Fluctuating particle motion during shear induced granular compaction

Using a refractive index matching method, we investigate the trajectories of particles in three dimensional granular packing submitted to cyclic shear deformation. The particle motion observed during compaction is not diffusive but exhibits a transient cage effect, similar to the one observed in colloidal glasses. We precisely study the statistics of the step size between two successive cycles and observe that it is proportional to the shear amplitude. The link between the microscopic observations and the macroscopic evolution of the volume fraction during compaction is discussed.     

Creep motion of a granular pile induced by thermal cycling

We report a time-resolved study of the dynamics associated with the slow compaction of a granular column submitted to thermal cycles. The column height displays a complex behavior: for a large amplitude of the temperature cycles, the granular column settles continuously, experiencing a small settling at each cycle. By contrast, for a small-enough amplitude, the column exhibits a discontinuous and intermittent activity: successive collapses are separated by quiescent periods whose duration is exponentially distributed. We then discuss potential mechanisms which would account for both the compaction and the transition at finite amplitude.     

Applications of compaction testing to the processability of rigid PVC compounds

A compaction test has been developed to examine the lubrication and fusion characteristics of PVC compounds. A model of the compaction process at low pressures is proposed which involves two distinct modes of compaction. Initial densification quickly reaches a plateau density, the magnitude of which is determined primarily by frictional properties and the elastic deformability. of the resin particles. A second slower rate densification is attributed to fusion within the PVC resin grains, as well as diffusion between grains. It is shown that compaction alone is insufficient for grain boundary destruction. As a result, significantly higher temperatures are needed to achieve a given state of elasticity development by compaction when compared to material produced by shear processing.     

Slow nonlinearity kinetics of the viscoelastic properties of oil during shear vibrations

Earlier we discovered the slow evolution of viscoelastic moduli of heavy crude oil. The shear modulus was measured at frequencies of 0.5, 5, and 50 Hz at different temperatures over 72 h. New studies of the dependence of the complex shear modulus on the strain amplitude revealed a logarithmic increase in the nonlinearity parameter as a function of time for this oil sample. It was experimentally established that the complex shear modulus is a linear function of the amplitude of shear perturbations. This is possible in the case of a linear dependence of values of the viscoelastic characteristics on the medium modulus of deformation.     

An elastic,plastic, viscous model for slow shear of a liquid foam

We suggest a scalar model for deformation and flow of an amorphous material such as a foam or an emulsion. To describe elastic, plastic and viscous behaviours, we use three scalar variables: elastic deformation, plastic deformation rate and total deformation rate; and three material-specific parameters: shear modulus, yield deformation and viscosity. We obtain equations valid for different types of deformations and flows slower than the relaxation rate towards mechanical equilibrium. In particular, they are valid both in transient or steady flow regimes, even at large elastic deformation. We discuss why viscosity can be relevant even in this slow shear (often called “quasi-static”) limit. Predictions of the storage and loss moduli agree with the experimental literature, and explain with simple arguments the non-linear large amplitude trends.     

Asymptotic Analysis of Vertical Branch-Cut Integral of Shear Waves in a Fluid-Filled Borehole Utilizing the Steepest-Descent Method

We obtain an asymptotic solution to the vertical branch-cut integral of shear waves excited by an impulsive pressure point source in a fluid-filled borehole, by taking the effect of the infinite singularity of the Hankel functions related to shear waves in the integrand at the shear branch point into account and using the method of steepest-descent to expand the vertical branch-cut integral of shear waves. It is theoretically proven that the saddle point of the integrand is located at ks-i/z, where ks and z are the shear branch point and the offset. The continuous and smooth amplitude spectra and the resonant peaks of shear waves are numerically calculated from the asymptotic solution. These asymptotic results are generally in agreement with the numerical integral results. It is also found by the comparison and analysis of two results that the resonant factor and the effect of the normal and leaking mode poles around the shear branch point lead to the two-peak characteristics of the amplitude spectra of shear waves in the resonant peak zones from the numerical integral calculations.     

Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model

The flexural vibration of the fluid-conveying single-walled carbon nanotube (SWCNT) is derived by the Timoshenko beam model, including rotary inertia and transverse shear deformation. The effects of the flow velocity and the aspect ratio of length to diameter on the vibration frequency and mode shape of the SWCNT are analyzed. Results show that the effects of rotary inertia and transverse shear deformation result in a reduction of the vibration frequencies, especially for higher modes of vibration and short nanotubes. The frequency is also compared with the previous study based on Euler beam model. In addition, if the ratio of length to diameter increased to 60, the influence of the shear deformation and rotary inertia on the mode shape and the resonant frequencies can be neglected. However, the influence is very obvious when the ratio decreased to 20. As the flow velocity of the fluid increases in the vicinity of 2π, the SWCNT reveals the divergence instability. It regains stability when the flow velocity reaches about 9. As the velocity increases further, the SWCNT undergoes a coupled-mode flutter and results in a larger amplitude.     

Initiation and evolution of current ripples on a flat sand bed under turbulent water flow

We investigate the formation and dynamics of sand ripples under a turbulent water flow. Our experiments were conducted in an open flume with spherical glass beads between 100 and 500μm in diameter. The flow Reynolds number is of the order of 10 000 and the particle Reynolds number of the order of 1 to 10. We study the development of ripples by measuring their wavelength and amplitude in course of time and investigate the influence of the grain size and the flow properties. In particular, we demonstrate two different regimes according to the grain size. For fine grains, a slow coarsening process (i.e., a logarithmic increase of the wavelength and amplitude) takes place, while for coarser grains, this process occurs at a much faster rate (i.e., with a linear growth) and stops after a finite time. In the later case, a stable pattern is eventually observed. Besides, we carefully analyze the wavelength of ripples in the first stages of the instability as a function of the grain size and the shear velocity of the flow, and compare our results with other available experimental data and with theoretical predictions based on linear stability analyses.     

Transient and oscillatory granular shear flow

The forces and particle motion during transient and oscillatory shear of granular material are investigated experimentally. In a shear cell of Taylor-Couette-type we find that how a granular shear flow starts depends strongly on the prior shear direction. If the shear direction is reversed, the material goes through a transient period during which the material compacts, the shear force is small, and the shear band is wide. Three-dimensional confocal imaging of particle rearrangements during shear reversal shows that bulk and surface flows are comparable. Repeated reversals, or oscillations of the shear direction, lead to additional compaction, which can be described by a stretched exponential, similar to compaction induced by tapping.     

Origin of the slow dynamics and the aging of a soft glass

We study by light microscopy a soft glass consisting of a compact arrangement of polydisperse multilamellar vesicles. We show that its slow and nonstationary dynamics results from the unavoidable small fluctuations of temperature, which induce intermittent local shear deformations in the sample, because of thermal expansion and contraction. Temperature-induced shear provokes both reversible and irreversible rearrangements whose amplitude decreases with time, leading to an exponential slowing down of the dynamics with sample age.     

Shear banding instability in wormlike micellar solutions

Using NMR velocimetry and mechanical measurements we study the flow dynamics, within a cone-and-plate rheometer, of the wormlike micelle system, cetylpyridinium chloride/sodium salicylate (CPyCl/NaSal) at 100 mM/60 mM concentration in distilled water. Depending on precise conditions within the system, two classes of behaviour are observed, one in which the boundary between different shear rate phases fluctuates rapidly (on the order of tens of milliseconds) and one in which it migrates slowly with a time constant of many seconds. These modes of behaviour may depend on minor solution impurities, which presumably affect the detailed constitutive properties, but also on the externally applied shear rate within a given system. We argue that the slow migrations are governed by stress relaxation effects while the rapid migrations are flow driven and arise from interfacial instability. Received: 2 June 1998 / Received in final form and Accepted: 27 July 1998     

Rapid and localized electron internal-transport-barrier formation during shear inversion in fully noninductive TCV discharges

Clear evidence is reported for the first time of a rapid localized reduction of core electron energy diffusivity during the formation of an electron internal-transport barrier. The transition occurs rapidly (approximately = 3 ms), during a slow (approximately = 200 ms) self-inductive evolution of the magnetic shear. This crucial observation, and the correlation of the transition with the time and location of the magnetic shear reversal, lend support to models attributing the reduced transport to the local properties of a zero-shear region, in contrast to models predicting a gradual reduction due to a weak or negative shear.     

On stochastic stabilization of the Kelvin-Helmholtz instability by three-wave resonant interaction

An analytical investigation of the effect of three-wave resonant interactions with the linearly unstable wave is proposed. We consider the waves in the Kelvin-Helmholtz model, consisting of two fluid layers with different densities and velocities. We suppose that the velocity shear is weakly supercritical, the instability is of the algebraic type, i.e., the amplitude of the unstable wave grows linearly, and the instability occurs within the framework of a single mode. The amplitudes of two other waves taking part in the nonlinear interaction are assumed to be stable. The initial amplitudes of these waves are supposed to be small in comparison with the initial amplitude of the unstable wave. We present an analysis of the system of amplitude equations derived for this case using JWKB-method. As a result, we obtain equations that couple solutions pre- and post-passing the singular point, i.e., the point where the amplitude of the unstable wave has a local minimum. These equations give us the transformation rule of a parameter that characterizes the phase shift between fast and slow waves and defines the behavior of the system. This parameter is constant between two singular points and varies by chance at a singular point. As long as it stays positive, the amplitude of the wave remains limited and performs stochastic oscillations. If this parameter passes over zero, then we leave the region of stabilization and turn out in the region, where the amplitude grows infinitely. Accordingly, the transition to the region of instability happens stochastically. However, if the time interval, when the amplitude remains bounded, is large enough, the proposed scenario can be treated as a partial stabilization of instability.     

Application of surface and normal ultrasonic waves for measuring the parameters of technical fluids: I. Shear viscosity measurements

The effect of the viscosity of a fluid on the propagation of the zero mode of a horizontally polarized normal wave in a thin (compared to the wavelength) waveguide immersed in the fluid is studied. It is shown that, to a first approximation in the ratio of the shear impedance of the fluid to the shear impedance of the waveguide, the wave amplitude decays exponentially as a function of the distance at a damping coefficient proportional to the square root of the shear viscosity of the fluid. The decrease in the wave amplitude induced by the shear viscosity of the fluid is numerically estimated, and the results obtained point to the possibility of developing a method for its measurement at a high accuracy. This method was developed and tested on a waveguide in the form of an aluminum ribbon 0.3 mm thick and 14 cm long at a frequency of 2 MHz. The decrease in the signal amplitude when the waveguide is immersed in distilled water (tabulated shear viscosity is 1.05 × 10^?3 Pa s) is found to be 0.42 dB as compared to the amplitude in the unloaded waveguide, which can be considered as the sensitivity of the experimental setup. A method for calibrating the sensor is described. The shear viscosities of solutions of saccharose in distilled water are measured, and the experimental results agree well with the theoretical estimates.     

Observation of ultraslow light propagation in a ruby crystal at room temperature

We have observed slow light propagation with a group velocity as low as 57.5+/-0.5 m/s at room temperature in a ruby crystal. A quantum coherence effect, coherent population oscillations, produces a very narrow spectral "hole" in the homogeneously broadened absorption profile of ruby. The resulting rapid spectral variation of the refractive index leads to a large value of the group index. We observe slow light propagation both for Gaussian-shaped light pulses and for amplitude modulated optical beams in a system that is much simpler than those previously used for generating slow light.     

Undulation instability of lamellar phases under shear: A mechanism for onion formation?

We consider a lamellar phase of bilayer membranes held between two parallel plates and subject to a steady shear. Accounting for the coupling with the shear flow of the short wavelength undulation modes that are responsible for the membrane excess area, we argue that the flow generates an effective force which acts to reduce the excess area. From the viewpoint of the macroscopic lamellar whose geometric dimensions are fixed, this force translates into an effective lateral pressure. At low shear rates this pressure is balanced by the elastic restoring forces of the lamellar. Above a critical shear rate , where d is the interlayer distance and D is the gap spacing, the lamellar buckles into a harmonic shape modulation, and we predict its wavelength and amplitude . We show that our model is isomorphic to a dilative strain, which is known to induce a similar buckling (undulation) instability. Indeed, at threshold the wavelength is and is identical in both cases. Using a non-linear analysis, we discuss how the wavelength and amplitude vary with shear rate away from the threshold. For we find and . We then focus on the coupling of the buckling modulation itself with the flow, and obtain a criterion for the limit of its stability. Motivated by experiments of D. Roux and coworkers, we assume that at this limit of stability the lamellar breakups into “onion"-like, multilamellar, vesicles. The critical shear rate for the formation of onions is predicted to scale as . The scaling with d is consistent with available experimental data. Received 15 April 1998 and Received in final form 4 March 1999     

Variations in,and Relationships of Surface Area,internal angle of friction and compact diametral fracture strength with degree of compaction

The progress of the compaction process to produce from an assembly of particles a coherent mass can be achieved by the application of shear and normal stress. The achievement of a densified coherent mass necessitates, together with the yielding of material, the movement of particles over and between each other. In uniaxial compaction the angle of internal friction, δ_E, is a projection of the unique critical state line which divides a three dimensional relationship between volume change (V), shear stress (?) and normal stress (σ) into yield domains and surfaces. There is one region for failure and flow (the Hvorslev surface) and another region for failure and consolidation (the Roscoe surface). In this paper the concepts of the Roscoe and Hvorslev surfaces together with the Coulomb yield criterion have been applied to the uniaxial compaction, over a range of compactable stresses, of titanium dioxide (20–2000 kPa). The characteristics of applied and shear stress, angle of internal friction (δ_E), angle of shearing resistance (?) and surface area (S_BET) were measured and correlated with the compaction stress (σ_c) and diametral strength (σ_f) of the compacts to investigate the phenomena of uniaxial compaction.     

Novel vibrational resonance in multistable systems

We investigate the role of multistable states on the occurrence of vibrational resonance in a periodic potential system driven by both a low-frequency and a high-frequency periodic force in both underdamped and overdamped limits. In both cases, when the amplitude of the high-frequency force is varied, the response amplitude at the low-frequency exhibits a series of resonance peaks and approaches a limiting value. Using a theoretical approach, we analyse the mechanism of multiresonance in terms of the resonant frequency and the stability of the equilibrium points of the equation of motion of the slow variable. In the overdamped system, the response amplitude is always higher than in the absence of the high-frequency force. However, in the underdamped system, this happens only if the low-frequency is less than 1. In the underdamped system, the response amplitude is maximum when the equilibrium point around which slow oscillations take place is maximally stable and minimum at the transcritical bifurcation. And in the overdamped system, it is maximum at the transcritical bifurcation and minimum when the associated equilibrium point is maximally stable. When the periodicity of the potential is truncated, the system displays only a few resonance peaks.     

Echo tracer dispersion in flows of polymer solutions through porous media: A tool for detecting weak permeability heterogeneities?

Tracer dispersion in Newtonian and shear-thinning fluids (scleroglucan-water polymer solutions) flowing through single and double porosity grain packings has been studied experimentally using both classical transmission dispersion and echo dispersion (in the latter, the concentration variation front is pumped back through a detector at the inlet after penetrating for a chosen distance into the sample). Transmission dispersion increases markedly in both types of samples with the shear thinning index of the fluid at all Péclet numbers (except when molecular diffusion is dominant). Echo and transmission experiments give nearly identical dispersivity values for Newtonian fluids while echo dispersivity is lower than transmission for shear thinning ones. The normalized dispersivity difference has same order of magnitude for single and double porosity samples and increases with the shear thinning exponent α (by a factor of 2 between α = 0.35 and α = 0.60). This difference may be due to heterogeneities inducing permeability variations of small amplitude over distances of the order of the sample section : their influence on tracer dispersion is partly reversible with respect to a change of the flow direction and is only detectable if it is amplified by the shear-thinning properties of the fluid. Received 19 September 2001     

Drift-wave instability excited by field-aligned ion flow velocity shear in the absence of electron current

The drift wave is observed to be destabilized by a magnetic-field-aligned ion flow velocity shear in the absence of field-aligned electron drift flow in laboratory experiments using a concentrically three-segmented plasma source. The fluctuation amplitude increases with increasing a shear strength, but the instability is found to be gradually stabilized when the shear strength exceeds a critical value. The destabilizing and stabilizing mechanisms are well explained by a plasma kinetic theory including the effect of radial density gradient.