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.

Double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones when they are heated uniformly from below. The fault zone is assumed to be more permeable than its surrounding rocks. In particular, we have derived exact analytical solutions to the total critical Rayleigh numbers of the double diffusion-driven convective flow. Using the corresponding total critical Rayleigh numbers, the double diffusion-driven convective instability of a fluid-saturated three-dimensional geological fault zone system has been investigated. The related theoretical analysis demonstrates that: (1) The relative higher concentration of the chemical species at the top of the three-dimensional geological fault zone system can destabilize the convective flow of the system, while the relative lower concentration of the chemical species at the top of the three-dimensional geological fault zone system can stabilize the convective flow of the system. (2) The double diffusion-driven convective flow modes of the three-dimensional geological fault zone system are very close each other and therefore, the system may have the similar chance to pick up different double diffusion-driven convective flow modes, especially in the case of the fault thickness to height ratio approaching 0. (3) The significant influence of the chemical species diffusion on the convective instability of the three-dimensional geological fault zone system implies that the seawater intrusion into the surface of the Earth is a potential mechanism to trigger the convective flow in the shallow three-dimensional geological fault zone system.

Numerical simulation of double-diffusion driven convective flow and rock alteration in three-dimensional fluid-saturated geological fault zones

Numerical methods are used to simulate the double-diffusion driven convective pore-fluid flow and rock alteration in three-dimensional fluid-saturated geological fault zones. The double diffusion is caused by a combination of both the positive upward temperature gradient and the positive downward salinity concentration gradient within a three-dimensional fluid-saturated geological fault zone, which is assumed to be more permeable than its surrounding rocks. In order to ensure the physical meaningfulness of the obtained numerical solutions, the numerical method used in this study is validated by a benchmark problem, for which the analytical solution to the critical Rayleigh number of the system is available. The theoretical value of the critical Rayleigh number of a three-dimensional fluid-saturated geological fault zone system can be used to judge whether or not the double-diffusion driven convective pore-fluid flow can take place within the system. After the possibility of triggering the double-diffusion driven convective pore-fluid flow is theoretically validated for the numerical model of a three-dimensional fluid-saturated geological fault zone system, the corresponding numerical solutions for the convective flow and temperature are directly coupled with a geochemical system. Through the numerical simulation of the coupled system between the convective fluid flow, heat transfer, mass transport and chemical reactions, we have investigated the effect of the double-diffusion driven convective pore-fluid flow on the rock alteration, which is the direct consequence of mineral redistribution due to its dissolution, transportation and precipitation, within the three-dimensional fluid-saturated geological fault zone system. (c) 2005 Elsevier B.V. All rights reserved.

Hydrothermal Synthesis of Layered Double Hydroxides (LDHs) from Mixed MgO and Al2O3: LDH Formation Mechanism

The formation of MgA1 layered double hydroxide (LDH) from physically mixed MgO and Al2O3 oxides upon hydrothermal treatment has been extensively investigated, and a formation mechanism has been proposed. We observed that the formation of LDH from the oxide mixture occurs upon heating at 110 degreesC. In general, LDH is the major component while the minor phases are mainly determined by the initial pH of the oxide suspension as well as the MgO/Al2O3 ratio. The neutrality in the initial suspension results in a minor Mg(OH)(2) as the impure phase, while the alkalinity in the suspension keeps some MgO unreacted throughout the whole hydrothermal treatment. We suggest that MgO and Al2O3 be hydrated into Mg(OH)(2) and Al(OH)(3), respectively, in the initial stage for all samples. We further Suggest that in the neutral condition Mg(OH)2 be quickly dissociated to Mg2+ and OH- which then deposit on the surface of Al(OH)(3)/Al2O3 to form a M-Al pre-LDH material. Al(OH)(4)(-), ionized from Al(OH)(3) in the basic solution, deposits on the surface of Mg(OH)(2)/MgO to result in a similar MgAl pre-LDH material. Such a pre-LDH material is then well crystallized upon continuous heating via the diffusion of metal ions in the solid lattice. Such a dissociation-deposition-diffusion mechanism via two pathways has been supported by the phase composition, morphological features of crystallites, and [Mg]/[Al] ratios on the crystallite surface. and presumably applied to the general formation of LDHs with various synthetic methods. Such as coprecipitation, homogeneous preparation, and reconstruction.

A diffusion approach to approximating preservation probabilities for gene duplicates

Consider a haploid population and, within its genome, a gene whose presence is vital for the survival of any individual. Each copy of this gene is subject to mutations which destroy its function. Suppose one member of the population somehow acquires a duplicate copy of the gene, where the duplicate is fully linked to the original gene's locus. Preservation is said to occur if eventually the entire population consists of individuals descended from this one which initially carried the duplicate. The system is modelled by a finite state-space Markov process which in turn is approximated by a diffusion process, whence an explicit expression for the probability of preservation is derived. The event of preservation can be compared to the fixation of a selectively neutral gene variant initially present in a single individual, the probability of which is the reciprocal of the population size. For very weak mutation, this and the probability of preservation are equal, while as mutation becomes stronger, the preservation probability tends to double this reciprocal. This is in excellent agreement with simulation studies.

Turbulence in Hydraulic Jumps: Experimental Measurements

A hydraulic jump is the transition from a supercritical open channel flow to a subcritical regime. It is characterised by a highly turbulent flow with macro-scale vortices, some kinetic energy dissipation and a bubbly two-phase flow structure. New air-water flow measurements were performed in hydraulic jump flows for a range of inflow Froude numbers. The experiments were conducted in a large-size facility using two types of phase-detection intrusive probes: i.e., single-tip and double-tip conductivity probes. These were complemented by some measurements of free-surface fluctuations using ultrasonic displacement meters. The present study was focused on the turbulence characteristics of hydraulic jumps with partially-developed inflow conditions. The void fraction measurements showed the presence of an advective diffusion shear layer in which the void fractions profiles matched closely an analytical solution of the advective diffusion equation for air bubbles. The present results highlighted some influence of the inflow Froude number onto the air bubble entrainment process. At the largest Froude numbers, the advected air bubbles were more thoroughly dispersed vertically, and larger amount of air bubbles were detected in the turbulent shear layer. In the air-water mixing layer, the maximum void fraction and bubble count rate data showed some longitudinal decay function in the flow direction. Such trends were previously reported in the literature. The measurements of interfacial velocity and turbulence level distributions provided new information on the turbulent velocity field in the highly-aerated shear region. The present data suggested some longitudinal decay of the turbulence intensity. The velocity profiles tended to follow a wall jet flow pattern. The air–water turbulent time and length scales were deduced from some auto- and cross-correlation analyses based upon the method of CHANSON (2006,2007). The results provided the integral turbulent time and length scales of the eddy structures advecting the air bubbles in the developing shear layer. The experimental data showed that the auto-correlation time scale Txx was larger than the transverse cross-correlation time scale Txz. The integral turbulence length scale Lxz was a function of the inflow conditions, of the streamwise position (x-x1)/d1 and vertical elevation y/d1. Herein the dimensionless integral turbulent length scale Lxz/d1 was closely related to the inflow depth: i.e., Lxz/d1 = 0.2 to 0.8, with Lxz increasing towards the free-surface. The free-surface fluctuations measurements showed large turbulent fluctuations that reflected the dynamic, unsteady structure of the hydraulic jumps. A linear relationship was found between the normalized maximum free-surface fluctuation and the inflow Froude number.

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.

Retinal and lenticular ultrastructure in the aestivating salamanderfish, Lepidogalaxias salamandroides (Galaxiidae, Teleostei) with special reference to a new type of photoreceptor mosaic

The salamanderfish, Lepidogalaxias salamandroides (Galaxiidae, Teleostei) is endemic to southwestern Australia and inhabits shallow, freshwater pools which evaporate during the hot summer months. Burrowing into the substrate in response to falling water levels allows these fish to aestivate for extended periods of time while encapsulated in a mucous cocoon even when the pools contain no water. Only a few minutes after a major rainfall, these fish emerge into relatively clear water which subsequently becomes laden with tannin, turning the water black and reducing the pH to approximately 4.3. As part of a large study of the visual adaptations of this unique species, the retinal and lenticular morphology of the aestivating salamanderfish is examined at the level of the light and electron microscopes. The inner retina is highly vascularised by a complex system of vitreal blood vessels, while the outer retina receives a blood supply by diffusion from a choriocapillaris. This increased retinal blood supply may be an adaptation for reducing the oxygen tension during critical periods of aestivation. Large numbers of Muller cells traverse the thickness of the retina from the inner to the outer limiting membranes. The ganglion cells are arranged in two ill-defined layers, separated from a thick inner nuclear layer containing two layers of horizontal cells by a soma-free inner plexiform layer. The photoreceptors can be divided into three types typical of many early actinopterygian representatives; equal double cones, small single cones and large rods (2:1:1). These photoreceptors are arranged into a unique regular square mosaic comprising a large rod bordered by four equal double cones with a small single cone located at the corner of each repeating unit. The double cones may optimise perception of mobile prey which it tracks by flexion of its head and neck and the large rods may increase sensitivity in the dark tannin-rich waters in which it lives. Each single cone also possesses a dense collection of polysomes and glycogen (a paraboloid) beneath its ellipsoid, the first such finding in teleosts. The retinal pigment epithelium possesses melanosomes, pha,oocytes and a large number of mitochondria. The anatomy of the retina and the photoreceptor mosaic is discussed in relation to the primitive phylogeny of this species and its unique life history.

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.