Evidence for re-entrant behavior in laponite–PEO systems

We observe evidence of re-entrant behavior in dispersions of a discotic clay, laponite, with added polymer. Under basic conditions, neat laponite forms a disordered colloidal glass. Rheologically, this phase behaves as a viscoelastic solid, and dynamic light scattering shows evidence of non-ergodic behavior. Addition of low molecular weight poly(ethylene oxide) (PEO) melts the glass, resulting in a low-viscosity liquid with fast dynamics. We believe this is due to a depletion force caused by excess PEO chains in solution. A viscoelastic solid is re-formed with the addition of high molecular weight PEO, which we believe to be caused by polymer chains bridging between laponite particles. The physics in our system is quite different from the hard sphere/nonadsorbing polymer systems for which re-entrant glass transitions have been reported in the literature; however, we believe there may be similarities between these phenomena. To our knowledge, this is the first evidence of a type of re-entrant behavior in anisotropic colloids.     

New insights on fumed colloidal rheology—shear thickening and vorticity-aligned structures in flocculating dispersions

We investigate the rheology of dilute dispersions of fumed colloidal particles with attractive interactions in hydrocarbon liquids. Surprisingly, these systems display shear thickening due to the breakdown of densified flocs and a concomitant increase in the effective volume fraction of the fractal particles in the fluid. We show that this shear thickening is controlled by a critical stress and accompanied by a positive increase in the first normal stress difference, N ₁, at the shear thickening transition. This is in contrast to the well-known hydrocluster mechanism of shear thickening in concentrated hard-sphere and repulsive systems. Gel elasticity depends strongly on the stress applied to suspensions in preshear, scaling roughly as \(G'\sim\sigma_{\text{preshear}}^{2}\). We propose a simple model to account for these results in terms of the cluster number density determined by the preshear stress. At low shear rates, vorticity-aligned aggregates are present at \(\dot\gamma\approx 10^0 {\rm{s}}^{-1}\) . In this regime, the system displays a small but noticeable increase in viscosity on increasing shear rate. We investigate the effect of tool roughness and find that wall slip is not responsible for the observed phenomena. Instead, the increase in the apparent viscosity results from increased flow resistance due to the presence of gap-spanning log-like flocs in rolling flow.     

On the rheology of ethylene–octene copolymers

It has previously been shown that the plateau modulus, G_N^o, and thus the entanglement molecular weight, M_e, of flexible polymers can be correlated to the unperturbed chain dimension, <R²>_o/M, and mass density, , via the use of the packing length, p. For polyolefins, a method was recently proposed whereby knowledge of the average molecular weight per backbone bond, m_b, allows <R²>_o/M and consequently G_N^o and M_e to be estimated. This is particularly valuable for polyolefin copolymers since the melt chain dimensions are often unknown. This work corroborates these theoretical predictions by studying the rheology of a series of carefully synthesized ethylene/octene copolymers with varying octene content (19–92 wt%). Furthermore, the results reported herein also allow the advancement of rheological characterization techniques of polymer melts. For instance, based on the analysis of the linear viscoelastic properties of these copolymers, it has been found that several rheological parameters scale with the copolymer comonomer content. Analysis of the viscoelastic material functions in terms of the evolution of the phase angle, , as a function of the absolute value of the complex modulus, |G*|, (the so-called van Gurp–Palmen plots), provides a fast and reliable rheological means for determining the composition of ethylene/-olefin copolymers. The crossover parameters, G_co(=G=G) and _co(=1/_co) also scale with copolymer composition.Submitted for publication to Rheologica Acta

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An erratum to this article is available at .     

The axisymmetric contraction–expansion: the role of extensional rheology on vortex growth dynamics and the enhanced pressure drop

The flow of a polystyrene Boger fluid through axisymmetric contraction–expansions having various contraction ratios (2≤β≤8) and varying degrees of re-entrant corner curvatures are studied experimentally over a large range of Deborah numbers. The ideal elastic fluid is dilute, monodisperse and well characterized in both shear and transient uniaxial extension. A large enhanced pressure drop above that of a Newtonian fluid is observed independent of contraction ratio and re-entrant corner curvature. Streak images, laser Doppler velocimetry (LDV) and digital particle image velocimetry (DPIV) are used to investigate the flow kinematics upstream of the contraction plane. LDV is used to measure velocity fluctuation in the mean flow field and to characterize a global elastic flow instability which occurs at large Deborah numbers. For a contraction ratio of β=2, a steady elastic lip vortex is observed while for contraction ratios of 4≤β≤8, no lip vortex is observed and a corner vortex is seen. Rounding the re-entrant corner leads to shifts in the onset of the flow transitions at larger Deborah numbers, but does not qualitatively change the overall structure of the flow field. We describe a simple rescaling of the deformation rate which incorporates the effects of lip curvature and allows measurements of vortex size, enhanced pressure drop and critical Deborah number for the onset of elastic instability to be collapsed onto master curves. Transient extensional rheology measurements are utilized to explain the significant differences in vortex growth pathways (i.e. elastic corner vortex versus lip vortex growth) observed between the polystyrene Boger fluids used in this research and polyisobutylene and polyacrylamide Boger fluids used in previous contraction flow experiments. We show that the role of contraction ratio on vortex growth dynamics can be rationalized by considering the dimensionless ratio of the elastic normal stress difference in steady shear flow to those in transient uniaxial extension. It appears that the differences in this normal stress ratio for different fluids at a given Deborah number arise from variations in solvent quality or excluded volume effects.     

Endoscopic effects on the peristaltic flow of an Eyring–Powell fluid

This study investigates the peristaltic flow of Eyring–Powell fluid in an endoscope. The governing equations for Eyring–Powell are modeled in cylindrical coordinates under the assumption of long wavelength and low Reynolds number approximation. The resulting nonlinear differential equations are solved analytically and numerically by employing perturbation method and shooting technique. Numerical integration have been done for pressure rise and frictional forces. Comparative study have been made for both the solutions to see the validity of the results. The effects of various emerging parameters are investigated for five different peristaltic waves. (Basically peristaltic phenomena is a natural phenomena so it is not necessary that peristaltic wave be always a sinusoidal wave it could be multisinusoidal, triangular, trapezoidal and square waves for example heartbeats.) Streamlines have been plotted at the end of the article.     

Simulations of radiative effects on the Rayleigh–Taylor instability using the CRASH code

Future experiments at the National Ignition Facility will be able to generate diagnosable Rayleigh–Taylor instability growth in the presence of locally generated, high radiation fluxes. This interplay of radiative energy transfer and hydrodynamic instability is relevant to many astrophysical systems, such as core-collapse red supergiant supernovae. Previous simulations of high-energy-density Rayleigh–Taylor instabilities in the presence of a hot environment near a radiative shock demonstrate behavior that differs from that found in non-radiative cases. However, these simulations considered only 1D or single wavelength cases. Here we report simulations of an entire experimental system using the CRASH code. These simulations lead to modified predictions, attributed to the effects of radial energy losses.     

Viscous effects on the non-classical Rayleigh–Taylor instability of spherical material interfaces

The viscous and conductivity effects on the instability of a rapidly expanding material interface produced by a spherical shock tube are investigated through the employment of a high-order WENO scheme. The instability is influenced by various mechanisms, which include (a) classical Rayleigh–Taylor (RT) effects, (b) Bell–Plesset or geometry/curvature effects, (c) the effects of impulsively accelerating the interface, (d) compressibility effects, (e) finite thickness effects, and (f) viscous effects. Henceforth, the present instability studied is more appropriately referred to as non-classical RT instability to distinguish it from classical RT instability. The linear regime is examined and the development of the viscous three-dimensional perturbations is obtained by solving a one-dimensional system of partial differential equations. Numerical simulations are performed to illustrate the viscous effects on the growth of the disturbances for various conditions. The inviscid analysis does not show the existence of a maximum amplification rate. The present viscous analysis, however, shows that the growth rate increases with increasing the wave number, but there exists a peak wavenumber beyond which the growth rate decreases with increasing the wave number due to viscous effects.     

Coriolis effects on the stability of pulsed flows in a Taylor–Couette geometry

Results steming from the linear stability of time-periodic flows in a Taylor–Couette geometry with cylinders oscillating in phase or out-of-phase are presented. Our analysis takes into account the gap size effects and investigates the influence of a superimposed mean angular rotation of the whole system.In case of no mean rotation, the finite gap geometry is found to affect the shape of the stability diagrams (critical Taylor number versus the frequency parameter) which consist of two distinct branches as opposed to being continuous in the narrow gap approximation. In particular, in the out-of-phase configuration a new branch for low frequencies was found, thus enabling better agreement with available experimental results.When cylinders are co-rotating and subject to rotation effects, our calculations provide the evolution of the critical Taylor number versus the rotation number for two values of the frequency. The stability curves are found to be in qualitative agreement with available experimental data revealing a maximum of instability for a rotation number of about 0.3.In the high rotation regime, enhancement of the critical Taylor number is investigated through an asymptotic analysis and the value of the rotation number at which restabilization occurs is found to depend on the frequency parameter.A restabilization of the flow also occurs when the rotation number and the gap size are of the same order, a phenomenon already pointed out in the case of steady flows and attributed to the near cancellation of Coriolis and centrifugal effects. Our investigation proves that the same mechanism still holds for time-periodic flows.     

Viscoelastic melt rheology and time–temperature superposition of polycarbonate–multi-walled carbon nanotube nanocomposites

This work investigates the linear and non-linear viscoelastic melt rheology of four grades of polycarbonate melt compounded with 3 wt% Nanocyl NC7000 multi-walled carbon nanotubes and of the matching matrix polymers. Amplitude sweeps reveal an earlier onset of non-linearity and a strain overshoot in the nanocomposites. Mastercurves are constructed from isothermal frequency sweeps using vertical and horizontal shifting. Although all nanocomposites exhibit a second plateau at ～10⁵ Pa, the relaxation times estimated from the peak in loss tangent are not statistically different from those of pure melts estimated from cross-over frequencies: all relaxation timescales scale with molar mass in the same way, evidence that the relaxation of the polymer network is the dominant mechanism in both filled and unfilled materials. Non-linear rheology is also measured in large amplitude oscillatory shear. A comparison of the responses from frequency and amplitude sweep experiments reveals the importance of strain and temperature history on the response of such nanocomposites.     

A new constitutive equation for solid propellant with the effects of aging and viscoelastic Poisson’s ratio

A new constitutive equation for solid propellant with the effects of aging and viscoelastic Poisson’s ratio is proposed. Effects of thermo-oxidative aging and viscoelastic Poisson’s ratio are considered in this comprehensive constitutive equation with two sets of reduced time system coping with the time and temperature dependence. In order to simulate the single and combined effects of aging and viscoelastic Poisson’s ratio, constitutive equation is rewritten into an incremental form and implemented in the user subroutine UMAT at the platform of finite element code ABAQUS. Detailed procedure for acquiring the parameters in constitutive equation is introduced and conducted for the subsequent applied analysis. Two typical loading cases during the service life of solid rocket motor and four sets of combined constitutive models are simulated. Von Mises strain and stress distribution and their changes versus time are utilized as the main analysis index. The results show that the effects of aging and viscoelastic Poisson’s ratio or their combinations will improve or decrease the level and change the distribution of Von Mises strain and stress in varying degrees.     

Study of the effects of inner pressure and surface tension on the fibre drawing process with the aid of an analytical asymptotic fibre drawing model and the numerical solution of the full N.–St. equations

Micro-structured optical fibres (i.e. fibres that contain holes) have assumed a high profile in recent years and given rise to many novel optical devices. The problem of manufacturing such fibres by heating and then drawing a preform is considered for the case of annular capillaries. A fluid mechanics model suggested in the literature that uses asymptotic analysis based on the small aspect ratio of capillaries has been compared with the full 3D set of the N.–St. equations, for modelling the fabrication of capillaries. The final asymptotic equations, analysed in some asymptotic limits, are solved numerically and then compared with the N.–St. solutions, obtained with a commercial finite elements solver. These asymptotic limits give valuable practical information about the control parameters that influence the drawing process, taking into account the effects of surface tension and inner pressure, since those are of essential importance during drawing. It is shown that the asymptotic method delivers reliable results as long as the inner pressure does not exceed too high values.     

Well-Posedness of the Multidimensional Fractional Stochastic Navier–Stokes Equations on the Torus and on Bounded Domains

In this work, we introduce and study the well-posedness of the multidimensional fractional stochastic Navier–Stokes equations on bounded domains and on the torus (briefly dD-FSNSE). For the subcritical regime, we establish thresholds for which a maximal local mild solution exists and satisfies required space and time regularities. We prove that under conditions of Beale–Kato–Majda type, these solutions are global and unique. These conditions are automatically satisfied for the 2D-FSNSE on the torus if the initial data has H ¹-regularity and the diffusion term satisfies growth and Lipschitz conditions corresponding to H ¹-spaces. The case of 2D-FSNSE on the torus is studied separately. In particular, we established thresholds for the global existence, uniqueness, space and time regularities of the weak (strong in probability) solutions in the subcritical regime. For the general regime, we prove the existence of a martingale solution and we establish the uniqueness under a condition of Serrin’s type on the fractional Sobolev spaces.     

Influence of nanoprecipitates on the creep strength and ductility of a Fe–Ni–Al alloy

Creep studies of a duplex Fe–Ni–Al intermetallic alloy, in two microstructural states, have been carried out at temperatures between 725 and 800 °C (about 0.6 T_m). In the as-cast state, the alloy contains a large volume fraction of nanoprecipitates (50–100 nm) which confer a very high creep strength with a stress exponent of 3 and an activation energy of 280 kJ/mol. The different microstructure obtained in the second state of the alloy, obtained after annealing at 1000 °C for 24 h, leads to a much lower creep strength with a higher stress exponent as well as a large value of the apparent activation energy. While volume diffusion appears to control creep in the as-cast state, both thermal and athermal processes seem to contribute to the different creep rate of material in the annealed state. The latter also exhibits a much larger ductility (12%) relative to that observed in the as-cast material (3%), due to the presence of large numbers of interfaces between the two phases present where strain incompatibilities can be accommodated.     

Grafting of polyamide 6 on a styrene–acrylonitrile maleic anhydride terpolymer: melt rheology at the critical gel state

In this work, we studied the melt rheology of multigraft copolymers with a styrene–acrylonitrile maleic anhydride (SANMA) terpolymer backbone and randomly grafted polyamide 6 (PA 6) chains. The multi-grafted chains were formed by interfacial reactions between the maleic anhydride groups of SANMA and the amino end groups of PA 6 during melt blending. Because of the phase separation of SANMA and PA 6, the grafted SANMA backbones formed nearly circular domains which were embedded in the PA 6 melt with a diameter in the order of 20 to 40 nm. The linear viscoelastic behaviour of PA 6/SANMA blends at a sufficiently large SANMA concentration displayed the characteristics of the critical gel state, i.e. the power relations G′ ∝ G′′ ∝ ω ^0.5. In elongation, the PA 6/SANMA blend at the critical gel state showed a non-linear strain hardening behaviour already at a very small Hencky strain. In contrast to neat PA 6, the elasticity of the PA 6/SANMA blends was strongly pronounced, which was demonstrated by recovery experiments. Rheotens tests agreed with the linear viscoelastic shear oscillations and the measurements using the elongational rheometer RME. Increasing the SANMA concentration led to a larger melt strength and a reduced drawability. The occurrence of the critical gel state can be interpreted by the cooperative motion of molecules which develops between the grafted PA 6 chains of neighbouring micelle-like SANMA domains.     

Influence of thermal radiation and Joule heating in the Eyring–Powell fluid flow with the Soret and Dufour effects

A two-dimensional magnetohydrodynamic boundary layer flow of the Eyring–Powell fluid on a stretching surface in the presence of thermal radiation and Joule heating is analyzed. The Soret and Dufour effects are taken into account. Partial differential equations are reduced to a system of ordinary differential equations, and series solutions of the resulting system are derived. Velocity, temperature, and concentration profiles are obtained. The skin friction coefficient and the local Nusselt and Sherwood numbers are computed and analyzed.     

Micron-scale origin of the shear-induced structure in Laponite–poly(ethylene oxide) dispersions

We study the transient response to simple shear of aqueous dispersions of Laponite clay particles and poly(ethylene oxide) at concentrations for which shear induces structure in the form of a network of polymer–clay bonds. We examine the effects of shear on the structure at the micrometer length scale. Bulk rheometric measurements give the material’s response to step changes in shear rate. We find that a critical value of the shear rate separates two regions with different rheological behaviors. Static small-angle light scattering shows a corresponding qualitative change in the anisotropy of the dispersion under shear at the micron scale. We interpret our results in terms of the effects of shear on the interactions between clay particles and polymer chains and on the aggregation mechanisms in the dispersion.