16 research outputs found

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

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    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 ff of spheres as an expansion parameter. The exact single particle tt-operator for partially absorbing boundary condition is used to obtain a closed form time-dependent diffusion coefficient D(t)D(t) accurate to first order in the volume fraction ff. Short and long time limits of D(t)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)=5a2/(12fD0t)+O((D0t/a2)2)D(t)=5 a^2/(12 f D_{0} t) +O((D_0t/a^2)^{-2}), to the first order of perturbation theory. Here ff is small but non-zero, D0D_0 the diffusion coefficient in the absence of spheres, and aa the radius of the spheres. The validity of this perturbative result is discussed

    Taylor dispersion with absorbing boundaries: A Stochastic Approach

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    We describe how to solve the problem of Taylor dispersion in the presence of absorbing boundaries using an exact stochastic formulation. In addition to providing a clear stochastic picture of Taylor dispersion, our method leads to closed-form expressions for all the moments of the convective displacement of the dispersing particles in terms of the transverse diffusion eigenmodes. We also find that the cumulants grow asymptotically linearly with time, ensuring a Gaussian distribution in the long-time limit. As a demonstration of the technique, the first two longitudinal cumulants (yielding respectively the effective velocity and the Taylor diffusion constant) as well as the skewness (a measure of the deviation from normality) are calculated for fluid flow in the parallel plate geometry. We find that the effective velocity and the skewness (which is negative in this case) are enhanced while Taylor dispersion is suppressed due to absorption at the boundary.Comment: 4 pages, 1 figur


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    The paper describes quantitatively how the conductivity and the dielectric constant of water-filled rocks depend on textural and interfacial effects. The grain shape determines the Archie's exponent for the dc conductivity as well as the frequency dependent dielectric constant. The large values of dielectric constant can arise from platey grains. Platey grains also give rise to large frequency and salinity dependences of the dielectric constant. The interfacial effects are particulary important in clayey systems. The polarization of interfacial ions gives rise to large values of dielectric constant and affects the rock conductivity.link_to_subscribed_fulltex

    Electromagnetic Interactions

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    Principles and applications of electromagnetism, starting from Maxwell's equations, with emphasis on phenomena important to nuclear engineering and radiation sciences. Solution methods for electrostatic and magnetostatic fields. Charged particle motion in those fields. Particle acceleration and focussing. Collisons with charged particles and atoms. Electromagnetic waves, wave emission by accelerated particles, Bremsstrahlung. Compton scattering. Photoionization. Elementary applications to ranging, shielding, imaging, and radiation effects