A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics

An approximate analytical technique employing a finite integral transform is developed to solve the reaction diffusion problem with Michaelis-Menten kinetics in a solid of general shape. A simple infinite series solution for the substrate concentration is obtained as a function of the Thiele modulus, modified Sherwood number, and Michaelis constant. An iteration scheme is developed to bring the approximate solution closer to the exact solution. Comparison with the known exact solutions for slab geometry (quadrature) and numerically exact solutions for spherical geometry (orthogonal collocation) shows excellent agreement for all values of the Thiele modulus and Michaelis constant.

Transient response of diffusion cell containing a porous solid

Transient response of an adsorbing or non-adsorbing tracer injected as step or square pulse input in a diffusion cell with two flowing streams across the pellet is theoretically investigated in this paper. Exact solutions and the asymptotic solutions in the time domain and in three different limits are obtained by using an integral transform technique and a singular perturbation technique, respectively. Parametric dependence of the concentrations in the top and bottom chambers can be revealed by investigating the asymptotic solutions, which are far simpler than their exact counterpart. In the time domain investigation, it is found that the bottom-chamber concentration is very sensitive to the value of the macropore effective diffusivity. Therefore this concentration could be used to extract diffusivity by fitting in the time domain. The bottom-chamber concentration is also sensitive to flow rate, pellet length chamber volume and the type of input (step and square input).

Short-term spatial diffusion in sigma o+ o- optical molasses

We have measured the spatial diffusion of atoms in a three-dimensional sigma(+)-sigma(-) optical molasses over twenty milliseconds timescale, starting from the initial interaction of the atoms with the molasses. We find that the diffusion constants agree well with a linear model for these short time scales and also compare favourably to other studies of diffusion made over longer time scales. These measurements enable us to quantify the detection method known as freezing molasses. We discuss this method, for detecting and measuring the momentum distribution of cold atoms, which relies on the slow diffusion of atoms in optical molasses to produce a freeze-frame of the spatial distribution of the atoms. This method enables a longer interrogation interval, providing a greatly increased signal-to-noise ratio. (C) 1998 Elsevier Science B.V.

Coalbed methane sorption related to coal composition

Gas sorption by coal is closely related to its physical and chemical properties, which are, in turn, governed by coal type and rank. The role of coal type (sensu maceral composition) is not fully established but it is clear that coal type may affect both adsorption capacity and desorption rate. Adsorption capacity is closely related to micropore (pores <2 nm) development, which is rank and maceral dependent. Adsorption isotherms indicate that in most cases bright (vitrinite-rich) coals have a greater adsorption capacity than their dull (often inertinite-rich) equivalents. However, no differences, or even the opposing trend, may be observed in relation to coal type. Desorption rate investigations have been performed using selected bright and dull coal samples in a high pressure microbalance. Interpretation of results using unipore spherical and bidisperse pore models indicate the importance of the pore structure. Bright, vitrinite-rich coals usually have the slowest desorption rates which is associated with their highly microporous structure. However, rapid desorption in bright coals may be related to development of extensive, unmineralised fracture systems. Both macro-and micro-pore systems are implicated in the more rapidly desorbing dull coals. Some dull, inertinite-rich coals may rapidly desorb due to a predominance of large, open cell lumina. Mineral matter is essentially nonadsorbent to coal gases and acts as a simple diluent. However, mineral-rich coals may be associated with more rapid desorption. Coal rank and type (maceral composition) per se do not appear to be the critical factors in controlling gas sorption, but rather the influence they exert over pore structure development. (C) 1998 Elsevier Science B.V.

Thermal diffusion in molecular dynamics simulations of thin film diamond deposition

Molecular dynamics simulations of carbon atom depositions are used to investigate energy diffusion from the impact zone. A modified Stillinger-Weber potential models the carbon interactions for both sp2 and sp3 bonding. Simulations were performed on 50 eV carbon atom depositions onto the (111) surface of a 3.8 x 3.4 x 1.0 nm diamond slab containing 2816 atoms in 11 layers of 256 atoms each. The bottom layer was thermostated to 300 K. At every 100th simulation time step (27 fs), the average local kinetic energy, and hence local temperature, is calculated. To do this the substrate is divided into a set of 15 concentric hemispherical zones, each of thickness one atomic diameter (0.14 nm) and centered on the impact point. A 50-eV incident atom heats the local impact zone above 10 000 K. After the initial large transient (200 fs) the impact zone has cooled below 3000 K, then near 1000 K by 1 ps. Thereafter the temperature profile decays approximately as described by diffusion theory, perturbed by atomic scale fluctuations. A continuum model of classical energy transfer is provided by the traditional thermal diffusion equation. The results show that continuum diffusion theory describes well energy diffusion in low energy atomic deposition processes, at distance and time scales larger than 1.5 nm and 1-2 ps, beyond which the energy decays essentially exponentially. (C) 1998 Published by Elsevier Science S.A. All rights reserved.

An evaluation of the time dependence of the anisotropy of the water diffusion tensor in acute human ischemia

We have performed MRI examinations to determine the water diffusion tensor in the brain of six patients who were admitted to the hospital within 12 h after the onset of cerebral ischemic symptoms. The examinations have been carried out immediately after admission, and thereafter at varying intervals up to 90 days post admission. Maps of the trace of the diffusion tensor, the fractional anisotropy and the lattice index, as well as maps of cerebral blood perfusion parameters, were generated to quantitatively assess the character of the water diffusion tensor in the infarcted area. In patients with significant perfusion deficits and substantial lesion volume changes, four of six cases, our measurements show a monotonic and significant decrease in the diffusion anisotropy within the ischemic lesion as a function of time. We propose that retrospective analysis of this quantity, in combination with brain tissue segmentation and cerebral perfusion maps, may be used in future studies to assess the severity of the ischemic event. (C) 1999 Elsevier Science Inc.

Water diffusion in hydroxyethyl methacrylate (HEMA)-based hydrogels formed by gamma-radiolysis

Polymer hydrogels based upon methacrylates are used extensively in the pharmaceutical industry, particularly as controlled release drug delivery systems. These materials are generally prepared by chemically initiated polymerization, but this can lead to the presence of unwanted initiator fragments in the polymer matrix. In the present work, initiation of polymerization by gamma-irradiation of hydroxyethyl methacrylate, with and without added crosslinkers, has been investigated, and the diffusion coefficients for water in the resulting polymers have been measured through mass uptake by the polymers. The diffusion of water in poly(hydroxyethyl methacrylate) at 310 K was found to be Fickian, with a diffusion coefficient of 1.96 +/- 0.1 x 10(11) m(2) s(-1) and an equilibrium water content of 58%, NMR imaging analyses confirmed the adherance to a Fickian model of the diffusion of water into polymer cylinders. The incorporation of small amounts (0.2-0.5 wt%) of added ethyleneglycol-dimethacrylate-based crosslinkers was found to have only a small effect on the diffusion coefficient and the equilibrium water content for the copolymers. (C) 1999 Society of Chemical Industry.

Increasing the efficiency of solute leaching: impacts of flow interruption with drainage of the "preferential flow paths"

Most soils contain preferential flow paths that can impact on solute mobility. Solutes can move rapidly down the preferential flow paths with high pore-water velocities, but can be held in the less permeable region of the soil matrix with low pore-water velocities, thereby reducing the efficiency of leaching. In this study, we conducted leaching experiments with interruption of the flow and drainage of the main flow paths to assess the efficiency of this type of leaching. We compared our experimental results to a simple analytical model, which predicts the influence of the variations in concentration gradients within a single spherical aggregate (SSA) surrounded by preferential flow paths on leaching. We used large (length: 300 mm, diameter: 216 mm) undisturbed field soil cores from two contrasting soil types. To carry out intermittent leaching experiments, the field soil cores were first saturated with tracer solution (CaBr2), and background solution (CaCl2) was applied to mimic a leaching event. The cores were then drained at 25- to 30-cm suction to empty the main flow paths to mimic a dry period during which solutes could redistribute within the undrained region. We also conducted continuous leaching experiments to assess the impact of the dry periods on the efficiency of leaching. The flow interruptions with drainage enhanced leaching by 10-20% for our soils, which was consistent with the model's prediction, given an optimised equivalent aggregate radius for each soil. This parameter quantifies the time scales that characterise diffusion within the undrained region of the soil, and allows us to calculate the duration of the leaching events and interruption periods that would lead to more efficient leaching. Application of these methodologies will aid development of strategies for improving management of chemicals in soils, needed in managing salts in soils, in improving fertiliser efficiency, and in reclaiming contaminated soils. (C) 2000 Elsevier Science B.V. All rights reserved.

Numerical modelling of double diffusion driven reactive flow transport in deformable fluid-saturated porous media with particular consideration of temperature-dependent chemical reaction rates

Numerical methods ave used to solve double diffusion driven reactive flow transport problems in deformable fluid-saturated porous media. in particular, thp temperature dependent reaction rate in the non-equilibrium chemical reactions is considered. A general numerical solution method, which is a combination of the finite difference method in FLAG and the finite element method in FIDAP, to solve the fully coupled problem involving material deformation, pore-fluid flow, heat transfer and species transport/chemical reactions in deformable fluid-saturated porous media has been developed The coupled problem is divided into two subproblems which are solved interactively until the convergence requirement is met. Owing to the approximate nature of the numerical method, if is essential to justify the numerical solutions through some kind of theoretical analysis. This has been highlighted in this paper The related numerical results, which are justified by the theoretical analysis, have demonstrated that the proposed solution method is useful for and applicable to a wide range of fully coupled problems in the field of science and engineering.

Loss of connectivity in Alzheimer's disease: an evaluation of white matter tract integrity with colour coded MR diffusion tensor imaging

A novel MRI method-diffusion tensor imaging-was used to compare the integrity of several white matter fibre tracts in patients with probable Alzheimer's disease. Relative to normal controls, patients with probable Alzheimer's disease showed a highly significant reduction in the integrity of the association white matter fibre tracts, such as the splenium of the corpus callosum, superior longitudinal fasciculus, and cingulum. By contrast, pyramidal tract integrity seemed unchanged. This novel finding is consistent with the clinical presentation of probable Alzheimer's disease, in which global cognitive decline is a more prominent feature than motor disturbance.

Diffusion- and perfusion-weighted MRI response to thrombolysis in stroke

Diffusion- and perfusion-weighted magnetic resonance imaging provides important pathophysiological information in acute bra-in ischemia. We performed a prospective study in 19 sub-6-hour stroke patients using serial diffusion- and perfusion-weighted imaging before intravenous thrombolysis, with repeat studies, both subacutely and at outcome. For comparison of ischemic lesion evolution and clinical outcome, we used a historical control group of 21 sub-6-hour ischemic stroke patients studied serially with diffusion- and perfusion-weighted imaging. The two groups were well matched for the baseline National Institutes of Health Stroke Scale and magnetic resonance parameters. Perfusion-weighted imaging-diffusion-weighted imaging mismatch was present in 16 of 19 patients treated with tissue plasminogen activator, and 16 of 21 controls. Perfusion-weighted imaging-diffusion-weighted imaging mismatch patients treated with tissue plaminogen activator had higher recanalization rates and enhanced reperfusion at day 3 (81% vs 47% in controls), and a greater proportion of severely hypoperfused acute mismatch tissue not progressing to infarction (82% vs -25% in controls). Despite similar baseline diffusion-weighted imaging lesions, infarct expansion was less in the recombinant tissue plaminogen activator group (14cm(3) vs 56cm(3) in controls). The positive effect of thrombolysis on lesion growth in mismatch patients translated into a greater improvement in baseline to outcome National Institutes of Health Stroke Scale in the group treated with recombinant tissue plaminogen activator, and a significantly larger proportion of patients treated with recombinant tissue plaminogen activator having a clinically meaningful improvement in National Institutes of Health Stroke Scale of;2:7 points. The natural evolution of acute perfusion-weighted imaging-diffusion-weighted imaging mismatch tissue may be altered by thrombolysis, with improved stroke outcome. This has implications for the use of diffusion- and perfusion-weighted imaging in selecting and monitoring patients for thrombolytic therapy.

NMR shim coil design utilising a rapid spherical harmonic calculation method

A rapid spherical harmonic calculation method is used for the design of Nuclear Magnetic Resonance shim coils. The aim is to design each shim such that it generates a field described purely by a single spherical harmonic. By applying simulated annealing techniques, coil arrangements are produced through the optimal positioning of current-carrying circular arc conductors of rectangular cross-section. This involves minimizing the undesirable harmonies in relation to a target harmonic. The design method is flexible enough to be applied for the production of coil arrangements that generate fields consisting significantly of either zonal or tesseral harmonics. Results are presented for several coil designs which generate tesseral harmonics of degree one.