Dispersion of solutes in porous media

A recently introduced theory of solute transport in porous media is tested by comparison with experiment. The solute transport is predicted using an adaptation of the cluster statistics of percolation theory to critical path analysis together with knowledge of how the structure of such percolation clusters affects the time of transport across them. Only the effects of a single scale of medium heterogeneity are incorporated, and a minimal amount of information regarding the structure of the medium is required. This framework is used to find effectively the distributions of solute velocities and travel distances and thus generate arrival time distributions. The comparison with experiment focuses on the dispersivity (the ratio of the second to the first moment of the spatial solute distribution). The predictions of the theory in the absence of diffusion are verified by comparing with over 2200 experiments over length scales from a few microns to 100 km. At larger length scales (centimeters on up) about 95% of the data lie within our predicted bounds. At smaller length scales approximately 99.8% of the data lie where we predict. These comparisons are not trivial as the typical values of the dispersivity increase by ten orders of magnitude over ten orders of magnitude of length scale. Noteworthy is that the classical advection-dispersion (ADE) equation predicts that the dispersivity should be independent of length scale! This agreement with experiment requires rethinking of the relevance of diffusion and multi-scale heterogeneity and would also appear to signal the complete inappropriateness of using the classical ADE or any of its derivatives to model solute transport.     

Evaluation of paint coating thickness variations based on pulsed Infrared thermography laser technique

In this paper, a pulsed Infrared thermography technique using a homogeneous heat provided by a laser source is used for the non-destructive evaluation of paint coating thickness variations. Firstly, numerical simulations of the thermal response of a paint coated sample are performed. By analyzing the thermal responses as a function of thermal properties and thickness of both coating and substrate layers, optimal excitation parameters of the heating source are determined. Two characteristic parameters were studied with respect to the paint coating layer thickness variations. Results obtained using an experimental test bench based on the pulsed Infrared thermography laser technique are compared with those given by a classical Eddy current technique for paint coating variations from 5 to 130 μm. These results demonstrate the efficiency of this approach and suggest that the pulsed Infrared thermography technique presents good perspectives to characterize the heterogeneity of paint coating on large scale samples with other heating sources.     

Magnetic resonance imaging in laboratory petrophysical core analysis

Magnetic resonance imaging (MRI) is a well-known technique in medical diagnosis and materials science. In the more specialized arena of laboratory-scale petrophysical rock core analysis, the role of MRI has undergone a substantial change in focus over the last three decades. Initially, alongside the continual drive to exploit higher magnetic field strengths in MRI applications for medicine and chemistry, the same trend was followed in core analysis. However, the spatial resolution achievable in heterogeneous porous media is inherently limited due to the magnetic susceptibility contrast between solid and fluid. As a result, imaging resolution at the length-scale of typical pore diameters is not practical and so MRI of core-plugs has often been viewed as an inappropriate use of expensive magnetic resonance facilities. Recently, there has been a paradigm shift in the use of MRI in laboratory-scale core analysis. The focus is now on acquiring data in the laboratory that are directly comparable to data obtained from magnetic resonance well-logging tools (i.e., a common physics of measurement). To maintain consistency with well-logging instrumentation, it is desirable to measure distributions of transverse (_T2$T_2$) relaxation time–the industry-standard metric in well-logging–at the laboratory-scale. These _T2$T_2$ distributions can be spatially resolved over the length of a core-plug. The use of low-field magnets in the laboratory environment is optimal for core analysis not only because the magnetic field strength is closer to that of well-logging tools, but also because the magnetic susceptibility contrast is minimized, allowing the acquisition of quantitative image voxel (or pixel) intensities that are directly scalable to liquid volume. Beyond simple determination of macroscopic rock heterogeneity, it is possible to utilize the spatial resolution for monitoring forced displacement of oil by water or chemical agents, determining capillary pressure curves, and estimating wettability. The history of MRI in petrophysics is reviewed and future directions considered, including advanced data processing techniques such as compressed sensing reconstruction and Bayesian inference analysis of under-sampled data. Although this review focuses on rock core analysis, the techniques described are applicable in a wider context to porous media in general, such as cements, soils, ceramics, and catalytic materials.     

Controlling the micro/nanostructure of self-cleaning polymer coating

Polypropylene bio-mimic self-cleaning surfaces with porous micro-nano-binary morphology structures were prepared by a simple casting method. The influence of the cooling process and solvent composition on water contact angle, sliding angles and self-cleaning properties has been investigated. Detailed SEM morphology studies revealed that the polymer used in this work is commercial-grade granular low-density polyethylene (LDPE) forms petal-like crystalline, which are of micrometer scale in length and nanometer scale in thickness. The nano-crystallines on the surface represent a porous three-dimensional micro-nano-binary structure. It was found that a compromise to the film porosity and crystal nano structure is essential for achieving a satisfied self-cleaning surface. Under optimum condition, a water contact angle of 152.2°, and a sliding angle of 1.7° can be obtained using this simple method.     

Fluorescence lifetime distributions in membrane systems

Membranes are complex biological systems that display heterogeneity at all spatial scales. At a molecular level, the heterogeneity arises from lipid and protein composition. At the cellular level, heterogeneity is due to membrane organization and large scale morphology. A quantitative evaluation of membrane heterogeneity at a microscopic level is very important for several fields of membrane studies. We have developed a method for the analysis of the decay of fluorescent membrane probes that can provide a quantity sensitive to membrane heterogeneity. This method is based on the analysis of the fluorescence decay using continuous lifetime distributions. The major challenge in the interpretation of the analysis results is in the identification, at a molecular level, of the mechanisms that influence the fluorescence decay. In this review we illustrate the principles of data analysis and we show examples of identification of the measured parameters with specific variables that affect membrane heterogeneity.     

RIMAPS and variogram analysis of the surface topography induced by laser interference micropatterning

A micropattern induced by laser interference on the surface of a copper alloy specimen is characterized using rotated image with maximum average power spectrum (RIMAPS) technique and the variogram method. The experimental bidimensional pattern is compared to the expected ideal regular one. Results confirm that the systematic use of RIMAPS and variograms, helps to determine how far the real surface obtained in the experiment differs from ideal regular micropattern. The dimensions of irregularities that cause the discrepancy between the obtained and ideal micropattern are also quantified.     

The Heterogeneous Mineral Content of Bone—Using Stochastic Arguments and Simulations to Overcome Experimental Limitations

On a sub-millimeter length scale, bone is a very heterogeneous material with varying mineral content. This heterogeneity can be measured by quantitative backscattered electron imaging (qBEI) and quantified by a probability distribution called the bone mineralization density distribution (BMDD). The stochastic nature of the backscattering of electrons during the measurement makes the results dependent on the acquisition time. In this work the influence of the measurement conditions was quantified and was corrected for using Tikhonov regularization. Deconvolution reduces the width of the BMDD and allows a more precise definition of a reference BMDD for healthy adults. The corrected information was used as input for a mathematical model that predicts the time evolution of the BMDD. Simulations of osteoporosis treatment reveal a double peak in the BMDD that is not observed in experiments due to limited acquisition time. Our method allows determining the necessary acquisition time to resolve such double peaks.     

Continuum reconstruction of the pore scale microstructure for Fontainebleau sandstone

A stochastic geometrical modeling technique is used to reconstruct a laboratory scale Fontainebleau sandstone with a sidelength of 1.5 cm. The model reconstruction is based on crystallite properties and diagenetic parameters determined from two-dimensional images. The three-dimensional pore scale microstructure of the sandstone is represented by a list of quartz crystallites defined geometrically and placed in the continuum. This allows generation of synthetic μ-CT images of the rock model at arbitrary resolutions. Quantitative microstructure comparison based on Minkowski functionals, two-point correlation function and local porosity theory indicates that this modeling technique can provide more realistic and accurate models of sandstones than many existing techniques used currently. Synthetic μ-CT images at different resolutions from a laboratory scale model of Fontainebleau sandstone are made available to the scientific community for resolution dependent petrophysical analysis.     

Vortex pinning: A probe for nanoscale disorder in iron-based superconductors

The pinning of quantized flux lines, or vortices, in the mixed state is used to quantify the effect of impurities in iron-based superconductors (IBS). Disorder at two length scales is relevant in these materials. Strong flux pinning resulting from nm-scale heterogeneity of the superconducting properties leads to the very disordered vortex ensembles observed in the IBS, and to the pronounced maximum in the critical current density j_c at low magnetic fields. Disorder at the atomic scale, most likely induced by the dopant atoms, leads to “weak collective pinning” and a magnetic field-independent contribution j_c^coll. The latter allows one to estimate quasiparticle scattering rates.     

Nano-optical imaging and spectroscopy of order,phases, and domains in complex solids

The structure of our material world is characterized by a large hierarchy of length scales that determines material properties and functions. Increasing spatial resolution in optical imaging and spectroscopy has been a long standing desire, to provide access, in particular, to mesoscopic phenomena associated with phase separation, order, and intrinsic and extrinsic structural inhomogeneities. A general concept for the combination of optical spectroscopy with scanning probe microscopy emerged recently, extending the spatial resolution of optical imaging far beyond the diffraction limit. The optical antenna properties of a scanning probe tip and the local near-field coupling between its apex and a sample provide few-nanometer optical spatial resolution. With imaging mechanisms largely independent of wavelength, this concept is compatible with essentially any form of optical spectroscopy, including nonlinear and ultrafast techniques, over a wide frequency range from the terahertz to the extreme ultraviolet. The past 10 years have seen a rapid development of this nano-optical imaging technique, known as tip-enhanced or scattering-scanning near-field optical microscopy (s-SNOM). Its applicability has been demonstrated for the nano-scale investigation of a wide range of materials including biomolecular, polymer, plasmonic, semiconductor, and dielectric systems.

We provide a general review of the development, fundamental imaging mechanisms, and different implementations of s-SNOM, and discuss its potential for providing nanoscale spectroscopic including femtosecond spatio-temporal information. We discuss possible near-field spectroscopic implementations, with contrast based on the metallic infrared Drude response, nano-scale impedance, infrared and Raman vibrational spectroscopy, phonon Raman nano-crystallography, and nonlinear optics to identify nanoscale phase separation (PS), strain, and ferroic order. With regard to applications, we focus on correlated and low-dimensional materials as examples that benefit, in particular, from the unique applicability of s-SNOM under variable and cryogenic temperatures, nearly arbitrary atmospheric conditions, controlled sample strain, and large electric and magnetic fields and currents. For example, in transition metal oxides, topological insulators, and graphene, unusual electronic, optical, magnetic, or mechanical properties emerge, such as colossal magneto-resistance (CMR), metal–insulator transitions (MITs), high-T _C superconductivity, multiferroicity, and plasmon and phonon polaritons, with associated rich phase diagrams that are typically very sensitive to the above conditions. The interaction of charge, spin, orbital, and lattice degrees of freedom in correlated electron materials leads to frustration and degenerate ground states, with spatial PS over many orders of length scale. We discuss how the optical near-field response in s-SNOM allows for the systematic real space probing of multiple order parameters simultaneously under a wide range of internal and external stimuli (strain, magnetic field, photo-doping, etc.) by coupling directly to electronic, spin, phonon, optical, and polariton resonances in materials. In conclusion, we provide a perspective on the future extension of s-SNOM for multi-modal imaging with simultaneous nanometer spatial and femtosecond temporal resolution.     

Heterogeneity of activated carbons with different surface chemistry in adsorption of phenol from aqueous solutions

The heterogeneity of activated carbons is investigated on the basis of adsorption isotherms of phenol from dilute aqueous solutions at different values of pH in the solution. The original carbon studied was prepared from polyethyleneterephtalate (PET). Its various oxygen surface functionalities were systematically changed by additional nitric acid and heat treatments. The Dubinin-Astakhov adsorption-isotherm equation was used to evaluate the parameters characterizing the adsorption of phenol from dilute water solutions on activated carbon surfaces. Adsorption energy distribution functions were calculated by the INTEG algorithm, based on a regularization method. Analysis of distribution functions for activated carbons provides significant comparative information about their energetic heterogeneity. Moreover, a comparison of the resulting energies obtained from the distributions can be made with enthalpic data.     

Nonhomogeneous electrostatic oscillations in two-dimensional systems

A new type of excitations — electrostatic oscillations (ESO) — are shown to exist in the finite superlattices (SL). The ESO are the limiting case of the surface magnetoplasmons when the scale length of the spatial variations in the fields and currents is comparable with the sample dimensions. The formal similarity is found between the ESO and the magnetization vibrations in ferromagnetic materials (Walker's modes [1,2]). The main feature of the ESO is the independence of their frequencis on the absolute dimensions of a sample.     

Systemic risk on different interbank network topologies

In this paper we develop an interbank market with heterogeneous financial institutions that enter into lending agreements on different network structures. Credit relationships (links) evolve endogenously via a fitness mechanism based on agents’ performance. By changing the agent’s trust on its neighbor’s performance, interbank linkages self-organize themselves into very different network architectures, ranging from random to scale-free topologies. We study which network architecture can make the financial system more resilient to random attacks and how systemic risk spreads over the network. To perturb the system, we generate a random attack via a liquidity shock. The hit bank is not automatically eliminated, but its failure is endogenously driven by its incapacity to raise liquidity in the interbank network. Our analysis shows that a random financial network can be more resilient than a scale free one in case of agents’ heterogeneity.     

Accuracy evaluation of an X-ray microtomography system

Microstructural parameter evaluation of reservoir rocks is of great importance to petroleum production companies. In this connection, X-ray computed microtomography (μ-CT) has proven to be a quite useful method for the assessment of rocks, as it provides important microstructural parameters, such as porosity, permeability, pore size distribution and porous phase of the sample. X-ray computed microtomography is a non-destructive technique that enables the reuse of samples already measured and also yields 2-D cross-sectional images of the sample as well as volume rendering. This technique offers an additional advantage, as it does not require sample preparation, of reducing the measurement time, which is approximately one to three hours, depending on the spatial resolution used. Although this technique is extensively used, accuracy verification of measurements is hard to obtain because the existing calibrated samples (phantoms) have large volumes and are assessed in medical CT scanners with millimeter spatial resolution. Accordingly, this study aims to determine the accuracy of an X-ray computed microtomography system using a Skyscan 1172 X-ray microtomograph. To accomplish this investigation, it was used a nylon thread set with known appropriate diameter inserted into a glass tube. The results for porosity size and phase distribution by X-ray microtomography were very close to the geometrically calculated values. The geometrically calculated porosity and the porosity determined by the methodology using the μ-CT was 33.4 ± 3.4% and 31.0 ± 0.3%, respectively. The outcome of this investigation was excellent. It was also observed a small variability in the results along all 401 sections of the analyzed image. Minimum and maximum porosity values between the cross sections were 30.9% and 31.1%, respectively. A 3-D image representing the actual structure of the sample was also rendered from the 2-D images.     

Homogenization for Periodic Heterogeneous Materials with Arbitrary Position-Dependent Material Properties

We present a rigorous homogenization approach for efficient computation of a class of physical problems in a one-dimensional periodic heterogeneous material. This material is represented by a spatially periodic array of unit cells with a length of ε. More specifically, the method is applied to the diffusion, heat conduction, and wave propagation problems. Heterogeneous materials can have arbitrary position-dependent continuous or discontinuous materials properties (for example heat conductivity) within the unit cell. The final effective model includes both effective properties at the leading order and high-order contributions due to the microscopic heterogeneity. A dimensionless heterogeneity parameter β is defined to represent high-order contributions, shown to be in the range of [-1/12, 0], and has a universal expression for all three problems. Both effective properties and heterogeneity parameter β are independent of ε, the microscopic scale of heterogeneity. The homogenized solution describing macroscopic variations can be obtained from the effective model. Solution with sub-unit-cell accuracy can be constructed based on the homogenized solution and its spatial derivatives. The paper represents a general approach to obtain the effective model for arbitrary periodic heterogeneous materials with position-dependent properties.     

第三代同步辐射光源X射线相干性测量研究

随着高性能第三代同步辐射光源的建成开放,基于X射线相干特性的实验方法得到了快速发展和广泛应用.作为一个典型的例子,X射线相位衬度成像已经成为常规的X射线实验方法并向用户开放.相干散射、相干衍射成像、光子关联谱等X射线实验方法正日益受到重视,在高空间分辨、时间分辨等研究领域已显示出其独特的优越性.因此,研究和测量第三代同步辐射的空间相干特性对进一步发展这些新的实验方法具有重要意义.基于Talbot自成像原理成功测量了上海光源X射线成像线站发射的X射线的空间相干长度,并进而测得了相应光源的空间尺度.光子能量为33.2 keV时,测得的X射线光束垂直方向空间相干长度为8.84μm,对应的光源尺寸为23μm,测量结果与理论分析相符.     

Filamentation and stimulated Brillouin scattering in a turbulent plasma

This paper presents a theory of filamentation and stimulated Brillouin scattering (SBS) of high-frequency electromagnetic radiation in a weakly collisional plasma with ion-acoustic turbulence. When the square of the wavelength of the plasma perturbations is less than the product of the two mean free path lengths of an electron with respect to its collisions with turbulent fluctuations and with electrons, the influence of cold highly collisional electrons on the parametric instabilities becomes apparent. It is shown that the plasma turbulence lowers the filamentation threshold, and the SBS threshold can be either lowered or raised. The dependence of the SBS and filamentation thresholds on the electron mean free path length in the turbulent plasma and on the anisotropy of the plasma turbulence is determined. The corresponding dependence of the spatial scale of the most efficiently growing filaments and their spatial growth rate are found. Zh. éksp. Teor. Fiz. 113, 629–645 (February 1998)     

Numerical study of the temperature and porosity effects on the fracture propagation in a 2D network of elastic bonds

This article reports results concerning the fracture of a 2d triangular lattice of atoms linked by springs. The lattice is submitted to controlled strain tests and the influence of both porosity and temperature on failure is investigated. The porosity is found on one hand to decrease the stiffness of the specimen but on the other hand it increases the deformation sustained prior to failure. Temperature is shown to control the ductility due to the presence of cavities that grow and merge. The rough surfaces resulting from the propagation of the crack exhibit self-affine properties with a roughness exponent = 0.59 ± 0.07 over a range of length scales which increases with temperature. Large cavities also have rough walls which are found to be fractal with a dimension, D, which evolves with the distance from the crack tip. For large distances, D is found to be close to 1.5, and close to 1.0 for cavities just before their coalescence with the main crack.     

Congestion analysis of traffic networks with direction-dependant heterogeneity

Traffic flow directionality and network weight asymmetry are widespread notions in traffic networks. This paper investigates the influence of direction-dependant heterogeneity on traffic congestion. To capture the effect of the link directionality and link weight asymmetry, the heterogeneity indexes of complex networks and the traffic flow model are introduced. The numerical results show that the critical value of heterogeneity determines congestion transition processes. The congestion degree increases with heterogeneity when the network heterogeneity is at a subcritical region. A network is more tolerant of congestion if the heterogeneity of the network is smaller or larger than the critical value. Furthermore, when heterogeneity reaches the critical value, the average number of accumulated vehicles arrives at the maximum and the traffic flow is under a serious congestion state. A significant improvement on the tolerance to congestion of traffic networks can be made if the network heterogeneity is controlled within a reasonable range.     

Anomalous dispersion in correlated porous media: a coupled continuous time random walk approach

We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through Darcy’s law and thus impacts on solute and particle transport. We consider purely advective transport in heterogeneity scenarios characterized by broad distributions of heterogeneity length scales and point values. Particle transport is characterized in terms of the stochastic properties of equidistantly sampled Lagrangian velocities, which are determined by the flow and conductivity statistics. The persistence length scales of flow and transport velocities are imprinted in the spatial disorder and reflect the distribution of heterogeneity length scales. Particle transitions over the velocity length scales are kinematically coupled with the transition time through velocity. We show that the average particle motion follows a coupled continuous time random walk (CTRW), which is fully parameterized by the distribution of flow velocities and the medium geometry in terms of the heterogeneity length scales. The coupled CTRW provides a systematic framework for the investigation of the origins of anomalous dispersion in terms of heterogeneity correlation and the distribution of conductivity point values. We derive analytical expressions for the asymptotic scaling of the moments of the spatial particle distribution and first arrival time distribution (FATD), and perform numerical particle tracking simulations of the coupled CTRW to capture the full average transport behavior. Broad distributions of heterogeneity point values and lengths scales may lead to very similar dispersion behaviors in terms of the spatial variance. Their mechanisms, however are very different, which manifests in the distributions of particle positions and arrival times, which plays a central role for the prediction of the fate of dissolved substances in heterogeneous natural and engineered porous materials.