsulated gas bubbles immersed in a viscoelastic liquid: first and second harmonics

The oscillations of gas bubbles, without shell, immersed in viscoelastic liquids and driven by an acoustic wave have been the subject of several investigations. They demonstrate that the viscosity coefficient and the spring constant of the liquid have significant influence on the scattering cross section of the gas bubble. For shell-encapsulated gas bubbles, the investigations have been concentrated to bubbles immersed in a pure viscous liquid. This present work computes the ultrasonic scattering cross section, first and second harmonics, of shell-encapsulated gas bubbles immersed in a viscoelastic liquid. The theoretical model of the bubble oscillation is based on the generalized Rayleigh-Plesset equation of motion of a spherical cavity immersed in a viscoelastic liquid represented by a three-parameter linear Oldroyd model. The scattering cross section is computed for Albunex type of bubble (shell thickness=15 nm, shell shear viscosity=1.77 Pas, shell modulus of rigidity=88.8 MPa) irradiated by a 3.5 MHz ultrasonic pressure wave with an amplitude of 30 kPa. The results demonstrate that encapsulated bubbles respond independently of the surrounding liquid being pure viscous or viscoelastic as long as the surrounding liquid shear viscosity is as low as 10(-3) Pas. Nevertheless, for higher shear viscosities, the bubble responds differently if the surrounding liquid is pure viscous or viscoelastic. In general, the scattering cross sections of first and second harmonics are larger for the viscoelastic liquid.     

Orientation dependence of void growth at triple junction of grain boundaries in nanoscale tricrystal nickel film subjected to uniaxial tensile loading

Molecular dynamics simulation was performed in order to investigate the dependence of void growth on crystallographic orientation at the triple junction of grain boundaries in nanoscale tricrystal nickel film subjected to uniaxial tensile loading. The nucleation, the emission and the transmission of Shockley partial dislocations play a predominant role in the growth of void at the triple junction of grain boundaries. The orientation factors of various slip systems are calculated according to Schmid law. The slip systems activated in a grain of tricrystal nickel film basically conform to Schmid law which is completely suitable for a single crystal. The activated slip systems play an important role in plastic deformation of nanoscale tricrystal nickel film subjected to uniaxial tensile loading. The slip directions exhibit great difference among the activated slip systems such that the void is caused to be subjected to various stress conditions, which further leads to the difference in void growth among the tricrystal nickel films with different orientation distributions. It can be concluded that the grain orientation distribution has a significant influence on void growth at the triple junction of grain boundaries.     

Multifrequency characterization of viscoelastic polymers and vapor sensing based on SAW oscillators

Simplified relations for the changes in SAW velocity and attenuation due to thin polymer coatings and vapor sorption are presented by making analytic approximations to the complex theoretical model developed earlier by Martin et al. [Anal. Chem. 66 (14) (1994) 2201–2219]. The approximate velocity relation is accurate within 4% for the film thicknesses up to 20% of the acoustic wavelength in the polymer film, and is useful for analyzing the mass loading, swelling and viscoelastic effects in SAW vapor sensors. The approximate attenuation relation is accurate within 20% for very thin films, (less than 2% of the acoustic wavelength in the film). Based on these relations, a new procedure for determination of polymer viscoelastic properties is described that exploits the frequency dependence of the velocity and attenuation perturbations, and employs multifrequency measurement on the same SAW platform. Expressions for individual contributions from the mass loading, film swelling and viscoelastic effects in SAW vapor sensors are derived, and their implications for the sensor design and operation are discussed. Also, a new SAW comb filter design is proposed that offers possibility for multimode SAW oscillator operation over a decade of frequency variation, and illustrates feasibility for experimental realization of wide bandwidth multifrequency SAW platforms.     

Boundary Slip and Surface Interaction： A Lattice Boltzmann Simulation

The factors affecting slip length in Couette geometry flows are analysed by means of a two-phase mesoscopic lattice Boltzmann model including non-ideal fluid-fluid and fluid-wall interactions. The main factors influencing the boundary slip are the strength of interactions between fluid-fluid and fluid-wall particles. Other factors, such as fluid viscosity, bulk pressure may also change the slip length. We find that boundary slip only occurs under a certain density （bulk pressure）. If the density is large enough, the slip length will tend to zero. In our simulations, a low density layer near the wall does not need to be postulated a priori but emerges naturally from the underlying non-ideal mesoscopic dynamics. It is the low density layer that induces the boundary slip. The results may be helpful to understand recent experimental observations on the slippage of micro flows.     

Peristaltic transport in a slip flow

Continuum-mechanic derivation of the entrainment of rarefied gases induced by a surface wave along walls (or peristaltic transport) in a confined parallel-plane microchannel is conducted by the perturbation method. Both no-slip and slip flow cases are investigated with the former ones matched with the previous approach by Fung and Yih. Critical reflux values due to first order slip-flow effects become trivial for the free pumping case, and decrease due to second order slip-flow effects after we compared them with no-slip cases. Received 27 August 1999 and Received in final form 10 January 2000     

The sharkskin instability of polymer melt flows

Flows of polymeric liquids undergo instabilities whose origins are quite different from those of Newtonian flows, due to their elastic character and the complexity of the fluid/solid boundary condition. This article reviews recent studies of one such instability, the sharkskin phenomenon observed during extrusion of many linear polymers. Key experimental observations are summarized; one important fact that has become clear is the importance of the interaction between the molten polymer and the solid walls of the flow channel, especially near the contact line at the exit of the channel. Recent developments in understanding the relationship between wall slip and disentanglement of wall-adsorbed polymers from the bulk flow are briefly described, and putative heuristic mechanisms relating the instability to slip and contact line motion are presented. Finally, we review mathematical analyses of the stability of viscoelastic shear flows with slip boundary conditions. Some recent analyses yield instability predictions that are consistent with experiments, but further work is required to discriminate between the various mechanisms that have been proposed. (c) 1999 American Institute of Physics.     

Comment on “The properties of free polymer surfaces and their influence on the glass transition temperature of thin polystyrene films” by J.S. Sharp,J.H. Teichroeb and J.A. Forrest

Sharp, Teichroeb and Forrest [J.S. Sharp, J.H. Teichroeb, J.A. Forrest, Eur. Phys. J. E 15, 473 (2004)] recently published a viscoelastic contact mechanics analysis of the embedment of gold nanospheres into a polystyrene (PS) surface. In the present comment, we investigate the viscoelastic response of the surface and conclude that the embedment experiments do not support the hypothesis of a liquid surface layer of sufficiently reduced “rheological temperature” to explain reports of very large reductions in the glass temperature of freely standing ultrathin polystyrene films. We also report some errors and discrepancies in the paper under comment that resulted in an inability to reproduce the reported calculations. We present our findings of error in a spirit of clarifying the problem of embedment of spheres into surfaces and in order that others can understand why they may not reproduce the results reported by Sharp, Teichroeb and Forrest. In the comment, we also examine the effects of the magnitude of the forces that result from the polymer surface-nanosphere particle interactions on the viscoelastic properties deduced from the embedment data and we provide a comparison of apparent surface or “rheological” temperature vs. experimental temperature that indicates further work needs to be performed to fully understand the surface embedment experiments. Finally, we comment that the nanosphere embedment measurements have potential as a powerful tool to determine surface viscoelastic properties.     

More on finite element modeling of damped composite systems

Finite element procedures are developed and verified for layered beams and rings having either continuously or discontinuously constrained viscoelastic damping layers. The two configurations considered are (1) a three-layered sandwich beam or ring (closed curved beam) consisting of two thin elastic layers with a viscoelastic core in between, and (2) a damped composite made of a thin-walled elastic structure having a finite number of mass segments or elastic segments adhered to it by a viscoelastic material. Viscoelastic material dependence on frequency and temperature is accounted for. Numerical predictions of transverse driving point impedances agree very well with available experimental data.     

Surface effects in plastic deformation of metals

It is now accepted that the appearance of slip bands on the surface of a plastically deformed metal is evidence that the deformation is not homogeneous but is concentrated on relatively few atomic planes. Recent microscopical experiments have suggested that this conclusion is only valid in the later stages of deformation and that the first fractional per cent of strain is much more nearly homogeneous. Theories to account for both these stages of deformation are examined in the light of microscopical evidence.

The validity of conclusions about internal processes based on experiments on the surface is discussed; it is shown that the surface finish affects not only the appearance of internal processes but also the processes themselves.

In cases where the deformation is not homogeneous the balance of evidence is that it is also not continuous in time: instead, slip on an active slip plane tends to a limit which is reached either gradually or suddenly depending on the nature of the metal and the conditions of stress. The same processes which stop slip on the active planes produce general hardening of the metal. However, slip can restart on or near to former slip planes as a result of mechanisms activated by temperature and stress, and can, in favourable cases, continue until fracture. Therefore slip bands, the sources of hardening, are also places of weakness.     

Plastic slip distribution in two-phase laminate microstructures: Dislocation-based versus generalized-continuum approaches

The size-dependent mechanical response of a simple model microstructure is investigated using continuum dislocation-based, Cosserat and strain-gradient models of crystal plasticity. The governing equations and closed-form analytical solutions for plastic slip and lattice rotation are directly compared. The microstructure consists of a periodic succession of hard (elastic) and soft (elastoplastic single-crystal) layers, subjected to single glide perpendicular to the layers. In the dislocation-based approach, inhomogeneous plastic deformation and lattice rotation are shown to develop in the soft channels, either because of bowing of dislocations or owing to pile-up formation. The generalized continuum non-local models are found to be able to reproduce the plastic slip and lattice rotation distribution. In particular, a correspondence was found between the generalized-continuum results and line tension effects; the additional or higher- order balance equations introduced in the non-local models turn out to be the counterparts of the equilibrium equation for bowed dislocations. The relevance and possible physical interpretation of additional or higher-order interface conditions responsible for the inhomogeneous distribution of plastic slip and lattice rotations are discussed.