Time dependent diffusion in a disordered medium with partially absorbing walls: A perturbative approach

We present an analytical study of the time dependent diffusion coefficient in a dilute suspension of spheres with partially absorbing boundary condition. Following Kirkpatrick (J. Chem. Phys. 76, 4255) we obtain a perturbative expansion for the time dependent particle density using volume fraction $f$ of spheres as an expansion parameter. The exact single particle $t$-operator for partially absorbing boundary condition is used to obtain a closed form time-dependent diffusion coefficient $D(t)$ accurate to first order in the volume fraction $f$. Short and long time limits of $D(t)$ are checked against the known short-time results for partially or fully absorbing boundary conditions and long-time results for reflecting boundary conditions. For fully absorbing boundary condition the long time diffusion coefficient is found to be $D(t)=5 a^2/(12 f D_{0} t) +O((D_0t/a^2)^{-2})$, to the first order of perturbation theory. Here $f$ is small but non-zero, $D_0$ the diffusion coefficient in the absence of spheres, and $a$ the radius of the spheres. The validity of this perturbative result is discussed

How the geometry makes the criticality in two - component spreading phenomena?

We study numerically a two-component A-B spreading model (SMK model) for concave and convex radial growth of 2d-geometries. The seed is chosen to be an occupied circle line, and growth spreads inside the circle (concave geometry) or outside the circle (convex geometry). On the basis of generalised diffusion-annihilation equation for domain evolution, we derive the mean field relations describing quite well the results of numerical investigations. We conclude that the intrinsic universality of the SMK does not depend on the geometry and the dependence of criticality versus the curvature observed in numerical experiments is only an apparent effect. We discuss the dependence of the apparent critical exponent $\chi_{a}$ upon the spreading geometry and initial conditions.Comment: Uses iopart.cls, 11 pages with 8 postscript figures embedde

Apparent Rate Constant for Diffusion-Controlled Three molecular (catalytic) reaction

We present simple explicit estimates for the apparent reaction rate constant for three molecular reactions, which are important in catalysis. For small concentrations and $d> 1$, the apparent reaction rate constant depends only on the diffusion coefficients and sizes of the particles. For small concentrations and $d\le 1$, it is also time -- dependent. For large concentrations, it gains the dependence on concentrations.Comment: 12 pages, LaTeX, Revised: missing ref. for important paper by G. Oshanin and A. Blumen was added and minor misprints correcte

On the evolution of nanocluster size distribution in a nanocluster aggregation source

This paper presents a detailed model of cluster formation from a supersaturated atomic vapor in an inert buffer gas. The population balance equations for the cluster size distribution are based on the Smoluchowski coagulation equation and take into account (i) convective diffusion of clusters, (ii) cluster loss to walls of an aggregation chamber, and (iii) formation of fractal-like aggregates. The model predictions are confronted to experimental observations, and they agree with experimental data on Cu particle formation in NC200-UHV nanocluster source. The model can be used as an aid in tuning the experimental parameters for attaining a desired nanoparticle size distribution.