Diffusion Fundamentals is a peer-reviewed interdisciplinary open-access online journal published as a part of the website Diffusion-Fundamentals.org. It publishes original research articles in the field of diffusion and transport. Main research areas include theory, experiments applications, methods and diffusion-like phenomena. The readers of Diffusion Fundamentals are academic or industrial scientists in all research disciplines. The journal aims at providing a broad forum for their communication.

The recent rise in interest of green technologies has led to significant adoption of the constructed wetland as a waste water treatment technique. This increased popularity has only been mired by the decline in operational lifetime of wetland units, leading to the need for more regular, time consuming, and expensive rejuvenation techniques to be performed than initially anticipated. To extend operational lifetimes and increase efficiency of wetland units, it is crucial to have an accurate method to determine the internal state of the wetland system. The most important parameter to measure within the reed bed is the clog state of the system, which is representative of the overall system health. In previous work, magnetic resonance (MR) measurements, parameters of T1 and T2 eff, have been demonstrated as extremely powerful tools to determine the internal clog state of a wetland [1, 2]. Measurements have been performed in a laboratory setting, using low field permanent magnet arrangements. This work presents an Earth’s Field Nuclear Magnetic Resonance (EFNMR) probe suitable for in situ measurements within constructed wetlands. We show T2eff and T1 measurements using the EFNMR probe. T1 values are shown to be sensitive to the change in the clog state with 1498 ms for the thickly clogged sample and 2728 ms for the thinly clogged sample. T2eff values are shown to be marginally more sensitive to clog state with 630 ms for a thickly clogged sample and 1212 ms for the thinly clogged sample. This gives distinguishable variation within both parameters suggesting that this probe is suitable for embedding into an operational constructed wetland. This work was conducted as part of an EU FP7 project to construct an Automated Reed Bed Installation, “ARBI”.

Liège Chalk is a limestone of considerable commercial interest to the petroleum industry and formation factor a quantity required in this context. In this work we compare the formation factors based on electrical conductivity and diffusional displacement in a long time limit both experimentally and numerically. Measurements are performed on Liège Chalk samples while simulations are performed on two model structures represented by randomly packed ellipsoids and utilizing a Gaussian random field approach. We ensure similarity in petrophysical sense of modelled media to Liège Chalk by matching experimental and simulated NMR relaxation response, Mercury Injection Capillary Pressure curves and electrical resistivity. Following this, the diffusional-based formation factor is estimated from a set of apparent diffusion coefficients in the tortuosity limit obtained with PGSTE NMR. All measurements have been numerically-simulated and are in good agreement with experiment. We have shown that for Liège Chalk, the NMR diffusion and electrical resistivity based formation factors do agree.

Pore length scales and pore surface relaxivities of sandstone were studied on a 2 MHz Rock Core Analyzer in this work. To determine the pore length scales of rock cores, high eigenmodes of diffusion equation were detected with optimized encoding periods in the presence of internal magnetic fields B in. The results were confirmed by a 64 MHz NMR system. Furthermore, this methodology was combined with relaxometry measurements , which provides the two-dimensional correlation of pore length with relaxation time and yield information on the surface relaxivity of rock cores. The estimated surface relaxivities were compared with the results from an independent NMR method.

Miniaturization plays an essential role in modern life of the 21st century. It is encountered, e.g., in communication, personalized and portable computers and in medicine. Miniaturization also affects NMR, one of the most versatile analytical tools, leading to dedicated sensors and portable devices which lead to new applications of NMR in different disciplines. The miniaturization of two portable stray-field NMR sensor types, the NMR-MOUSE ® and an inside-out sensor are reported in this work. The sensors are critically evaluated and compared to other standard probes. Applications in material testing and civil engineering are evaluated.

We have investigated model systems in which effects from non-Gaussian restricted diffusion could be separated from effects caused by multiple diffusion coefficients. We applied various models to analyze the experimental data. An analysis based on multi-exponential models does not account correctly for effects caused by restricted diffusion in a system with multiple compartments. However, separating the components due to differences in dynamic behavior prior to the diffusion analysis, combined with a diffusion analysis based on the second cumulant approximation, was more robust, and was able to handle effects from restricted diffusion in the presence of multi-component diffusion.

In this study we have applied 2D NMR experiments where the spatial inhomogeneous magnetic field (Bi) inside a porous sample is correlated to respectively internal gradient (G0), diffusion coefficient (D), and transverse relaxation time (T2) of a confined liquid. Experiments were performed on samples having different pore system geometry and heterogeneity, leading to different types of confinement of the liquid. The results show that the correlation between G0 and Bi is more sensitive to the type of confinement, and thus also of the pore geometry and heterogeneity, compared to the corresponding correlations involving D and T2.

The two most successful methods of estimating the distribution of NMR relaxation times from two dimensional data are firstly a data compression stage followed by application of the Butler-Reeds-Dawson (BRD) algorithm, and secondly a primal dual interior point method using a preconditioned conjugate gradient (PCG). Both of these methods have been presented in the literature as requiring a truncated singular value decomposition of matrices representing the exponential kernels. Other matrix factorisations are applicable to each of these algorithms, and which demonstrate the different fundamental principles behind the operation of the algorithms. In the case of the data compression approach the most appropriate matrix decomposition specifically designed for this task is the rank-revealing QR (RRQR) factorisation. In the case of the interior point method, the most appropriate method is the LDL factorisation with diagonal pivoting, also known as the Bunch-Kaufman-Parlett factorisation. The details of these differences are discussed, and the performances of the algorithms are compared numerically.

Determining the composition of solid materials is of high interest in areas such as material research or quality assurance. There are several modalities at disposal with which various parameters of the material can be observed, but of those only magnetic resonance imaging (MRI) or computer tomography (CT) offer anon-destructive determination of material distribution in 3D. A novel non-destructive imaging method is Magnetic Particle Imaging (MPI), which uses dynamic magnetic fields for a direct determination of the distribution of magnetic materials in 3D. With this approach, it is possible to determine and differentiate magnetic and non-magnetic behaviour. In this paper, the first proof-of-principle measurements of magnetic properties in solid environments are presented using a home-built traveling wave magnetic particle imaging scanner.

Chemical reaction speed is frequently enhanced at a surface, particularly when materials like platinum are present. It is well known that porous materials such as sol-gel silicas, controlled pore glasses, templated porous materials such as SBA-15, MCM-41, MCM-48, and zeolites, offer large surface areas. This in turn makes them ideal for catalysing chemical reactions. Thus an important use for porous materials is as a substrate and media to promote chemical reactions. However small pores are not always easily accessed by some of the organic liquids in which these catalytic reactions ideally take place. Cryoporometric techniques offer the possibility of directly probing the fraction of a pore that is actually accessible to a probe liquid. This fractional volume has significant impact on the catalytic efficacy of a particular solvent that is used to promote a reaction in the pores. Pore size, pore geometry, pore throat, pore surface material (hydrophilic/hydrophobic) and choice of probe liquid all influence the accessible fraction. By performing an NMR cryoporometric measurement using a particular liquid of interest, it is possible to directly access this information, which is of prime importance for catalysis, and financially very significant on an industrial scale. Results are reported here for a set of liquids, some simple alkanes (dodecane, tetradecane and hexadecane) plus water and cyclohexane, accessing pores in sol-gel silicas of nominal pore diameters 60Å, 100Å, 200Å, 500 Å. The key conclusions were that for the alkanes, the dimension of chain length was not relevantto the filling fraction, however for the cyclohexane a molecular diameter of 3.8 Å fitted the data well.