Microstructure and velocity fluctuations in sheared suspensions

The velocity fluctuations present in macroscopically homogeneous suspensions of neutrally buoyant, non-Brownian spheres undergoing simple shear flow, and their dependence on the microstructure developed by the suspensions, are investigated in the limit of vanishingly small Reynolds numbers using Stokesian dynamics simulations. We show that, in the dilute limit, the standard deviation of the velocity fluctuations is proportional to the volume fraction, in both the transverse and the flow directions, and that a theoretical prediction, which considers only for the hydrodynamic interactions between isolated pairs of spheres, is in good agreement with the numerical results at low concentrations. We also simulate the velocity fluctuations that would result from a random hard-sphere distribution of spheres in simple shear flow, and thereby investigate the effects of the microstructure on the velocity fluctuations. Analogous results are discussed for the fluctuations in the angular velocity of the suspended spheres. In addition, we present the probability density functions for all the linear and angular velocity components, and for three different concentrations, showing a transition from a Gaussian to an Exponential and finally to a Stretched Exponential functional form as the volume fraction is decreased. We also show that, although the pair distribution function recovers its fore-aft symmetry in dilute suspensions, it remains anisotropic and that this anisotropy can be accurately described by assuming the complete absence of any permanent doublets of spheres. We finally present a simple correction to the analysis of laser-Doppler velocimetry measurements.Comment: Submitted to Journal of Fluid Mechanic

Deterministic and stochastic behaviour of non-Brownian spheres in sheared suspensions

The dynamics of macroscopically homogeneous sheared suspensions of neutrally buoyant, non-Brownian spheres is investigated in the limit of vanishingly small Reynolds numbers using Stokesian dynamics. We show that the complex dynamics of sheared suspensions can be characterized as a chaotic motion in phase space and determine the dependence of the largest Lyapunov exponent on the volume fraction $\phi$. The loss of memory at the microscopic level of individual particles is also shown in terms of the autocorrelation functions for the two transverse velocity components. Moreover, a negative correlation in the transverse particle velocities is seen to exist at the lower concentrations, an effect which we explain on the basis of the dynamics of two isolated spheres undergoing simple shear. In addition, we calculate the probability distribution function of the velocity fluctuations and observe, with increasing $\phi$, a transition from exponential to Gaussian distributions. The simulations include a non-hydrodynamic repulsive interaction between the spheres which qualitatively models the effects of surface roughness and other irreversible effects, such as residual Brownian displacements, that become particularly important whenever pairs of spheres are nearly touching. We investigate the effects of such a non-hydrodynamic interparticle force on the scaling of the particle tracer diffusion coefficient $D$ for very dilute suspensions, and show that, when this force is very short-ranged, $D$ becomes proportional to $\phi^2$ as $\phi \to 0$. In contrast, when the range of the non-hydrodynamic interaction is increased, we observe a crossover in the dependence of $D$ on $\phi$, from $\phi^2$ to $\phi$ as $\phi \to 0$.Comment: Submitted to J. Fluid Mec

Optical Studies of Metal- Semiconductor Transmutations Produced by Intercalation

Spectra of the alkali metal intercalation products of MoS2 and NbSc2 arc interpreted in terms of a previously published band model

Shear-induced particle diffusivities from numerical simulations

Using Stokesian dynamics simulations, we examine the flow of a monodisperse, neutrally buoyant, homogeneous suspension of non-Brownian solid spheres in simple shear, starting from a large number of independent hard-sphere distributions and ensemble averaging the results. We construct a novel method for computing the gradient diffusivity via simulations on a {\em homogeneous} suspension and, although our results are only approximate due to the small number of particles used in the simulations, we present here the first values of this important parameter, both along and normal to the plane of shear, which have ever been obtained directly either experimentally or numerically. We show furthermore that, although the system of equations describing the particle motions is deterministic, the particle displacements in the two directions normal to the bulk flow have Gaussian distributions with zero mean and, a variance which eventually grows linearly in time thereby establishing that the system of particles is diffusive. In addition we show that although the particle evolution equations are, in principle, reversible, the suspension has in fact a finite correlation time $T_c$ of the order of the inverse shear rate. For particle concentrations up to 45%, we compute the corresponding tracer diffusivities both from the slope of the mean square particle displacement as well as by integrating the corresponding velocity autocorrelations and find good agreement between the two sets of results.Comment: 51 pages ; 16 figures ; 5 tables; submitted to J.Fluid Mec

Mott g-Ratios in Rbx(NH3)1-x and Oxidation state of Rubidium Compounds from XAS

The x-ray absorption spectra (XAS) of Rb metal, Rh,( JH,J, ,, 2H-NbSe2Rb111x and RbBr near the Rb K-edge have been used to ascertain that the oxidation state V of rubidium dissolved in ammonia and intt:rcalated in the layer compound is in the range 0 \u3c V \u3c I. Theobservededge shifts with temperature for semimctals are explainedin terms of the population of band states, and the ratio of the density states near the mobility edge over that calculated for a free electron model, i.e. the Mott ratio g, is ascertained using a semiempirical relation developed for the x-ray absorbance from Is levels to empty states ncar the mobility edge

Forced Convection and Sedimentation Past a Flat Plate

The steady laminar flow of a well-mixed suspension of monodisperse solid spheres, convected steadily past a horizontal flat plate and sedimenting under the action of gravity, is examined. It is shown that, in the limit as Re approaches infinity and epsilon approaches 0, where Re is the bulk Reynolds number and epsilon is the ratio of the particle radius a to the characteristic length scale L, the analysis for determining the particle concentration profile has several aspects in common with that of obtaining the temperature profile in forced-convection heat transfer from a wall to a fluid stream moving at high Reynolds and Prandtl numbers. Specifically, it is found that the particle concentration remains uniform throughout the O(Re(exp -1/2)) thick Blasius boundary layer except for two O(epsilon(exp 2/3)) thin regions on either side of the plate, where the concentration profile becomes non-uniform owing to the presence of shear-induced particle diffusion which balances the particle flux due to convection and sedimentation. The system of equations within this concentration boundary layer admits a similarity solution near the leading edge of the plate, according to which the particle concentration along the top surface of the plate increases from its value in the free stream by an amount proportional to X(exp 5/6), with X measuring the distance along the plate, and decreases in a similar fashion along the underside. But, unlike the case of gravity settling on an inclined plate in the absence of a bulk flow at infinity considered earlier, here the concentration profile remains continuous everywhere. For values of X beyond the region near the leading edge, the particle concentration profile is obtained through the numerical solution of the relevant equations. It is found that, as predicted from the similarity solution, there exists a value of X at which the particle concentration along the top side of the plate attains its maximum value phi(sub m) and that, beyond this point, a stagnant sediment layer will form that grows steadily in time. This critical value of X is computed as a function of phi(sub s), the particle volume fraction in the free stream. In contrast, but again in conformity with the similarity solution, for values of X sufficiently far removed from the leading edge along the underside of the plate, a particle-free region is predicted to form adjacent to the plate. This model, with minor modifications, can be used to describe particle migration in other shear flows, as, for example, in the case of crossflow microfiltration

Investigation of the anisotropy of dissipation processes in single crystal of Yba2Cu3O7-d system

By means of contactless mechanical method of the measurement of energy losses in superconductors, the anisotropy of dissipation processes has been studied in single crystal high-temperature layered superconductors of Yba2Cu3O7-d system, being in mixed state. The observed anisotropy of energy losses indicates the possibility of the existence of the symmetry of order parameter of dx2-y2 type in these single crystals.Comment: 4 pages, 3 figure

Measurement of Synchrotron x-ray energies and line shapes using diffraction markers

Standard reference markers for accurate, reproducible synchrotron x-ray energies are obtained using a three Si crystal spectrometer. The first two crystals are in the monochromator and the third is used to obtain diffraction markers which monitor the energy. Then for any value of the glancing angle on the reference Si crystal the energy for the (333) diffraction must occur at 3/4 that of the (444) and 3/5 of that for the (555). This establishes for the first time an absolute synchrotron energy scale. Higher-order diffractions are used to determine excitation line profiles. We conclude that the use of reference diffractions is necessary to measure reproducible x-ray energies and to analyze the incident photons\u27 line profile. The detection of diffractions near the edge of measurement and near the Cu edge will provide a fast secondary standard which will allow comparison of edge data between different laboratories. The diffraction profiles will allow the proper analysis of spectral line widths

Wetting and particle adsorption in nanoflows

Molecular dynamics simulations are used to study the behavior of closely-fitting spherical and ellipsoidal particles moving through a fluid-filled cylinder at nanometer scales. The particle, the cylinder wall and the fluid solvent are all treated as atomic systems, and special attention is given to the effects of varying the wetting properties of the fluid. Although the modification of the solid-fluid interaction leads to significant changes in the microstructure of the fluid, its transport properties are found to be the same as in bulk. Independently of the shape and relative size of the particle, we find two distinct regimes as a function of the degree of wetting, with a sharp transition between them. In the case of a highly-wetting suspending fluid, the particle moves through the cylinder with an average axial velocity in agreement with that obtained from the solution of the continuum Stokes equations. In contrast, in the case of less-wetting fluids, only the early-time motion of the particle is consistent with continuum dynamics. At later times, the particle is eventually adsorbed onto the wall and subsequently executes an intermittent stick-slip motion.We show that van der Walls forces are the dominant contribution to the particle adsorption phenomenon and that depletion forces are weak enough to allow, in the highly-wetting situation, an initially adsorbed particle to spontaneously desorb