Probing four orders of magnitude of the diffusion time in porous silica glass with unconventional NMR techniques

The combined use of two unconventional NMR diffusometry techniques permits measurements of the self-diffusion coefficient of fluids confined in porous media in the time range from 100 microseconds to seconds. The fringe field stimulated echo technique (FFStE) exploits the strong steady gradient in the fringe field of a superconducting magnet. Using a standard 9.4 T (400 MHz) wide-bore magnet, for example, the gradient is 22 T/m at 375 MHz proton resonance and reaches 60 T/m at 200 MHz. Extremely short diffusion times can be probed on this basis. The magnetization grid rotating frame imaging technique (MAGROFI) is based on gradients of the radio frequency (RF) field. The RF gradients not necessarily need be constant since the data are acquired with spatial resolution along the RF gradient direction. MAGROFI is also well suited for unilateral NMR applications where all fields are intrinsically inhomogeneous. The RF gradients reached depend largely on the RF coil diameter and geometry. Using a conic shape, a value of at least 0.3 T/m can be reached which is suitable for long-time diffusion measurements. Both techniques do not require any special hardware and can be implemented on standard high RF power NMR spectrometers. As an application, the influence of the tortuosity increasing with the diffusion time is examined in a saturated porous silica glass.     

NMR microimaging studies of water diffusivity in saturated, microporous systems

A novel microimaging method is described for measuring the effective diffusion coefficient (D_∞) of water in saturated, microporous materials. A simple multicompartment computer simulation was used to show how the value of D_∞, when combined with measurements of water proton relaxation times and pulsed field gradient spin-echo amplitudes, allows the pore size distribution and pore connectivity to be characterized.     

The effect of the properties of porous media on light scattering

Numerical wave-optical methods for light scattering simulations are used to asses the effect of porosity on the optical properties of paper coating. Both constant porosity profile and media with porosity contrast between layers at different depths are considered. We can predict optimal paper coating structures for both brightness and gloss from the results.     

Observation of molecular migration in porous media using 2D exchange spectroscopy in the inhomogeneous magnetic field

We present a new method for observing fluid diffusion in a porous medium. The method employs 2D exchange spectroscopy for molecules diffusing in the presence of local magnetic field inhomogeneities, in our case distilled water in various sized glass bead packs. Our experiment involves an acquisition and evolution time domain with the two Fourier domains corresponding to the spectral distribution of local fields. We show that exchange in the internal magnetic field can be seen in a 2D spectrum with a characteristic time on the order of that required to diffuse 0.15 sphere diameters with similar behavior found for computer simulations. The method is potentially useful for studying the internal migrations in more complicated systems such as sandstones or other porous media.     

A cumulant analysis for non-Gaussian displacement distributions in Newtonian and non-Newtonian flows through porous media

We use displacement encoding pulsed field gradient (PFG) nuclear magnetic resonance to measure Fourier components S(q) of flow displacement distributions P(zeta) with mean displacement (zeta) for Newtonian and non-Newtonian flows through rocks and bead packs. Displacement distributions are non-Gaussian; hence, there are finite terms above second order in the cumulant expansion of ln(S(q)). We describe an algorithm for an optimal self-consistent cumulant analysis of data, which can be used to obtain the first three (central) moments of a non-Gaussian P(zeta), with error bars. The analysis is applied to Newtonian and non-Newtonian flows in rocks and beads. Flow with shear-thinning xanthan solution produces a 15.6+/-2.3% enhancement of the variance sigma(2) of displacement distributions when compared to flow experiments with water.     

Initially linear echo-spacing dependence of 1/T2 measurements in many porous media with pore-scale inhomogeneous fields

For a liquid sample with unrestricted diffusion in a constant magnetic field gradient g, the increase R in R2=1/T2 for CPMG measurements is 1/3(taugammag)2D, where gamma is magnetogyric ratio, tau is the half the echo spacing TE, and D is the diffusion constant. For measurements on samples of porous media with pore fluids and without externally applied gradients there may still be significant pore-scale local inhomogeneous fields due to susceptibility differences, whose contributions to R2 depend on tau. Here, diffusion is not unrestricted nor is the field gradient constant. One class of approaches to this problem is to use an "effective gradient" or some kind of average gradient. Then, R2 is often plotted against tau2, with the effective gradient determined from the slope of some of the early points. In many cases, a replot of R2 against tau instead of tau2 shows a substantial straight-line interval, often including the earliest available points. In earlier work [G.C. Borgia, R.J.S. Brown, P. Fantazzini, Phys. Rev. E 51 (1995) 2104; R.J.S. Brown, P. Fantazzini, Phys. Rev. B 47 (1993) 14823] these features were noted, and attention was called to the fact that very large changes in field and gradient are likely for a small part of the pore fluid over distances very much smaller than pore dimensions. A truncated Cauchy-Lorentz (C-L) distribution of local fields in the pore space was used to explain observations, giving reduced effects of diffusion because of the averaging properties of the C-L distribution, the truncation being at approximately +/-1/2chiB0, where chi is the susceptibility difference. It was also noted that, when there is a narrow range of pore size a, over a range of about 40 of the parameter xi=1/3chinua2/D, where nu is the frequency, R2 does not depend much on pore size a nor on diffusion constant D. Examples are shown where plots of R2 vs tau show better linear fits to the data for small tau values than do plots vs tau2. The present work shows that, if both grain-scale and sample-scale gradients are present for samples with narrow ranges of T2, it may be possible to identify the separate effects with the linear and quadratic coefficients in a second-order polynomial fit to the early data points. Of course, many porous media have wide pore size and T2 distributions and hence wide ranges of xi. For some of these wide distributions we have plotted R2 vs tau for signal percentiles, normalized to total signal for shortest tau, again showing initially linear tau-dependence even when available data do not cover the longest and/or shortest T2 values for alltau values. For the examples presented, both the intercepts and the initial slopes of the plots of R2 vs tau increase systematically with signal percentile, starting at smallest R2.     

孔隙介质包裹的充液管道结构中导波传播特性

研究孔隙介质包裹的充液管道中纵向导波传播特性,分析孔隙介质参数对频散曲线的影响。建立了孔隙介质包裹充液管道的结构模型,利用孔隙介质弹性波动理论,建立对应的频散方程,数值模拟计算得到该模型的频散曲线和时域波形,并分析了孔隙介质参数以及管壁厚度对频散曲线的影响。结果表明孔隙介质的渗透率对于导波频散的影响较小,孔隙度的改变对时域波形的位移幅度影响较大。同时,导波存在衰减,且衰减随孔隙度增大而增大。所得结论为埋地管道无损检测方面提供一定理论参考。     

The effects of porosity and permeability on fluid flow and heat transfer of multi walled carbon nano-tubes suspended in oil (MWCNT/Oil nano-fluid) in a microchannel filled with a porous medium

The forced convection heat transfer and laminar flow in a two-dimensional microchannel filled with a porous medium is numerically investigated. The nano-particles which have been used are multi walled carbon nano-tubes (MWCNT) suspended in oil as the based fluid. The assumption of no-slip condition between the base fluid and nano-particles as well as the thermal equilibrium between them allows us to study the nanofluid in a single phase. The nanofluid flow through the microchannel has been modeled using the Darcy–Forchheimer equation. It is also assumed that there is a thermal equilibrium between the solid phase and the nanofluid for energy transfer. The walls of the microchannel are under the influence of a fluctuating heat flux. Also, the slip velocity boundary condition has been assumed along the walls. The effects of Darcy number, porosity and slip coefficients and Reynolds number on the velocity and temperature profiles and Nusselt number will be studied in this research.     

NMR study of the vapor phase contribution to diffusion in partially filled silica glasses with nanometer and micrometer pores

The contribution of the vapor phase to molecular diffusion in porous silica glasses with nanometer (Vycor) and micrometer (VitraPor#5) pores partially filled with water (polar) or cyclohexane (nonpolar) was investigated with the aid of field-gradient NMR diffusometry. Due to the vapor phase, the effective diffusion coefficient of cyclohexane filling micrometer pores (VitraPor#5) increased up to 10 times relative to the value in bulk liquid upon reduction of the pore space filling factor. On the other hand, the effective diffusion coefficient of water first decreases and then increases when the liquid content is reduced. The dependence of the effective diffusion coefficient on the pore filling factor is strongly related to the pore dimension. A general two-phase exchange model is presented that is well accounting for all experimental diffusion features.     

Effect of thermal stratification on free convection in a square porous cavity filled with a nanofluid using Tiwari and Das' nanofluid model

Natural convection in a square porous cavity filled with a nanofluid in conditions of thermal stratification has been numerically studied. The mathematical model has been formulated in terms of the dimensionless stream function and temperature using the Darcy–Boussinesq approximation and Tiwari and Das' nanofluid model with new more realistic empirical correlations for the physical properties of the nanofluids. Formulated partial differential equations along with the corresponding boundary conditions have been solved by the finite difference method. Particular efforts have been focused on the effects of the Rayleigh number, thermal stratification parameter, porosity of the porous medium, solid volume fraction parameter of nanoparticles, and the solid matrix of the porous medium (glass balls and aluminum foam) on the local and average Nusselt numbers, streamlines and isotherms. It has been observed an essential effect of thermal stratification parameter on heat and fluid flow fields.     

Velocity autocorrelation spectra of fluid in porous media measured by the CPMG sequence and constant magnetic field gradient

Carr-Purcell-Meiboom-Gill (CPMG) train of radiofrequency pulses applied to spins in the constant magnetic field gradient is an efficient variant of the modulated magnetic field gradient spin echo method, which provides information about molecular diffusion in the frequency domain instead of in the time domain as with the two-pulse gradient spin echo. The frequency range of this novel technique is broad enough to sample the power spectrum of displacement fluctuation in water-saturated pulverized silica (SiO2) and provides comprehensive information about the molecular restricted motion as well as about the structure of the medium.     

Restricted diffusion and exchange of water in porous media: average structure determination and size distribution resolved from the effect of local field gradients on the proton NMR spectrum

NMR Pulsed field gradient measurements of the restrained diffusion of confined fluids constitute an efficient method to probe the local geometry in porous media. In most practical cases, the diffusion decay, when limited to its principal part, can be considered as Gaussian leading to an apparent diffusion coefficient. The evolution of the latter as a function of the diffusion interval yields average information on the surface/volume ratio of porosities and on the tortuosity of the network. In this paper, we investigate porous model systems of packed spheres (polystyrene and glass) with known mean diameter and polydispersity, and, in addition, a real porous polystyrene material. Applying an Inverse Laplace Transformation in the second dimension reveals an evolution of the apparent diffusion coefficient as a function of the resonance frequency. This evolution is related to a similar evolution of the transverse relaxation time T2. These results clearly show that each resonance frequency in the water proton spectrum corresponds to a particular magnetic environment produced by a given pore geometry in the porous media. This is due to the presence of local field gradients induced by magnetic susceptibility differences at the liquid/solid interface and to slow exchange rates between different pores as compared to the frequency differences in the spectrum. This interpretation is nicely confirmed by a series of two-dimensional exchange experiments.     

The directionality of partially coherent beams expressed in terms of the far-field divergence angle and of the far-field radiant intensity distribution

Taking the partially coherent cosh-Gaussian beam (ChG) as an illustrative example, the far-field divergence angle and directionality of partially coherent beams are studied. There are three competing physical mechanisms, i.e., the spatial coherence, diffraction and decentration, which affect the far-field divergence angle of partially coherent ChG beams. Two partially coherent ChG beams may generate the same far-field divergence angle, and partially coherent ChG beams may also have the same far-field divergence angle as a fully coherent ChG beam or as a fully coherent Gaussian laser beam if the three physical mechanisms are appropriately balanced. The consistency of the directionality of partially coherent beams expressed in terms of the far-field divergence angle and in terms of the far-field radiant intensity distribution is examined. Generally, two partially coherent beams with the same far-field divergence angle have not certainly the same far-field radiant intensity distribution. However, under certain conditions, it is possible to achieve the consistency of the directionality expressed in terms of the far-field divergence angle and of the normalized far-field radiant intensity distribution.     

Structure and transport mechanisms of Si/porous Si n-p junctions prepared by liquid phase epitaxy

Heterojunction devices of n-Si/p-PSi were fabricated by growing n-Si films onto p-type porous Si substrates by liquid phase epitaxy. The structure of the grown films was checked using scanning electron microscopy and X-ray diffraction spectroscopy. X-ray diffraction measurements showed that the grown films have monocrystalline structure oriented along (1 1 1) direction with mainly cubic phase. Current-voltage (I-V) and capacitance-voltage (C-V) characteristics were measured over the temperature range from 298 to 398 K. The analysis of the dark I-V characteristics of n-Si/p-PSi at several temperatures is done to elucidate the conduction mechanisms and the evaluation of the heterojunction parameters is presented. Two carrier transport mechanisms are believed to be at the origin of the forward current. At low bias voltage (V ≤ 0.4 V) the forward current is dominated by the recombination at the porous silicon side of the space charge region. In the 0.5 V ≤ V ≤ 1.4 V region, the current transport is due to the space charge—limited current mechanism dominated by a single trapping level of energy 0.41 eV. The reverse current is considered to be mainly generated in the depletion region of the porous silicon. The capacitance-voltage results confirm an abrupt junction with a homogenous distribution of the impurities inside the space charge region. Information on the depletion region, built-in voltage and net carrier concentration were obtained from the dark C-V characteristics.     

Time domain numerical modeling of wave propagation in 2D heterogeneous porous media

This paper deals with the numerical modeling of wave propagation in porous media described by Biot’s theory. The viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity, which is valid in the low-frequency range. The coexistence of propagating fast compressional wave and shear wave, and of a diffusive slow compressional wave, makes numerical modeling tricky. To avoid restrictions on the time step, the Biot’s system is splitted into two parts: the propagative part is discretized by a fourth-order ADER scheme, while the diffusive part is solved analytically. Near the material interfaces, a space–time mesh refinement is implemented to capture the small spatial scales related to the slow compressional wave. The jump conditions along the interfaces are discretized by an immersed interface method. Numerical experiments and comparisons with exact solutions confirm the accuracy of the numerical modeling. The efficiency of the approach is illustrated by simulations of multiple scattering.     

Quantum effects on the Rayleigh-Taylor instability of stratified fluid/plasma through porous media

Quantum effect on Rayleigh-Taylor instability of stratified plasma layer through a porous medium are investigated. The linear growth rate is obtained analytically and is analyzed. In the presence of quantum effect, both the porosity of porous medium and the medium permeability has different influence on the coup point () for stability, but they do not have influence on the critical point () for stability. The quantum effect plays the principal role of the complete stability case for the system considered.     

IR study on the effect of chloride ion on porous silicon

Infrared (IR) studies have been carried out on porous silicon samples to infer on the changes in the surface bonding in the porous silicon (PS) layer due to chloride (Cl⁻) and subsequent fluoride (F⁻) ion exposures with respect to time. It is observed that silicon hydride linkages decreases and silicon oxide linkages increases with time of exposure to HCl, suggesting a possible oxidation of the porous layer. IR study revealed the formation of SiO (silanones) bonds. A possible mechanism for the formation of silanones from SiOH species has been proposed to explain the observation. We also observed a saturation of silicon oxide groups with complete disappearance of silicon hydride peaks indicating the complete conversion of silicon hydride to oxides. Furthermore on exposure to F⁻, the IR spectrum showed a rapid destruction of silicon oxygen linkages.     

The effect of etching time of porous silicon on solar cell performance

Porous silicon (PS) layers based on crystalline silicon (c-Si) n-type wafers with (1 0 0) orientation were prepared using electrochemical etching process at different etching times. The optimal etching time for fabricating the PS layers is 20 min. Nanopores were produced on the PS layer with an average diameter of 5.7 nm. These increased the porosity to 91%. The reduction in the average crystallite size was confirmed by an increase in the broadening of the FWHM as estimated from XRD measurements. The photoluminescence (PL) peaks intensities increased with increasing porosity and showed a greater blue shift in luminescence. Stronger Raman spectral intensity was observed, which shifted and broadened to a lower wave numbers of 514.5 cm⁻¹ as a function of etching time. The lowest effective reflectance of the PS layers was obtained at 20 min etching time. The PS exhibited excellent light-trapping at wavelengths ranging from 400 to 1000 nm. The fabrication of the solar cells based on the PS anti-reflection coating (ARC) layers achieved its highest efficiency at 15.50% at 20 min etching time. The I-V characteristics were studied under 100 mW/cm² illumination conditions.     

Effect of magnetic field gradients induced by microvasculature on NMR measurements of molecular self-diffusion in biological tissues

Presence of induced mesoscopic gradients of magnetic field in magnetically heterogeneous samples affects the measured value of apparent diffusion coefficient. This effect is investigated theoretically in the context of diffusion measurements in perfused biological tissues with blood as the paramagnetic compartment. It is shown that the apparent diffusion coefficient is sensitive to mutual correlations in vessel positions. Neglect of these correlations results in a failure of the commonly used model of microvasculature in which vessels are described as independently placed cylinders. The model is modified to account for intervessel correlations. The results indicate an underestimation of apparent diffusion coefficient in proportion to the magnetic susceptibility of intravascular compartment in agreement with published experimental data. The proportionality coefficient depends on the microvascular architecture. Comparison with experimental data yields a numerical value for a new model parameter that characterises the correlation in mutual positions of blood vessels.     

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采用由脉冲负偏压调节的等离子体增强化学气相沉积方法,以硅烷为源气体,在玻璃基片上沉积得到了多孔二氧化硅薄膜。将反应过程中加在沉积区域的脉冲偏压固定在-350V,当占空比从0.162增大到0.864时,薄膜样品的形貌、成份和结构均不相同。扫描电镜照片表明,组成多孔氧化硅薄膜的颗粒在占空比增大时变得细腻,并且薄膜整体变得多孔且蓬松。拉曼光谱和红外光谱结果显示,薄膜样品中的非晶硅和Si-H键在较高的占空比下减弱甚至消失。占空比升高时氧化硅桥键所占比例持续增加。