225 research outputs found
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 . 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 , 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 for very dilute
suspensions, and show that, when this force is very short-ranged, becomes
proportional to as . In contrast, when the range of the
non-hydrodynamic interaction is increased, we observe a crossover in the
dependence of on , from to as .Comment: Submitted to J. Fluid Mec
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
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 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
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