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The expressions for the friction coefficient of a diffusing particle, obtained from a completely molecular theory in a previous paper, are solved for a Brownian particle in a compressible fluid. In appropriate limits the exact forms of the hydrodynamic friction coefficients in the slip and stick limits are reproduced. The use of the hydrodynamic results in describing the velocity autocorrelation function (VACF) of a molecule is discussed.

Comparaison des donnees experimentales existantes sur la diffusion d'especes macroparticulaires, a haute concentration avec quelques-unes des theories proposees pour expliquer ce comportement (theories semimicroscopiques et theories microscopiques)

The diffusion coefficient $D$ and the Ostwald solubility $\ensuremath{\alpha}$ have been measured for $^{133}\mathrm{Xe}$ atoms in water-sucrose solutions ranging in viscosity $\ensuremath{\eta}$ from 1 to 289 cP, i.e., 0.68% sucrose by weight. In water $D(20\ifmmode^\circ\else\textdegree\fi{}\mathrm{C})=(1.32\ifmmode\pm\else\textpm\fi{}0.05)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ ${\mathrm{cm}}^{2}$/sec, in agreement with the Stokes-Einstein (SE) law. Over the entire range studied the observed dependence is $D\ensuremath{\propto}{\ensuremath{\eta}}^{\ensuremath{-}0.63\ifmmode\pm\else\textpm\fi{}0.02}$, significantly departing from the SE law. In water $\ensuremath{\alpha}(20\ifmmode^\circ\else\textdegree\fi{}\mathrm{C})=0.108\ifmmode\pm\else\textpm\fi{}0.005$. For water-sucrose solutions $\ensuremath{\alpha}$ is approximately proportional to the volume fraction of water in solution.

An empirical relation between diffusion coefficients and viscosities is proposed which interpolates between the kinetic theory of dilute gases and the Stokes-Einstein equation of liquids. This extended Stokes-Einstein-relationship is tested with experimental examples. It is useful for studies of reaction processes over large density ranges.

The autocorrelation function of the density of a tagged particle is studied using the Mori formalism. The variables used are the collective conserved variables, the tagged-particle density, and bilinear products thereof. The case of point particles is considered in two dimensions, and, in three dimensions, self-diffusion by a particle of arbitrary size is treated. It is found that the bilinear-hydrodynamic approach automatically separates the self-diffusion coefficient of the tagged particle into a nonhydrodynamic part, and a hydrodynamic part which resembles the Stokes-Einstein law. In two dimensions, it is found that the mean-square displacement of a particle increases as $t\mathrm{ln}t$, and that certain natural redefinitions of the diffusion and friction coefficients leave Einstein's law invariant. In three dimensions, for a large particle, the Stokes-Einstein law is reproduced. The relation between the well-known ${t}^{(\frac{\ensuremath{-}3}{2})}$ "tails" on correlation functions, and the Stokes-Einstein law, is discussed.

Diffusion quasi elastique de la lumiere de spheres de latex de polystyrene carboxyle dans des solutions polyoxyde d'ethylene-eau

The diffusion coefficient associated with the order-parameter fluctuations near the critical point of fluids is expected to vanish asymptotically as $D=\frac{\mathrm{RkT}}{6\ensuremath{\pi}\ensuremath{\eta}\ensuremath{\xi}}$, where $\ensuremath{\eta}$ is the viscosity, $\ensuremath{\xi}$ the correlation length, and $R$ a universal constant. Our experiments, using 3-methylpentane-nitroethane, yield $R=1.02\ifmmode\pm\else\textpm\fi{}0.06$, in agreement with the mode-coupling theory of critical fluctuations, but in disagreement with the value $\frac{R}{6\ensuremath{\pi}}=\frac{1.2}{6\ensuremath{\pi}}\ensuremath{\simeq}\frac{1}{5\ensuremath{\pi}}$, recently suggested by several investigators.

Environmental concern has been recently more and more directed towards the emission of soot particles from engines and flames, because of the carcinogenic properties of such particulates which are carried deeply inside the lungs. New methods of in situ measurements of soot diameters are thus desired in order to study the phenomenon of soot growing or to continuously control emission from various devices. Such measurements carried out by means of Diffusion Broadening Spectroscopy (DBS) are here reported.

Mesure du coefficient de diffusion, D, d'atomes 133 Xe diffusant a travers 12 n-alkanes liquides, du n-pentane au n-hexadecane, a 20,0°C. Les variations de D (cm 2 /s) en fonction de la viscosite η(P) est donnee par D=(1,26±0,06)×10 −6 η −0,686±0,011 , ou η 20,0°C varie de facon monotone dans ces solvants de 0,235 cP (pour n-C 5 H 12 ) a 3,48 cP (pour n-C 16 H 34 ). L'observation que D est proportionnel a η a la puissance ∼-2/3, est en accord avec d'autres observations faites sur differents systemes solute-solvant. On suggere quelques ramifications de cette variation

Significant progress has been made concerning the understanding of several aspects of microstructure and dynamics of concentrated suspensions. Among these aspects are the proper description of the small-angle peak observed in scattering from aggregating colloids, the theories for the phase behaviour of colloid-polymer mixtures as well as of binary hard-sphere suspensions and the quantitative calculation of the effects of hydrodynamic interaction on the short dynamics of charge-stabilized colloids. There have been several theoretical and experimental investigations on possible generalizations of the Stokes Einstein relation to concentrated suspensions. Mode-coupling theory for the glass transition describes nearly monodisperse hard-sphere systems well, but is found to fail partially for other systems.

Empirically motivated modifications of the Stokes–Einstein formula, in which the diffusion coefficient is inversely proportional to a fractional power of the viscosity, are discussed. We suggest that the results should be analyzed in terms of an effective hydrodynamic radius.

By adopting a simple notion of the volume of a molecule it has been possible to produce an empirical correction factor for the Stokes equation to enable one to apply it to molecules down to two angstroms in radius.