Transport properties of saturated and unsaturated porous fractal materials

Inviscid, irrotational flow through fractal porous materials is studied. The key parameter is the variation of tortuosity with the filling fraction phi of fluid in the porous material. Altering the filling fraction provides a way of probing the effect of the fractal structure over all its length scales. The variation of tortuosity with phi is found to follow a power law of the form alpha approximately phi (-E) for deterministic and stochastic fractals in two and three dimensions. A phenomenological argument for the scaling of tortuosity alpha with filling fraction phi is presented and is given by alpha approximately phi(D_{w}-2/D_{f}-d_{E}), where D_{f} is the fractal dimension, D_{w} is the random walk dimension, and d_{E} is the Euclidean dimension. Numerically calculated values of the exponents show good agreement with those predicted from the phenomenological argument for both the saturated and the unsaturated model.     

Tortuosity measurement and the effects of finite pulse widths on xenon gas diffusion NMR studies of porous media.

We have extended the utility of NMR as a technique to probe porous media structure over length scales of approximately 100-2000 microm by using the spin 1/2 noble gas 129Xe imbibed into the system's pore space. Such length scales are much greater than can be probed with NMR diffusion studies of water-saturated porous media. We utilized Pulsed Gradient Spin Echo NMR measurements of the time-dependent diffusion coefficient, D(t), of the xenon gas filling the pore space to study further the measurements of both the pore surface-area-to-volume ratio, S/V(p), and the tortuosity (pore connectivity) of the medium. In uniform-size glass bead packs, we observed D(t) decreasing with increasing t, reaching an observed asymptote of approximately 0.62-0.65D(0), that could be measured over diffusion distances extending over multiple bead diameters. Measurements of D(t)/D(0) at differing gas pressures showed this tortuosity limit was not affected by changing the characteristic diffusion length of the spins during the diffusion encoding gradient pulse. This was not the case at the short time limit, where D(t)/D(0) was noticeably affected by the gas pressure in the sample. Increasing the gas pressure, and hence reducing D(0) and the diffusion during the gradient pulse served to reduce the previously observed deviation of D(t)/D(0) from the S/V(p) relation. The Pade approximation is used to interpolate between the long and short time limits in D(t). While the short time D(t) points lay above the interpolation line in the case of small beads, due to diffusion during the gradient pulse on the order of the pore size, it was also noted that the experimental D(t) data fell below the Pade line in the case of large beads, most likely due to finite size effects.     

Xenon NMR measurements of permeability and tortuosity in reservoir rocks

In this work we present measurements of permeability, effective porosity and tortuosity on a variety of rock samples using NMR/MRI of thermal and laser-polarized gas. Permeability and effective porosity are measured simultaneously using MRI to monitor the inflow of laser-polarized xenon into the rock core. Tortuosity is determined from measurements of the time-dependent diffusion coefficient using thermal xenon in sealed samples. The initial results from a limited number of rocks indicate inverse correlations between tortuosity and both effective porosity and permeability. Further studies to widen the number of types of rocks studied may eventually aid in explaining the poorly understood connection between permeability and tortuosity of rock cores.     

Scale invariance and viscosity of a two-dimensional Fermi gas

We investigate collective excitations of a harmonically trapped two-dimensional Fermi gas from the collisionless (zero sound) to the hydrodynamic (first sound) regime. The breathing mode, which is sensitive to the equation of state, is observed with an undamped amplitude at a frequency 2 times the dipole mode frequency for a large range of interaction strengths and different temperatures. This provides evidence for a dynamical SO(2,1) scaling symmetry of the two-dimensional Fermi gas. Moreover, we investigate the quadrupole mode to measure the shear viscosity of the two-dimensional gas and study its temperature dependence.     

How to measure the bogoliubov quasiparticle amplitudes in a trapped condensate

We propose an experiment, based on two consecutive Bragg pulses, to measure the momentum distribution of quasiparticle excitations in a trapped Bose gas at low temperature. With the first pulse one generates a bunch of excitations carrying momentum q, whose Doppler line is measured by the second pulse. We show that this experiment can provide direct access to the amplitudes u(q) and v(q) characterizing the Bogoliubov transformations from particles to quasiparticles. We simulate the behavior of the nonuniform gas by numerically solving the time dependent Gross-Pitaevskii equation.     

Fermi-liquid behavior of the normal phase of a strongly interacting gas of cold atoms

We measure the magnetic susceptibility of a Fermi gas with tunable interactions in the low-temperature limit and compare it to quantum Monte Carlo calculations. Experiment and theory are in excellent agreement and fully compatible with the Landau theory of Fermi liquids. We show that these measurements shed new light on the nature of the excitations of the normal phase of a strongly interacting Fermi gas.     

Dynamics and thermodynamics of the low-temperature strongly interacting Bose gas

We measure the zero-temperature equation of state of a homogeneous Bose gas of (7)Li atoms by analyzing the in situ density distributions of trapped samples. For increasing repulsive interactions our data show a clear departure from mean-field theory and provide a quantitative test of the many-body corrections first predicted in 1957 by Lee, Huang, and Yang [Phys. Rev. 106, 1135 (1957).]. We further probe the dynamic response of the Bose gas to a varying interaction strength and compare it to simple theoretical models. We deduce a lower bound for the value of the universal constant ξ > 0.44(8) that would characterize the universal Bose gas at the unitary limit.     

Determination of transport parameters in air-saturated porous materials via reflected ultrasonic waves

An ultrasonic reflectivity method of evaluating the acoustic parameters of porous materials saturated by air (or any other gas) is discussed. The method is based on experimental detection of waves reflected at normal incidence by the first and second interface of the material. This method is based on a temporal model of direct and inverse scattering problems for the propagation of transient ultrasonic waves in a homogeneous isotropic slab of porous material with a rigid frame [Fellah et al., J. Acoust. Soc. Am. 113, 61-73 (2003)]. Generally, the conventional ultrasonic approach can be used to determine tortuosity, and viscous and thermal characteristic lengths via transmitted waves. Porosity cannot be estimated in transmitted mode because of its very weak sensitivity. First interface use of the reflected wave at oblique incidence leads to the determination of porosity and tortuosity [Fellah et al., J. Acoust. Soc. Am. 113, 2424-2433 (2003)] but this is not possible at normal incidence. Using experimental data of reflected waves by the first and second interface at normal incidence simultaneously leads to the determination of porosity, tortuosity, viscous and thermal characteristic lengths. As with the classic ultrasonic approach for characterizing porous material saturated with one gas, both characteristic lengths are estimated individually by assuming a given ratio between them. Tests are performed using weakly resistive industrial plastic foams. Experimental and numerical results, and prospects are discussed.     

Raman-resonance-enhanced composite nonlinearity of air-guided modes in hollow photonic-crystal fibers

Coherent anti-Stokes Raman scattering (CARS) is used to measure relations between the resonant (Raman) and nonresonant (Kerr-type) optical nonlinearities of air-guided modes in a hollow-core photonic-crystal fiber (PCF). We demonstrate that, due to its interference nature, CARS provides a convenient tool for measuring the contribution of the fiber cladding to the total nonlinearity sensed by air-guided modes in hollow PCFs. On a Raman resonance with molecular vibrations in the gas that fills the fiber core, a two-color laser field is shown to induce optical nonlinearities that are several orders of magnitude higher than the nonresonant Kerr-type nonlinearities typical of air-guided PCF modes.     

Transmission characteristics of photonic crystal fiber gas cell used in frequency stabilized laser

We measure the transmission characteristics of hollow-core photonic crystal fiber （HC-PCF） gas cells with ferrule- and fusion-spliced configurations, and near- and far-field images of the HC-PCF are observed. Results show that the center of mass （COM） of the far-field image varies with the laser frequency and temperature, and the moving COM relates to the oscillatory transmission. Using a model of the spatial interference, we first demonstrate that mainly the modes with asymmetric phase distributions affect the COM position. The frequency stabilization performances of the lasers are compared. The fusion-spliced gas cell shows better performance than the ferrule-spliced one.     

Rashba spin-orbit interaction and shot noise for spin-polarized and entangled electrons

We study shot noise for spin-polarized currents and entangled electron pairs in a four-probe (beam-splitter) geometry with a local Rashba spin-orbit (s-o) interaction in the incoming leads. Within the scattering formalism we find that shot noise exhibits Rashba-induced oscillations with continuous bunching and antibunching. We show that entangled states and triplet states can be identified via their Rashba phase in noise measurements. For two-channel leads, we find an additional spin rotation due to s-o induced interband coupling which enhances spin control. We show that the s-o interaction deter-mines the Fano factor, which provides a direct way to measure the Rashba coupling constant via noise.     

Statistical mechanics of a one-dimensional lattice gas

We study the statistical mechanics of an infinite one-dimensional classical lattice gas. Extending a result ofvan Hove we show that, for a large class of interactions, such a system has no phase transition. The equilibrium state of the system is represented by a measure which is invariant under the effect of lattice translations. The dynamical system defined by this invariant measure is shown to be aK-system.     

基于电化学-热耦合模型研究隔膜孔隙结构对锂离子电池性能的影响机制

隔膜孔隙结构对锂离子电池性能具有重要的影响,本文提出了可准确描述充放电过程中锂离子电池内部复杂物理化学现象的电化学-热耦合模型,发现该模型较文献中模型的计算结果更接近实验测试数据.利用该模型探讨了隔膜孔隙率与扭曲率分别对锂离子电池性能的影响规律,发现减小孔隙率或增大扭曲率,电池输出电压、最大放电容量和平均输出功率均不断降低,电池表面温度和温升速度均不断升高;当孔隙率减小或扭曲率增大到一定程度时,放电初期电池输出电压均会出现先下降后回升的现象,且孔隙率越小或扭曲率越大,其下降的幅度越大、速度越快,回升所需时间也越长;要确保其不低于截止电压,隔膜扭曲率必须小于临界扭曲率(其下降至最低点刚好等于截止电压时的隔膜扭曲率).综合分析了放电过程中电池内部各电化学参量和产热量的动态分布规律,发现隔膜孔隙率和扭曲率主要影响放电末期电极膜片内部电化学反应以及其他放电时刻电解液中有效Li~+扩散(传导)系数.     

Potentials for almost Markovian random fields

A positive almost Markovian random field is a probability measure on a lattice gas whose finite set conditional probabilities are continuous and positive. We show that each such random field has a potential and in the translation invariant case an absolutely convergent potential. We give a criterion for determining which random fields correspond to pair potentials, or in generaln-body potentials. We show that two translation invariant positive almost Markovian random fields have the same finite set conditional probabilities if and only if one minimizes the specific free energy of the other.     

Effect of the internal microstructure in rapid-prototyped polycaprolactone scaffolds on physical and cellular properties for bone tissue regeneration

Biomedical scaffolds should be designed to optimize their inter-microstructure to enable cell infiltration and nutrient/waste transport. To acquire these properties, several structural parameters, such as pore size, pore shape, porosity, pore interconnectivity, permeability, and tortuosity are required. In this study, we explored the effect of tortuosity on the viable cell proliferation and mineralization of osteoblast-like-cells (MG63) in polycaprolactone scaffolds. For analysis, we designed four different scaffolds of various tortuosities ranging from 1.0 to 1.3 under the same porosity (56?%) and 100?% pore interconnectivity. The pore size of the scaffolds was set as 150 and 300?μm, and a mixture of these sizes. We found that despite the porosity being same, the elastic modulus was dependent on the pore size of the scaffolds due to the distributed stress concentration. In addition, the relative water movement within scaffolds was also related to the internal microstructure. Cell viability and Ca²⁺ deposition of the cell-seeded scaffolds showed that the proliferation of viable cells and mineralization in the scaffolds with appropriate tortuosity (1.2) was relatively high compared to those of the scaffolds displaying low (1.05 and 1.1) or high (1.3) tortuosity. Our findings indicated that the internal microstructure of the scaffolds may influence not only the physical properties, but in addition the cellular behavior.     

The running coupling at finite temperature

We propose the ensemble averaged running coupling as the meaningful measure of the coupling strength of an equilibrium gas and consider its scaling behaviour. We show that the high temperature limit of the average coupling is obtained by keeping the temperature to the renormalization point ratio,T/μ, fixed. In hot QCD gas this implies asymptotic freedom and a beta function which is independent ofT up to two loops. In the MOM scheme a minimal sensitivity to temperature is obtained with the choice μ=2.6T.     

Number fluctuations of sparse quasiparticles in a superconductor

We have directly measured quasiparticle number fluctuations in a thin film superconducting Al resonator in thermal equilibrium. The spectrum of these fluctuations provides a measure of both the density and the lifetime of the quasiparticles. We observe that the quasiparticle density decreases exponentially with decreasing temperature, as theoretically predicted, but saturates below 160 mK to 25-55/μm(3). We show that this saturation is consistent with the measured saturation in the quasiparticle lifetime, which also explains similar observations in qubit decoherence times.     

Characterizing the Evolution of Porosity during Controlled Drug Release

Nuclear magnetic resonance (NMR) techniques have been successfully used to characterize the evolving pore structure of partially soluble pharmaceutical pellets as they absorb water and release soluble components. The restricted diffusivity of water trapped within pellets, which have been immersed in water for differing times, has been measured by pulsed field gradient NMR. These measurements have been used to calculate the surface-to-volume ratio and tortuosity of the pore structure. A one-shot Carr–Purcell–Meiboom–Gill sequence has been used to measure the spin–spin (T ₂) relaxation time of water trapped within the pellets. These data have been regularized and then analyzed by the Brownstein–Tarr model to provide a pore size distribution for the pellets as a function of increasing immersion time. It has been found that pore structure changes significantly as water enters the pellet matrix. Two pellet formulations (herein referred to as placebo and drug-loaded) were studied and showed the same trends of a decreasing surface-to-volume ratio and tortuosity with increasing immersion time. At an immersion time of 10 min, both of these parameters decreased to approximately 70% of their values compared to an immersion time of 2 min. The placebo material tested consistently had both a higher tortuosity and surface-to-volume ratio than the drug-loaded material. At an immersion time of 2 min, the tortuosity for the placebo and drug-loaded materials were about 18 and about 10, respectively, and surface-to-volume ratios of about 6 μm⁻¹ and about 5 μm⁻¹, respectively. The materials tested also show changes in their pore size distribution with immersion time. In both formulations the mean and modal pore sizes increase with immersion time. The placebo material maintains an approximately similar mean and modal pore size, about 2 μm over the timescales studied, suggesting a more symmetric pore size distribution. In the drug-loaded pellets the mean pore size is much higher than the modal pore size, their values being 6.5 and 2.1 μm after 10 min immersion time, respectively. Authors' address: Michael D. Mantle, Department of Chemical Engineering, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, UK     

Treatment of submicron particles using an electrostatic agglomerator in DC-negative voltage: Re-entrainment experimental study and modeling

The aim of this study is to highlight the re-entrainment phenomenon encountered with an electrostatic agglomerator having a fibrous collecting electrode and treating submicron particles. The idea is to propose a process to control the particle number emitted by automotive diesel engines. Rather than trying to directly measure agglomerates of diesel particles exiting the agglomerator, we propose working with a synthetic submicron aerosol dispersed in ambient filtered air as a representative exhaust gas. The study will contribute to build a numerical modeling of the behavior of particles in such a process. The particular point that will be treated here is the collected particle re-entrainment as micron-sized agglomerates. We propose a joint experimentation/modeling approach to approximate the re-entrained aerosol size distribution in controlled conditions. From the modeling point of view, a local approach which uses the method of the balance of moments on agglomerates provides the re-entrained particle size in the agglomerator, according to the filtration conditions. The experimental approach confirms the clearly micron-sized character of the re-entrained agglomerates. This is unambiguously shown by measuring a greater micron particle numerical concentration downstream from the agglomerator than upstream. We show that the fluorescein submicron particles use can greatly simplify the characterization of an electrostatic agglomerator by allowing the use of a commercial laser granulometer to measure the size and the number of the generated agglomerates.     

Population of closed-channel molecules in trapped Fermi gases with broad Feshbach resonances

We compute the fraction of closed-channel molecules in trapped atomic Fermi gases, over the entire range of accessible fields and temperatures. We use a two-channel model of Bardeen-Cooper-Schrieffer-Bose-Einstein-condensation crossover theory at general temperature , and show that this fraction provides a measure of the T-dependent pairing gap. Our calculations, containing no free parameters, are in good quantitative agreement with recent low- measurements in (6)Li. We present readily testable predictions for the dependencies of the closed-channel fraction on temperature and Fermi momentum.