Usual Diffusion Research Articles

Modelling a junction diode in a two-dimensional array

Guided by the simple physical and geometrical considerations, an analytical approach is presented to model a junction diode in a two-dimensional array. The proposed model includes the contributions of the lateral diffusion current and the surface leakage current from the surface area of the material between the neighbouring diodes in an area array, in addition to the usual thermal diffusion currents from the material just beneath the junction.

Square root singularity in the viscosity of neutral colloidal suspensions at large frequencies

The asymptotic frequency $\omega$, dependence of the dynamic viscosity of neutral hard sphere colloidal suspensions is shown to be of the form $\eta_0 A(\phi) (\omega \tau_P)^{-1/2}$, where $A(\phi)$ has been determined as a function of the volume fraction $\phi$, for all concentrations in the fluid range, $\eta_0$ is the solvent viscosity and $\tau_P$ the P\'{e}clet time. For a soft potential it is shown that, to leading order steepness, the asymptotic behavior is the same as that for the hard sphere potential and a condition for the cross-over behavior to $1/\omega \tau_P$ is given. Our result for the hard sphere potential generalizes a result of Cichocki and Felderhof obtained at low concentrations and agrees well with the experiments of van der Werff et al, if the usual Stokes-Einstein diffusion coefficient $D_0$ in the Smoluchowski operator is consistently replaced by the short-time self diffusion coefficient $D_s(\phi)$ for non-dilute colloidal suspensions.

Removal of phosphorus from wastewater by activated alumina adsorbent

The adsorption characteristics of activated alumina treated with aluminum sulfate were studied to develop a new removal process for low concentration phosphorus in the waters of rivers and lakes. The equilibrium study showed that the adsorption capacity was enhanced about 1.7-fold by treating with aluminum sulfate. The effective intraparticle diffusion coefficients, determined by the Boyd's method based on batch runs, were hardly affected by such a low phosphorus concentration as observed in the water of rivers and lakes under investigation. The temperature dependence of the intraparticle diffusion coefficients based on the concentration in solid showed the activation energy of 29.7kJ·mol−1, which was a little higher than that in usual pore diffusion. The maximum continuous operation term (regeneration cycle) of the present phosphorus adsorption system was estimated. Under the conditions of influent phosphorus concentration of 0.1 g·m−3, removal extent of 90%, particle size of 2 × 10−3m, temperature of 298K and space velocity of 1.39 × 10−3s−1 (5h−1), the present removal system remained effective for about 500 days.

A microscopic mechanism for the porous medium equation

The porous medium equation on a d-dimensional torus is obtained as a hydrodynamic scaling limit, with the usual diffusion scaling, of the empirical measures of a sequence of reversible Markov jump processes on approximating periodic lattices. Each process can be viewed as a randomly interacting configuration of sticks (or energies, etc.). The configuration evolves through exchanges of stick portions that occur between nearest neighbours through a zero-range pressure mechanism, with conservation of total sticklength.

Removal of phosphorus from wastewater by activated alumina adsorbent

The adsorption characteristics of activated alumina treated with aluminum sulfate were studied to develop a new removal process for low concentration phosphorus in the waters of rivers and lakes. The equilibrium study showed that the adsorption capacity was enhanced about 1.7-fold by treating with aluminum sulfate. The effective intraparticle diffusion coefficients, determined by the Boyd9s method based on batch runs, were hardly affected by such a low phosphorus concentration as observed in the water of rivers and lakes under investigation. The temperature dependence of the intraparticle diffusion coefficients based on the concentration in solid showed the activation energy of 29.7kJ·mol −1 , which was a little higher than that in usual pore diffusion. The maximum continuous operation term (regeneration cycle) of the present phosphorus adsorption system was estimated. Under the conditions of influent phosphorus concentration of 0.1 g·m −3 , removal extent of 90%, particle size of 2 × 10 −3 m, temperature of 298K and space velocity of 1.39 × 10 −3 s −1 (5h −1 ), the present removal system remained effective for about 500 days.

Evolution of vorticity in perturbed flow in a pipe

Flows in long pipes often include “slugs” or “puffs” of complex or chaotic patterns interspersed with regions of relative calm. A similar phenomenon can occur in boundary layers, where “turbulent spots” can exist between rather calm regions of flow, especially in regions of transition from a laminar flow to a turbulent form. The vorticity field plays a significant role in these phenomena, and it is an aim of this paper to examine this feature from a point of view that might be thought to be unusual. Some forty years ago, G. I. Taylor initiated his theory of dispersion of a contaminant in the flow in a long pipe. He showed that a combination of longitudinal (axial) convection by the flow coupled with radial diffusion by molecular (or by turbulent) action produces an effective longitudinal diffusion process, which is governed approximately by the usual one-dimensional diffusion equation. Astonishingly, the effective longitudinal diffusivity coefficient depends inversely on the molecular (or turbulent or eddy) diffusivity. This remarkable phenomenon is now known as Taylor diffusion and has been much studied both experimentally and theoretically over the intervening forty years. The object of this paper is to study the development of vorticity in the flow in a pipe, with the vorticity treated as if it were a passive contaminant on a longitudinal flow through the pipe. In general, this requires an approximation, because the interaction between the velocity and vorticity fields is ignored. But, in a particular case—namely, that of a small swirling vortex perturbation on a flow in a pipe—a theoretical construction becomes possible in which the major approximation is simply that of linearization for small perturbation amplitudes. As a result, it is found that the swirl amplitude satisfies a one-dimensional diffusion equation, just as it does for a scalar contaminant in Taylor's classical work. There is, however, a significant difference in our problem of the evolution of vorticity or swirl: the effective longitudinal diffusion coefficient, which, like Taylor's, depends inversely on the molecular diffusivity, changes sign at a particular value of the Reynolds number. Thus, for Reynolds numbers lower than the critical value, the effective longitudinal diffusion coefficient is positive; in contrast, it is negative for Reynolds numbers larger than the critical value. The latter result implies that a focusing takes place instead of dispersion. The implications of this are discussed.

Non-equilibrium surface diffusion in the [formula omitted] system

In this Letter, we present results of an extensive Monte Carlo study of the O W(110) system under non-equilibrium conditions. We study the mean square displacements and long wavelength density fluctuations of adatoms. From these quantities, we define effective and time-dependent values for the collective and tracer diffusion mobilities. These mobilities reduce to the usual diffusion constants when equilibrium is reached. We discuss our results in view of existing experimental measurements of effective diffusion barriers, and the difficulties associated with interpreting non-equilibrium data.

Anomalous non-gaussian diffusion in small disordered rings

We analyze an equilibrium classical diffusion of a Brownian particle confined to a ring coated on a two-dimensional disordered film. The random potential modeling the interaction with the inhomogeneous medium is assumed to be Gaussian with a finite correlation length. With a microscopic method, we derive the second and fourth cumulant function of the particle's displacement at large times. It is shown that the disorder gives rise to a quadratic time dependence of the fourth cumulant (anomalous non-Gaussian diffusion), whereas the usual diffusion covered by the second cumulant remains normal. This points to the fact that the motion of a Brownian particle along the disordered ring is attended by nonergodic fluctuations in its diffusion coefficient.

Pressure-induced reentrant phase behavior in the poly(N-vinyl-2-pyrrolidone)-water system.

Phase separation and dynamic light scattering experiments were performed on aqueous solutions of poly(N-vinyl-2-pyrrolidone) under high pressure conditions to help elucidate the role that hydrogen bonding plays in the solution behavior of water-soluble polymers. From the pressure-induced phase separation experiments we observe reentrant phase behavior in the pressure-temperature plane at fixed composition. Variation of the phase separation pressure with both composition and molecular weight is also investigated. The concentration dependence on the phase separation pressure is weak and the molecular weight dependence exhibits an approximately ${\mathit{M}}_{\mathit{w}}^{\mathrm{\ensuremath{-}}1/2}$ scaling. All this behavior can be explained through a modified Flory-Huggins theory that includes the effect of pressure and temperature on hydrogen bonds and the hydrophobic interactions. We use our data to derive fit parameters for this model and the results suggest that not only does the hydrogen bond weaken at high pressure but hydrophobic interactions increase. Dynamic light scattering (DLS) experiments on solutions within the one-phase region of the phase diagram quantify the influence of changing solvent quality on the polymer's conformation. For dilute solutions, which at ambient temperature and pressure exhibit classic good-solvent behavior, a pressure-induced crossover from good to poor solvent behavior is found. Such measurements are shown to give a measure of ${\mathit{A}}_{2}$, an otherwise difficult to measure property at elevated pressure. Above the overlap concentration, this polymer system exhibits aggregate formation. The autocorrelation spectrum contains two relaxations: a fast relaxation mode associated with the usual cooperative diffusion and a slow relaxation mode associated with internal dynamics of the aggregates. Through DLS experiments in the semidilute regime we show that these two modes merge upon increasing pressure, an effect that is completely reversible. The dispersal of the aggregates under pressure suggests that the aggregates depend strongly on water-mediated hydrogen bonds between monomers. \textcopyright{} 1996 The American Physical Society.

The effect of silicon substrate orientation on the formation of Gd-silicide phases

The formation and epitaxy of Gd-silicide compounds were investigated in the solid phase reaction of Gd thin film on (111) and (100) oriented Si substrate by X-ray diffraction, Rutherford backscattering and transmission electron microscopy. It was recognised that the effect of substrate orientation on the phase formation became dominant for Gd films thinner than 30 nm. To determine the role of the substrate orientation on the phase formation, 20 nm Gd films were annealed in-situ under the same conditions for (111) and (100) pairs. At low temperature (320°C for 5 min) the first phase (hexagonal GdSi 2− x ) was formed epitaxially on Si(111), while on Si(100) an amorphous alloy formed. At higher temperatures — 350, 430, 500, 550 and 650°C, and 5 min annealing — epitaxial hexagonal GdSi 2− x was found on Si(111), that could not transform into the second phase (orthorhombic GdSi 2), in contrast to the case, where films were thicker than 30 nm. Meanwhile on Si(100) epitaxial orthorhombic GdSi 2 was found under the same annealing conditions. It was demonstrated, that under a certain thickness (30 nm) the formed phase was determined by the substrate orientation instead of the usual diffusion and reaction processes. Our results show the possibility of amorphous phase formation in GdSi reaction, which is reasonable because of the high mobility difference of the diffusing species.

Anomalous diffusion of water in biological tissues

This article deals with the characterization of biological tissues and their pathological alterations. For this purpose, diffusion is measured by NMR in the fringe field of a large superconductor with a field gradient of 50 T/m, which is rather homogenous and stable. It is due to the unprecedented properties of the gradient that we are able not only to determine the usual diffusion coefficient, but also to observe the pronounced Non-Debye feature of the relaxation function due to cellular structure. The dynamics of the probability density follow a stretched exponential or Kohlrausch-Williams-Watts function. In the long time limit the Fourier transform of the probability density follows a long-tail Lévy function, whose asymptotic is related to the fractal dimension of the underlying cellular structure. Some of the properties of Lévy walk statistics are discussed and its potential importance in understanding certain biophysical phenomena like diffusion processes in biological tissues are pointed out. We present and discuss for the first time NMR data giving evidence for Lévy processes that capture the essential features of the observed power law (scaling) dynamics of water diffusion in fresh tissue specimens: carcinomas, fibrous mastopathies, adipose and liver tissues.

In Situ Study of Simultaneous Adsorption of Surfactant at Model Solid-Liquid and Liquid-Liquid Interfaces Using the Two-Liquid Contact Angle Method

Abstract A direct method of in situ investigation of adsorption mechanisms at related solid/liquid and liquid/liquid interfaces is presented, based on the two-liquid-phase contact angle measurement. Using a model system represented by a self-assembled monolayer (SAM) surface/hydrocarbon drop/aqueous surfactant solution, it is shown that the method constitutes a simple way to characterize both the dynamic behavior and equilibrium quantities of adsorption. In addition to the consistency of these results with the usual diffusion controlled models, some interesting phenomena such as structural transitions in the adsorbed layer are clearly evidenced from adsorption kinetics.

Supported polymeric liquid membranes for removing organics from aqueous solutions I. Transport characteristics of polyglycol liquid membranes

The removal or elimination of organic residues from aqueous waste streams represents a major need in the chemical industry. We have developed a class of membrane called supported polymeric liquid membranes (SPLMs) capable of removing and concentrating low molecular weight organic compounds from dilute aqueous solutions, especially those that also contain high levels of inorganic salts. The membranes are prepared by filling the pores of microfiltration or ultrafiltration membranes with functional, polymeric (oligomeric) liquids having affinity for the organic compounds of interest. Data obtained with para-nitrophenol (PNP) as the permeating organic and polyglycols as the polymeric liquid membranes show that the slow diffusion rates due to the viscous polymeric liquids are more than compensated for by the very high solubility resulting from specific interactions and high density of the polymers functional groups. This is a powerful concept that can be extended to other types of polymeric liquids. Quite interestingly, the transport rates of PNP through the supported polyglycol liquid membranes appear remarkably insensitive to the molecular weight and the viscosity of the polymeric liquids. This behavior may signal a more complex and very different transport mechanism than the usual liquid diffusion.

Telematics and freight transport: a Dutch case study

Telematics applications have been introduced in the transport sector in order to improve the effective use of infrastructure networks, on the one hand, and to optimize the performance of the firm, on the other. In general, there is a lack of micro-based research in analyzing telematics applications. In this paper we study the familiarity, adoption, use, and investment plans of commercial freight transporters with respect to a number of these technologies, on the basis of a survey conducted in the Netherlands in 1994. Results show, amongst other things, that: (1) markets for the various technologies are far from saturated; (2) adoption follows usual innovation diffusion patterns, with large firms being the first adopters; (3) automatic vehicle location systems are used only in combination with mobile telecommunications technologies.

Chronoamperometry for the determination of metallic interdiffusion coefficients. Rapid transport processes in the first atomic layers

The potential step technique was used to study the interdiffusion in the solid state at high temperature using a molten electrolyte. The method was applied to several binary metal systems and proved to be efficient for the determination of the interdiffusion coefficient D as a function of the temperature and composition of the generated alloys. The electrochemical response at short times showed a net departure from the usual diffusion laws and could be interpreted in terms of a very fast transport in the initial layers of the metal interface. Analysis of the transients was carried out by digital simulation in order to take into account the dependence of D on the concentration and distance.

Relativistic electron precipitation enhancements near the outer edge of the radiation belt

We examined characteristics of relativistic electron precipitation bursts observed by the Heavy Ion Large Telescope (HILT) experiment onboard the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) satellite. We report on relatively narrow, persistent, latitudinal bands of precipitation with time scales of 10∼30 sec near the outer edge of the radiation belt: these develop and decay with a time scale of a few hours. Acceleration processes more effective than the usual radial diffusion process or scattering process would be needed to explain this strong precipitation band phenomenon. Another prominent signature is microbursts with a time scale down to a few hundred milliseconds. It is suggest that these microbursts are due to wave‐particle interaction involving a relaxation‐oscillator type of mechanism.

Effects of Finite Gradient-Pulse Widths in Pulsed-Field-Gradient Diffusion Measurements

The effects of finite gradient-pulse widths on NMR diffusion measurements for fluids in restricting geometries are studied. It is shown that the echo amplitude is the spatial Fourier transform of a "center-of-mass" propagator, which reduces to the usual diffusion propagator in the limit of zero pulse widths. A finite gradient-pulse width δ effectively changes the pore shape, making isolated pores appear smaller than their actual size. The diffraction analogy still holds for long diffusion times, with the fluid density ρ( r) being replaced by p cm( r, δ). This quantity, the "center-of-mass distribution function," is the spatial probability distribution of the center of mass of Brownian trajectories of duration δ in the pore space. For a periodic pore space, "Bragg" peaks still appear in the amplitude at the reciprocal lattice vectors. The heights of these peaks are enhanced for small δ but reduced for δ. A number of results valid for small δ and piecewise smooth pore surfaces are presented.

The quasi-diffusive approximation in transport theory: Local solutions

The one velocity, plane geometry integral neutron transport equation is transformed into a system of two equations, one of them being the equation of continuity and the other a generalized Fick`s law, in which the usual diffusion coefficient is replaced by a self-adjoint integral operator. As the kernel of this operator is very close to the Green function of a diffusion equation, an approximate inversion by means of a second order differential operator allows to transform these equations into a purely differential system which is shown to be equivalent, in the simplest case, to a diffusion-like equation. The method, the principles of which have been exposed in a previous paper, is here extended and applied to a variety of problems. If the inversion is properly performed, the quasi-diffusive solutions turn out to be quite accurate, even in the vicinity of the interface between different material regions, where elementary diffusion theory usually fails. 16 refs., 3 tabs.

Thin superconductors in a perpendicular magnetic ac field. II. Circular disk.

The electromagnetic response of a thin type-II superconductor disk of constant thickness d to an applied perpendicular magnetic field is calculated and compared with the response of a thin strip and of bars and cylinders in a longitudinal field. The strip and disk are characterized completely by their sheet resistivity, which may be either nonlinear and static or linear, complex, and frequency dependent. The equations of motion for the sheet current in the strip and disk are derived and discussed. Iterative and numerical-solution methods are presented that account for the infinities of the integral kernel and of the ideal screening current. The linear Ohmic response, realized during flux flow or thermally activated flux flow, is calculated for a jump in the applied field and for an ac field. Simple approximate expressions for the complex ac susceptibilities of an Ohmic strip and disk are given and compared with longitudinal geometry. The penetration of perpendicular flux into an Ohmic strip or disk is not a usual diffusion since a logarithmic infinity of the prpendicular-field component occurs at the edges at all times t and the sheet current always flows over the entire surface. Near the edges, the sheet current has a universal profile, with a maximum which initially penetrates with constant velocity v=0.77D/d and decreases as 1/ \ensuremath{\surd}t (D=\ensuremath{\rho}/${\mathrm{\ensuremath{\mu}}}_{0}$, where \ensuremath{\rho} is the resistivity). At large times t\ensuremath{\gg}${\mathrm{\ensuremath{\tau}}}_{0}$ the current and magnetic moment decrease as exp(-t/${\mathrm{\ensuremath{\tau}}}_{0}$), where ${\mathrm{\ensuremath{\tau}}}_{0}$=0.2492ad/D for a strip with half width a and ${\mathrm{\ensuremath{\tau}}}_{0}$=0.1815ad/D for a disk with radius a.

Exit times and chaotic transport in Hamiltonian systems.

A new statistical diagnostic tool for chaotic transport in Hamiltonian systems is proposed. The method, based on the concept of exit times, has an advantage over the calculation of diffusion coefficients in that it remains valid for nondiffusive transport processes. This method is tested on the Chirikov-Taylor standard map: One finds that it is more robust than the usual diffusion coefficient D and conveys the same information as D when the latter is meaningful, for all values of the nonlinearity parameter K.