Waves In Porous Materials Research Articles

Finite element analysis of sound absorbing material with periodic decreasing hole profiles

The propagation of acoustic waves in porous materials attenuates with distance. When the thickness of the porous material is equal to the acoustic penetration depth, or critical depth, the sound absorption coefficient reaches an asymptotic value so that any additional thickness of the porous layer provides no significant increase of the sound absorption. To overcome the limitations of the critical depth, a design of sound absorbing material containing periodic holes with decreasing profile diameter is proposed in this paper. The finite element method is used to demonstrate the improved sound absorption over a large frequency band. An extraordinary improvement of the sound absorption coefficient using a periodic conical hole is demonstrated where the critical depth of the porous material is eliminated. The results using the finite element method are compared with theoretical results from a transfer matrix method using a double porosity model, and a good agreement is obtained. A parametric analysis is presented using finite element simulations to illustrate the effects of the different parameters of the decreasing hole profile diameter on the sound absorption coefficient. Different hole shapes with decreasing profile diameters distributed periodically inside the porous layer are compared, and the results show good acoustic performance. The proposed sound absorbing material is applied in a rectangular room as anechoic termination. The result of the reflection coefficient obtained by a mirror source method is close to zero over a large frequency band. This illustrates good sound attenuation of the proposed design.

Quantifying Tortuosity in Porous Lithium-Ion Battery Materials Using Ultrasound

Active electrode materials in lithium-ion batteries are porous. These materials are composed of a solid frame containing interconnected pores/channels, in which mass transport follows a tortuous pathway. Tortuosity is defined as the ratio of the average tortuous pathway to the projected straight path, and is a particularly important parameter indicating the diffusivity and conductivity properties of porous battery materials; so quantifying tortuosity is highly desirable to safeguard battery performance. Existing quantification methods are mostly based on impedance and polarisation measurements from specially-fabricated cells and numerical diffusion simulations using the microstructural tomographic images of porous materials. These methods, however, are generally cumbersome and barely applicable to in-production measurement. Here we report a novel alternative quantification method based on ultrasonic Biot waves in porous materials. This method utilises the fundamental fact that in a porous material with a rigid frame (which the electrode sheets are when immersed in the air), the slow Biot wave only travels in the liquid/gaseous phase, through the same tortuous pathway that the diffusion of ions and electrons happens in a finished battery. To achieve the quantification, we first develop a physical model relating the propagation of ultrasonic Biot waves to the tortuosity of porous battery materials. Based on this physical model, we then propose an inversion method to infer tortuosity from ultrasonic readings. The readings are acquired using air-coupled ultrasonic transducers in a non-destructive fashion, thus enabling real-time tortuosity quantification. This ultrasonic method measures the average tortuosity in a range of ~20 mm across the testing material, and can easily scan over a sheet to provide spatially resolved information. With these exciting features, the proposed method could offer a next-generation tortuosity quantification tool for quality control of porous battery material productions and a better understanding of battery performance.

Transient Propagation of Spherical Waves in Porous Material: Application of Fractional Calculus

A fractional-order wave equation is established and solved for a space of three dimensions using spherical coordinates. An equivalent fluid model is used in which the acoustic wave propagates only in the fluid saturating the porous medium; this model is a special case of Biot’s theory obtained by the symmetry of the Lagrangian (invariance by translation and rotation). The basic solution of the wave equation is obtained in the time domain by analytically calculating Green’s function of the porous medium and using the properties of the Laplace transforms. Fractional derivatives are used to describe, in the time domain, the fluid–structure interactions, which are of the inertial, viscous, and thermal kind. The solution to the fractional-order wave equation represents the radiation field in the porous medium emitted by a point source. An important result obtained in this study is that the solution of the fractional equation is expressed by recurrence relations that are the consequence of the modified Bessel function of the third kind, which represents a physical solution of the wave equation. This theoretical work with analytical results opens up prospects for the resolution of forward and inverse problems allowing the characterization of a porous medium using spherical waves.

An Experiment‐Based Numerical Treatment of Spin Wave Modes in Periodically Porous Materials

To determine a general correlation between structure and dynamic magnetic properties of porous materials, the frequencies of magnetic spin waves are studied by Brillouin light scattering from nickel inverse opals and backed up by micromagnetic simulations. Within the observed unit cell size regime between 400 and 800 nm, discrete thickness standing modes are found to change with unit cell size. By applying pair correlation functions of the inverse opal solid phase normal to the applied field to an equation for perpendicular standing modes, the directional and unit cell size‐dependent spectral intensities above the surface mode region can be traced. Thus, an accessible general approach for the prediction of standing spin waves in porous materials is obtained.

Non‐destructive testing of porous media by means of sound wave analysis

AbstractThe theoretical investigation of sound waves in porous materials is motivated by the possible construction of non‐destructive testing methods. Here, geotechnical applications are of interest where low frequencies from zero to 100 Hz occur but also systems with higher frequency ranges may be tested non‐invasively. Examples are concrete and other construction materials, road surfaces and pavements (some MHz), biological materials like bones and soft tissues, e.g. the surface of the heart (up to 3 MHz) right up to surface coatings by nanomaterials (approximately 100 MHz). (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Strong ellipticity and progressive waves in elastic materials with voids

In the present paper, we investigate a model for propagating progressive waves associated with the voids within the framework of a linear theory of porous media. Owing to the use of lighter materials in modern buildings and noise concerns in the environment, such models for progressive waves are of much interest to the building industry. The analysis of such waves is also of interest in acoustic microscopy where the identification of material defects is of paramount importance to the industry and medicine. Our analysis is based on the strong ellipticity of the poroelastic materials. We illustrate the model of progressive wave propagation for isotropic and transversely isotropic porous materials. We also study the propagation of harmonic plane waves in porous materials including the thermal effect.

Propagation characteristics of airborne ultrasonic waves in porous materials

The attenuation coefficient and propagation speed of an airborne ultrasound wave are measured for highly porous open-cell polyurethane foams and fibers at frequencies from I kHz to 1.7MHz. A theoretical model is proposed to explain physically the frequency responses of the insertion loss and the speed of an air-coupled wave in porous materials. The model is derived from Biot's flow resistance and density, Lambert's bulk modulus for fluids in pores, and Zwikker and Kosten's concept for the compliance of the side holes with entrance resistance. Using measured data of static flow resistance to determine the mean pore size and the proposed model, theoretical prediction is performed for the transmission losses and sound speeds. Good agreement between theory and experiment over the entire frequency range confirms the usefulness of the present model. In addition, the model provides findings for Nagy's extra attenuation coefficient for a slow wave measured in cemented glass bead specimens and in sandstone for high-frequency ranges.

Guided elastic waves in porous materials saturated by air under Lamb conditions

The propagation of guided elastic waves in porous materials saturated by air under Lamb conditions is studied theoretically and experimentally. The modes are derived from expressing the boundary conditions on the normal and tangential stresses and the displacements at the interfaces between the porous layer and the surrounding fluid. The stresses and the fluid pressure inside the porous medium are obtained from Biot’s equations of poroelasticity. Symmetrical and antisymmetrical modes are found when the porous layer is loaded by the same fluid on both sides. Damping mechanisms include viscous and thermal exchanges between the solid and the fluid, in addition to the classical structural damping. Using an experimental setup based on the generation of standing waves in the layer and taking the spatial Fourier transform of the displacement profile, the phase velocities of three modes were measured for two porous materials in a frequency range between 80 Hz and 4 kHz. The measurements confirm the theoretical predictions and provide information on the shear modulus of a sound-absorbing material in a wide frequency range.

Dynamic Effective Properties of Particle-Reinforced Composites with Viscoelastic Matrix

The frequency-dependent dynamic effective properties of the particle-reinforced composites with the viscoelastic matrix are studied. Several equations to predict the effective wavenumber of the coherent plane waves propagating through particle-reinforced composites are discussed and the equation given by Gubernatis, J.E., [‘Effects of microstructure on speed and attenuation of elastic waves in porous materials’, Wave Motion, 6, 1984, 579–589] based on the independent scattering approximation is used in this paper. The effective phase velocity, the effective attenuation and the effective elastic moduli are evaluated. Numerical calculations are carried out for two kinds of composites, namely, Lead-Epoxy and Glass-Epoxy and the numerical results show that the frequency-dependent dynamic effective properties are related to both the multiple scattering effects among the distributed particles and the viscous dissipative effects of the viscoelastic matrix. However, these effects in the composites with distributed heavy particles (lead) and light particles (glass) are of evidently different features.

Verification of Kramers–Kronig relationship in porous materials having a rigid frame

The propagation of acoustic waves in porous materials having a rigid frame is well described by several models. A doubt about the causality of these models has been raised recently in the literature. A verification of the causality of these models is studied in this paper using the Kramers–Kronig dispersion relations adapted to the frequency power law dependence of the attenuation. It is shown that these models are causal in the high- and low-frequency range. A time domain wave equation and time-causal theory have been treated.

Modification of Biot’s theory of porous materials

Acoustic waves in porous material are traditionally investigated by using Biot’s theory to describe the elastic wave propagation in such materials. However, experimental results obtained by models of porous media made of cohesionless particles forming loose solid matrix with fluid-filled pores, contradict the above theory at high frequencies. These results show that the acoustic wave speed as a function of frequency and particle size goes through a maximum and then decreases with frequency until a cutoff frequency is reached, whereas Biot’s theory predicts an asymptotic increase of propagation speed with frequency, without a wave cutoff frequency. The theoretical analysis and the experimental investigation are presented that modify and adapt Biot’s theory to the cohesionless porous materials. The equations describing these modifications to the theory take into account the following effects: the contact surfaces between the solid particles, their number concentration, the size of the solid particles, the depth at which they are situated, the external pressure, their random arrangement, and the propagation direction of the acoustic waves.

Shock waves in dynamic compacting powders and porous bodies. II. Propagation of shock waves in porous materials with a reinforcing frame

The main special feature of dynamic compacting of powders in rigid dies is the formation of shock waves and the associated piecewise-constant distribution of the axial component of speed and density If]. This is the largest difference between dynamic and quasistatic compacting. The results show [i, 2] that these phenomena are closely linked with the nature of the stress-strain or pressure-density dependence.

A Stochastic Theory of Propagation of Elastic Waves in Porous Solids for Nondestructive Pore Characterization

A new theory of propagation of elastic waves in porous materials was developed for pore characterization. The idea is based on the arrival probability of a direct ray, reflecting ray, and creeping ray. The theory gives a good account of the nature of elastic waves propagated in porous solids not only qualitatively, but also quantitatively. The authors show a rather good correlation between pore characteristics (porosity and pore size) and ultrasonic characteristics (waveform and arrival time), and propose a nondestructive technique based on the presented theory for evaluating the porosity and pore size.

A stochastic theory of propagation of elastic waves in porous solids for nondestructive pore characterization.

A new theory of propagation of elastic waves in porous materials was developed for the pore characterization. The idea is based on the arrival probability of a direct ray, reflecting ray and creeping ray. The theory gives a good account of the nature of elastic waves propagated in porous solids not only quantitatively but also quantitatively. The authors showed a rather good correlation between pore characteristics (porosity and pore size) and ultrasonic characteristics (waveform and arrival time), and proposed a nondestructive technique based on the presented theory for evaluating the porosity and pore size.

Analysis of Steady Compaction Waves in Porous Materials

A two-phase continuum mixture model is used to analyze steady compaction waves in porous materials. It is shown that such a model admits both subsonic and supersonic steady compaction waves in response to a piston-driven boundary condition when a Tait equation is used to describe a solid matrix material and a generic static compaction relation is used to describe collapse of the matrix. Parameters for the Tait equation are chosen to match shock and compaction wave data. The model is able to predict compaction wave speed, final pressure, and final volume fraction in porous HMX. The structure of the compaction wave is also studied. A shock preceding the compaction wave structure is predicted for compaction waves travelling faster than the ambient sound speed of the solid. For subsonic compaction waves no leading shock is predicted. The compaction zone length is studied as a function of initial volume fraction, piston velocity, and compaction viscosity.

Effects of microstructure on the speed and attenuation of elastic waves in porous materials

We investigated the effects of microstructure statistics on the speed and attenuation of an elastic wave propagating through a porous material. We derived a general set of equations from which the effective wavenumber (and hence the phase velocity, group velocity and attenuation) can be found, depending on the level of statistical information known. We solved this equation in the independent scatterer approximation and computed the effective wavenumber for several distribution of pore radii. We found the effective wavenumber to be most sensitive to the most probable pore radius and more sensitive to radii larger than this value than to those smaller.