[en] Diffusion is an important process in many biological and industrial processes. Diffusion coefficients are traditionally measured using integrated solutions of Fick's law for systems with well-defined boundary conditions. We report a simple method for measuring diffusion coefficients in processes without well-defined boundary conditions or without a simple integrated solution using the differential form of Fick's law. Magnetic resonance imaging (MRI) was used to obtain spatially and time-resolved profiles of the diffusion of H₂O from an agarose gel to a neighboring D₂O reservoir. The differential form of Fick's second law was used to solve for the diffusion coefficient, D=1.3x10^-9 m² s^-1. MRI is well suited to this type of analysis as it naturally generates time- and space-resolved images. This analytical method allows for the determination of diffusion coefficients in systems that lack an integral solution to the diffusion equation.

[en] The aim of the study is to measure the diffusion coefficients at temperatures about 20-27 ^oC, and determine the type of transport mechanism of diffusion of pyridine in macromolecular structure of Turkish Cayirhan lignite (C: 57.1 wt %, dmmf). The raw coal sample was demineralized with HCl and HF by standard methods. The raw and demineralized coal samples were extracted with pyridine. In order to investigate the diffusion of pyridine vapour in coal samples, the mass of pyridine uptake per mass of coal sample (M_t/M_∞) was calculated as a function of time. The diffusion coefficients were measured from the slope of graphs of M_t/M_∞ versus t^1/2. The diffusion coefficient of pyridine in the raw coal increased from 10.04 x 10^-15 m²/s to 11.86 x 10^-15 m²/s when the temperature was elevated from 21.1 ^oC to 26.9 ^oC, respectively. The diffusion coefficients of pyridine raw coal, treated with HCl and HF were 11.86 x 10^-15 m²/s, 4.26 x 10^-15 m²/s, 4.75 x 10^-15 m²/s at 26.9 ^oC, respectively. the studies in the present work on pyridine vapor diffusion in raw coals have generally indicated that the diffusion obeyed the Fickian diffusion mechanism at the temperature 20-27 ^oC. Generally, The values of diffusion exponent increased when the temperature elevated from 20 ^oC to 27 ^oC. But this raise placed the diffusion of pyridine between the Fickian diffusion mechanism and Case II diffusion mechanism. (author)

[en] Ferric ion diffusion is one of the main problems that still restrains the dosimetric application of Fricke-agarose gels. In this work, we model this process within finite length gel samples. The temporal evolution of the ion concentration as a function of the initial concentration is derived by solving Fick's second law in two dimensions with boundary reflections. The influence of ion concentration gradient, elapsed time, diffusion coefficient and spatial resolution is studied. Due to the main drawbacks of MRI for studying these systems, i.e. high cost and acquisition time often non-negligible compared to diffusion time, we also investigate the possibility of using a microdensitometer. The application of this technique for Fricke gel dosimetry is proposed here for the first time. The estimate of the ion diffusion coefficient is in a very agreement with those reported in literature

[en] The long-term limit motions of individual heavy-tailed (power-law) particle jumps that characterize anomalous diffusion may have different scaling rates in different directions. Operator stable motions {Y(t):t≥0} are limits of d-dimensional random jumps that are scale-invariant according to c^HY(t)=Y(ct), where H is a dxd matrix. The eigenvalues of the matrix have real parts 1/α_j, with each positive α_j≤2. In each of the j principle directions, the random motion has a different Fickian or super-Fickian diffusion (dispersion) rate proportional to t^1/α_j. These motions have a governing equation with a spatial dispersion operator that is a mixture of fractional derivatives of different order in different directions. Subsets of the generalized fractional operator include (i) a fractional Laplacian with a single order α and a general directional mixing measure m(θ); and (ii) a fractional Laplacian with uniform mixing measure (the Riesz potential). The motivation for the generalized dispersion is the observation that tracers in natural aquifers scale at different (super-Fickian) rates in the directions parallel and perpendicular to mean flow

[en] Iron particles, under the shape of tubes, with a diameter ranging between 1 and 100 μm and wall thickness between x0.1 and x1 μm constitute the object of the paper. The condition for iron micro-tubes formation and its correlation with the main technological parameters for the generation of these particles in plasma are presented. Using the model for the rebuilding of the surface, the paper shows that the duration of iron micro-tubes formation in the plasma of the transferred arc ranges between x10^-11 and x10^-6 s

[en] Published in summary form only

[en] Experiments have been conducted to verify the suitability of Fick's second law to describe moisture flow in wood. The moisture content change with time were plotted for absorption and desorption, and it was observed that these variations follow the same trend as modelled on the computer. The mean integral diffusion coefficient D-bar for the wood species were calculated on the basis of Boltzmann's solution of Fick's second law, D-bar ranges from 2.0 x 10^-3cm²/s to 4.2 x 10^-3cm²/s for both absorption and desorption. (author). 5 refs, 4 figs, 2 tabs

[en] Complete text of publication follows. Diffusion on the nano/atomic scales in multilayers, thin films has many challenging features even if the role of structural defects can be neglected and 'only' the effects related to the nano/atomic scale raise. The most basic equations to describe the diffusion are Fick's equations. It is important to emphasize that the diffusion coefficient in Fick's equations is in general composition independent and Fick's classical equations do not include the stress effects, which can have important influence onto the diffusion especially on the nano/atomic scale. We illustrate that the continuum descriptions of the diffusion cannot be applied automatically on such short distances, the classical continuum approximations (Fick's laws) cannot describe correctly the atomic movements. They predict faster kinetics than the atomistic models and the interface shift is always proportional to the square root of the time. However, the kinetics can be even linear on the nano/atomic scale. We have shown from computer simulations that Fick's laws violate on the nanoscale either in completely or restricted miscible systems. This is strongly related to the discrete character of the system on the nanoscale and to the highly neglected fact in the literature that the diffusion coefficients depend on the composition. As will be seen the composition dependence of D is very important and has very significant influence on the diffusion kinetics on the nano/atomic scales. It originates from the fact that usually the diffusion coefficients are different in an A and in a B matrix. Consequently in case of a real interface, which is not atomically sharp, i.e. there is a more or less intermixed region between the pure A and B matrixes, the diffusion coefficient changes continuously while e.g. an A atom diffuses from the pure A matrix into the pure B. This feature can be also called diffusion asymmetry. We have also illustrated that in this case not only the composition profile develops highly asymmetrically but also the stress profile. Moreover, we have also seen that the stress effects usually slow down the intermixing process, and the slowing down is more pronounced in case of asymmetric diffusion. Computer simulations also have shown that on the nanoscale, for strongly composition dependent diffusion coefficients, diffuse interfaces can sharpen rather broaden in completely miscible binary systems during annealing independently of the different kind of stress effects considered. The stress effects influence only the timescale of the process. This phenomenon could provide a useful tool for the improvement of interfaces and offer a way to fabricate of e.g. better Xray or neutron mirrors, microelectronic devices or multilayers with giant magnetic resistance. These phenomena predicted by computer simulations have been proved experimentally as well

[en] We summarize the formula for the diffusion of a radioactive product from a solid target or catcher material in the form of foils, fibers and particles for the case of vanishing surface density of the diffusing isotopes, in which the analytical expression for the diffusion yield, i.e., the probability for radioisotope to escape before decaying is newly obtained for diffusion from a solid in the form of a fiber. (orig.)

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