Stochastic reaction-diffusion phenomena in porous media with nonlinear kinetics: effects of quenched porosity fluctuations

We study the effects of quenched porosity fluctuations in the presence of nonlinear kinetics in a reaction-diffusion porous system. Adopting a weak-noise approximation and a mean-field assumption, a renormalized equation of motion for the average concentration of a chemical species is obtained. It is characterized by a smaller effective diffusion coefficient and by the presence of supplementary nonlinear reactive terms. Explicit results are given for a Gaussian porosity distribution and for a long-ranged one. Comparisons with simulations in one dimension are presented.     

Acoustic phenomena in filled porous glasses by time-resolved spectroscopy

We studied the propagation of ultrasonic acoustic waves in two porous glasses characterized by different pore diameters (4 and 200 nm) filled with carbon tetrachloride. Using a time-resolved optical spectroscopic technique (Transient Grating) we can measure the acoustic dynamics of these systems. The sound velocities, measured in both the samples, show high values compared with the sound velocity of bulk carbon tetrachloride; they cannot be predicted by the simple effective medium model, but are in good agreement with the estimate obtained from the Biot theory.     

Acoustic response characteristics of unsaturated porous media

By employing the plane wave analysis method, the dispersion equations associated with compressional and shear waves using Santos’s three-phase poroelastic theory were driven. Considering the reservoir pressure, the high frequency corrections and the coupling drag of two fluids in pores, the influences of frequency and gas saturation on the phase velocities and the inverse quality factors of four body waves predicted by Santos’s theory were discussed in detail. The theoretical velocities of the fast compressional and shear waves were compared with the results of the low and high frequency experiments from open publications, respectively. The results showed that they are in good agreement in the low frequency case rather than in the high frequency case. In the latter case, several popular poroelastic models were considered and compared with the experimental data. In the models, the results of White’s theory fit the experimental data, but the parameter b in White’s model has a significant impact on the results. Under the framework of the linear viscoelasticity theory, the attenuation mechanism of Santos’s model was extended, and the comparisons between the experimental and theoretical results were also made with respect to attenuation. For the case of water saturation less than 90%, the extended model makes good predictions of the inverse quality factor of shear wave. There is a significant difference between the experimental and theoretical results for the compressional wave, but the difference can be explained by the experimental data available.     

Acoustic wave propagation in two-phase heterogeneous porous media

The propagation of an acoustic wave through two-phase porous media with spatial variation in porosity is studied. The evolutionary wave equation is derived, and the propagation of an acoustic wave is numerically analyzed in application to marine sediments with various physical parameters.     

Aging kinetics of porous media due to freezing-thawing cycles

The two-dimensional Ausloos et al. model of fluid invasion, freezing and thawing in a porous medium is elaborated upon and investigated in order to take into account the pore volume redistribution and conservation during freezing. The results are qualitatively different from previous work, since the damaged pore sizes are found to be much less than the possible maximum value and is reached after a large number of invasion-freezing-thawing cycles, e.g. the material is “slowly damaged”. The pore size distribution is thus found in better agreement with expected practical findings. The successive invasion percolation clusters are still found to be self-avoiding with aging. The cluster size decreases with a power law as a function of invasion-frost-thaw iterations. The aging kinetics is also discussed through the normalized totally invaded pore volume. Received 24 September 1999 and Received in final form 5 January 2000     

Acoustic behaviour of high pressure air-filled porous media

This paper deals with the acoustic behaviour of porous media when the saturating fluid is high pressured. These observations are performed by ultrasonic transmission through a porous sample with variations of the static pressure of the saturating fluid. Previous works have experimentally demonstrated that a high frequency asymptotic equivalent fluid model allows to model the behaviour of such media for low pressure (between 0.2 and 6 bars). In this paper, in order to characterize high damping materials, measurements are performed for higher static pressure (up to 18 bars). It is shown that the behaviour of transmission coefficient and speed with pressure follows Biot’s theory. Moreover, measurements are dependant on temperature variations. Temperature variations have been accounted for in this study, but this does not explain entirely the high sensitivity of the transmission coefficient with static pressure. It remains that the mechanical properties of the porous medium vary strongly with the thermodynamic variables.     

Statics and kinetics at the nematic-isotropic interface in porous media

We extend the random anisotropy nematic spin model to study nematic-isotropic transitions in porous media. A complete phase diagram is obtained. In the limit of relative low randomness the existence of a triple point is predicted. For relatively large randomness we have found a depression in temperature at the transition, together with a first order transition which ends at a tricritical point, beyond which the transition becomes continuous. We use this model to investigate the motion of the nematic-isotropic interface. We assume the system to be isothermal and initially quenched into the metastable régime of the isotropic phase. Using an appropriate form of the free energy density we obtain the domain wall solutions of the time-dependent Ginzburg-Landau equation. We find that including a random field leads to smaller velocity of the interface and to larger interface width. Received 12 November 1998 and Received in final form 15 March 1999     

Simulating finger phenomena in porous media with a moving finite element method

The non-equilibrium Richards equation is solved using a moving finite element method in this paper. The governing equation is discretized spatially with a standard finite element method, and temporally with second-order Runge–Kutta schemes. A strategy of the mesh movement is based on the work by Li et al. [R.Li, T.Tang, P.W. Zhang, A moving mesh finite element algorithm for singular problems in two and three space dimensions, Journal of Computational Physics, 177 (2002) 365–393]. A Beckett and Mackenzie type monitor function is adopted. To obtain high quality meshes around the wetting front, a smoothing method which is based on the diffusive mechanism is used. With the moving mesh technique, high mesh quality and high numerical accuracy are obtained successfully. The numerical convergence and the advantage of the algorithm are demonstrated by a series of numerical experiments.     

Diffusion studies in porous media with the "inside-out" technique

Diffusion measurements of water in a glass beads porous media were carried out by the "One-Sided Access" sensor. An approach to determine the long time mean square displacement of hydrogen molecules by measuring the ratio of stimulated echo to primary echo in a three pulse sequence in the presence of permanent static field gradient is analysed. The difference between the apparent diffusion coefficient in a pure water sample and in water/glass beads mixtures becomes visible.     

Acoustic phenomena observed in lung auscultation

The results of studying respiratory noise at the chest wall by the method of acoustic intensimetry reveal the presence of frequency components with different signs of the real and imaginary parts of the cross spectrum obtained for the responses of the receivers of vibratory displacement and dynamic force. An acoustic model is proposed to explain this difference on the basis of the hypothesis that the contributions of both air-borne and structure-borne sound are significant in the transmission of respiratory noise to the chest wall. It is shown that, when considered as an acoustic channel for the basic respiratory noise, the respiratory system of an adult subject has two resonances: in the frequency bands within 110–150 and 215–350 Hz. For adults in normal condition, the air-borne component of the basic respiratory noise predominates in the region 100–300 Hz in the lower parts of lungs. At forced respiration of healthy adults, the sounds of vesicular respiration are generated by the turbulent air flow in the 11th-through 13th-generation bronchi, and the transmission of these sounds to the chest wall in normal condition is mainly through air and is determined by the resonance of the vibratory system formed by the elasticity of air in the respiratory ducts of lungs and by the surface mass density of the chest wall. It is demonstrated that the distance from the chest wall to the sources of structure-borne additional respiratory noise, namely, wheezing with frequencies above 300 Hz, can be estimated numerically from the ratio between the real and imaginary parts of the cross spectrum on the assumption that the source is of the quadrupole type.     

SPIRAL-SPRITE: a rapid single point MRI technique for application to porous media.

This study presents the application of a new, rapid, single point MRI technique which samples k space with spiral trajectories. The general principles of the technique are outlined along with application to porous concrete samples, solid pharmaceutical tablets and gas phase imaging. Each sample was chosen to highlight specific features of the method.     

Acoustic phenomena in a steam generating unit

With the increased capacity of modern power plants, the study of flow-induced vibrations in heat exchangers has become an important problem. Tube-banks are sources of noise. This noise can be amplified by the acoustical resonances of the circuit and induce severe stresses in the structures. In this paper, it is shown that the acoustic behaviour of a complex circuit, such as a steam generating unit, can be calculated with good accuracy.     

Acoustic attenuation in self-affine porous structures

As acoustic waves propagate through fluid-filled porous materials possessing heterogeneity in the elastic compressibility at scales less than wavelengths, the local wave-induced fluid-pressure response will also possess spatial heterogeneity that correlates with the compressibility structure. Such induced fluid-pressure gradients equilibrate via fluid-pressure diffusion causing wave energy to attenuate. This process is numerically simulated using finite-difference modeling. It is shown here, both numerically and analytically, that in the special case where the compressibility structure is a self-affine fractal characterized by a Hurst exponent H, the wave's quality factor Q (where Q(-1) is a measure of acoustic attenuation) is a power law in the wave's frequency omega given by Q proportional to omega(H) when /H/<1, and given by Q proportional to omega(tanhH) in general.     

Polarization phenomena in the optical properties of porous silicon

We examine the polarization memory effect for porous Si excited by linearly polarized light. The various observations for the red-luminescing, slow band are discussed in the general framework of particle shape asymmetry. We show that because of the intrinsically nonlinear luminescence response, measurement parameters influence the polarization response. The preparation of porous Si with photoassisted etching is found to control the polarization retention parameter ρ. Using linearly polarized light during etching produces in-plane asymmetries. We find a substantial ρ-anisotropy linked to crystal symmetry planes and axes as a consequence of anisotropic etching. The effects are discussed with reference to current models of the light emission mechanism.     

Theory of swimming filaments in viscoelastic media

Motivated by our desire to understand the biophysical mechanisms underlying the swimming of sperm in the non-Newtonian fluids of the female mammalian reproductive tract, we examine the swimming of filaments in the nonlinear viscoelastic upper convected Maxwell model. We obtain the swimming velocity and hydrodynamic force exerted on an infinitely long cylinder with prescribed beating pattern. We use these results to examine the swimming of a simplified sliding-filament model for a sperm flagellum. Viscoelasticity tends to decrease swimming speed, and changes in the beating patterns due to viscoelasticity can reverse swimming direction.