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

Taylor dispersion with absorbing boundaries: A Stochastic Approach

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

FREQUENCY DEPENDENT DIELECTRIC AND CONDUCTIVITY RESPONSE OF SEDIMENTARY ROCKS.

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

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

Time-of-flight flow imaging using NMR remote detection

A time-of-flight imaging technique is introduced to visualize fluid flow and dispersion through porous media using NMR. As the fluid flows through a sample, the nuclear spin magnetization is modulated by RF pulses and magnetic field gradients to encode the spatial coordinates of the fluid. When the fluid leaves the sample, its magnetization is recorded by a second RF coil. This scheme not only facilitates a time-dependent imaging of fluid flow, it also allows a separate optimization of encoding and detection subsystems to enhance overall sensitivity. The technique is demonstrated by imaging gas flow through a porous rock

Time-of-flight flow imaging using NMR remote detection

A time-of-flight imaging technique is introduced to visualize fluid flow and dispersion through porous media using NMR. As the fluid flows through a sample, the nuclear spin magnetization is modulated by RF pulses and magnetic field gradients to encode the spatial coordinates of the fluid. When the fluid leaves the sample, its magnetization is recorded by a second RF coil. This scheme not only facilitates a time-dependent imaging of fluid flow, it also allows a separate optimization of encoding and detection subsystems to enhance overall sensitivity. The technique is demonstrated by imaging gas flow through a porous rock