This work revisits an indirect characterization method that exploits visco-inertial and thermal frequency response functions to estimate the macroscopic parameters of fibrous media [Panneton and Olny, J. Acoust. Soc. Am. 119, 2027-2040 (2006); Olny and Panneton, J. Acoust. Soc. Am. 123, 814-824 (2008)]. In practice, this method faces major challenges for highly resistive materials because the transition frequencies fall outside the measurable range of the standing-wave tube. To overcome this limitation, an alternative approach combining the equivalent characteristic-length relation derived from ultrasound measurements with a Kozeny-Carman-type relation is proposed. The methodology and its validation on resistive felts demonstrate improved estimation of viscous and thermal characteristic lengths from measurable parameters.

This study develops a comprehensive methodology for estimating the dynamic thermal behaviour of the solid skeleton in porous materials from analytical, numerical and experimental approaches. Thermal exchange is driven by oscillating fluid flows within the porous material, as seen in acoustic and thermoacoustic applications. The limitations of the commonly assumed isothermal behaviour of the solid skeleton are addressed, emphasizing the impact of the finite thermal capacity of the solid skeleton on its overall dynamic effective volumetric heat capacity. The semi-phenomenological models of Champoux-Allard (CA) and Champoux-Allard-Lafarge (CAL) are used to predict the dynamic thermal behaviour of the solid skeleton of porous materials. Results indicate that while both models effectively predict the frequency-dependent and complex heat capacity ratio, the CAL model outperforms the CA model as geometric complexity increases, such as for configurations encountered in longitudinal pin arrays. Three thermal transport parameters are introduced for the solid geometry: the solid volume fraction phi(s), the solid thermal characteristic length A(s)' and the solid static thermal permeability k(0,s)'. A methodology accounting for the calculation of the solid thermal characteristic length A(s)' and the solid volume fraction phi(s) is presented, along with a Poisson problem formulation to estimate the static thermal permeability of the solid phase k(0,s)'. Numerical simulations for three kinds of microstructural classes of porous media are presented: Three-dimensional cellular structures (foams), tetragonal pin arrays (structured fibrous media), and granular materials. Numerical data reveal that there exist a logarithmic relationship between the thermal permeabilities ratio k(0)'/k(0,s)' and the volume fractions ratio phi/phi(s). A measurement methodology of the dynamic heat capacity ratio is also presented, addressing intrinsic challenges associated with these measurements.

Thin low-frequency acoustic absorbers that are economical to produce using a large-scale manufacturing process are scarce, and their efficiency is often limited to a narrow frequency range. In this paper, perforated gypsum foams are shown to achieve high absorption levels for layers thinner than 1/15 of a wavelength. With a mass density of 150 kg/m3, they are as practical in use as conventional porous absorbers. To reach acoustic absorption levels higher than 0.7, perforations with a diameter smaller than 1 mm open a fraction of the initially closed pores. To allow additional design freedom, the foams' pore size can be varied between 1 and 3 mm, while keeping the wall thickness as low as 0.1 mm. Simulations of the microscopic fluid flow in a representative volume element show how the combination of foam properties and perforation patterns can be combined such that sub-wavelength absorption is obtained. Comparing the predicted sound absorption with impedance tube measurements demonstrates that the solution can yield a wideband low-frequency sound absorption peak. The most remarkable example exhibits an absorption peak higher than 0.7 between 525 Hz and 875 Hz for a layer of 25 mm, a result equivalent to 1/21 of the incident sound wavelength.

A theoretical approach is developed to describe the acoustic behavior of humid air-saturated porous media. Humid air is here considered as a binary mixture of dry air and water vapor, in which water vapor is likely to precondense (i.e., to be adsorbed) on a solid wall. The formulation of the acoustic problem includes the Navier-Stokes, mass conservation, heat diffusion, and mutual diffusion of water vapor in air equations. The boundary conditions account for the velocity continuity and the mass and heat flux conservation at the gas-liquid-solid interfaces. Indeed, precondensed water vapor forms a thin liquid film on the walls that undergoes thickness variations, resulting in non-zero vibration velocity at the liquid-gas interface. This film also acts as a mass and heat source. Its overall behavior is determined by the expression of its thermodynamic equilibrium with water vapor. The problem is analytically solved for straight pores having a constant cross section shape. The results obtained highlight the specific contributions of precondensation to the dynamic behavior of simple porous structures. These contributions, which are significant under extreme environmental conditions, essentially result in increasing the low-frequency limit of the normalized dynamic compressibility. Based on this analysis, a simple generalization to porous media is also proposed.

The distribution of fiber diameters plays a crucial role in the transport and sound absorbing properties of a three-dimensional random fibrous (3D-RF) medium. Conventionally, volume-weighted averaging of fiber diameters has been utilized as an appropriate microstructural descriptor to predict the static viscous permeability of 3D-RF media. However, the long wavelength acoustical properties of a 3D-RF medium are also sensitive to the smallest fibers, this is particularly true in the high-frequency regime. In our recent research, we demonstrated that an inverse volume-weighted averaging of fiber diameters can effectively serve as a complementary microstructural descriptor to capture the high-frequency behavior of polydisperse fibrous media. In the present work, we reexamine the identification of two representative volume elements (RVEs) which relies on the reconstruction of 3D-RF microstructures having volume-weighted and inverse-volume weighted averaged fiber diameters, respectively in the low-frequency and high frequency regimes. We investigate the implication of such a weighting procedure on the transport and sound absorbing properties of polydisperse fibrous media, highlighting their potential advantages. Furthermore, we discuss the challenges associated with this research field. Finally, we provide a brief perspective of the future directions and opportunities for advancing this area of study.

\textit{Thermal and viscous energy conversion in a thermoacoustic device occurs inside a particular porous material, named stack/regenerator. Viscous losses and thermal exchanges arise thanks to the interaction of an acoustic field and the solid skeleton of a porous material. Its microstructure strongly influences the amount of energy which can be converted or dissipated due to viscous and thermal boundary layers. Thermal and viscous losses are strictly interconnected, meaning that by altering the pore size (i.e. the hydraulic radius) of the microstructure, both thermal and viscous effects are generally affected. However, there are cases where independent control of thermal or viscous effects could be crucial such as in the thermoacoustics devices. Enhancing heat exchanges while minimizing viscous losses becomes necessary to enhance power conversion. This work paves the way to the design of a microstructure suitable for controlling viscous and thermal effects in a relatively independent way.

Transport parameters play a key role in characterizing the thermo-viscous behaviour of the microgeometry. Semi-phenomenological models provide valuable tools to establish a connection between the dynamic behaviour of porous materials and these transport parameters. However, each model has its limitations in terms of the frequency range and material types it can accurately represent. One of the most used semi-phenomenological acoustic models in the literature is the Johnson-Champoux-Allard-Lafarge (JCAL) model [J. Fluid. Mech. 176 (1987) 379–402, J. App. Phy. 70 (1998) 1975, J. Ac. Soc. Am. 102 (1998) 1995]. This model requires the knowledge of six transport parameters, known as the porosity φ, airflow resistivity σ, thermal characteristic length Λ′, viscous characteristic length Λ, high-frequency limit of tortuosity α∞, and static thermal permeability k0′, which establish a connection between the micro-geometrical features of the porous material and its macroscopic behaviour when subjected to sound waves. The JCAL model is applicable to all types of porous materials, and the required transport parameters can be measured using suitable devices. With recent advancements in additive manufacturing, it is now possible to create porous materials with precise and controlled geometries. Therefore, understanding the relationships between microgeometry and transport parameters is crucial for designing porous materials with specific acoustic properties. This study provides a comprehensive overview of all the transport parameters involved in characterizing the JCAL model. It synthesizes various direct, indirect, and inverse measurement techniques used to assess these parameters. Additionally, computational approaches for evaluating the transport parameters from representative elementary volumes (REV) of materials are presented. Finally, the study compiles the existing correlations between transport parameters and the microgeometry of the unit cell from the available literature.

A technique is proposed that uses a multi-scale approach to calculate transport properties of compressed felts using only image analysis and numerical calculations. From the image analysis fiber diameter distribution and fiber orientation are determined. From a known porosity and the latter two characteristics, two representative elementary volumes (REV) are constructed: one based on the volume-weighted average diameter and one on an inverse volume-weighted average diameter. Numerical calculations on the former showed that it correctly estimates viscous and thermal permeabilities, while the latter correctly estimates tortuosity and viscous and thermal characteristic lengths. From these calculations, micro-macro analytical expressions are developed to estimate the transport properties of polydisperse composite felts based solely on open porosity, fiber diameter polydiversity, and fiber orientation. Good agreements are obtained between analytical predictions and measurements of transport properties. The predicted transport properties are also used in the Johnson-Champoux-Allard-Lafarge (JCAL) equivalent fluid model to predict the sound absorption coefficient of the felts. Excellent agreements are obtained with impedance tube measurements.

Porous materials are integrated components across various industries, offering unique properties such as high surface area, low density, and good permeability. They have a wide range of applications including energy conversion, with relevance in sound absorption and thermoacoustic phenomena. Understanding the intricate energy conversion mechanisms within the microstructure of porous materials under oscillating flows, such as sound waves, is paramount for optimizing their performance in these applications. The techniques currently used for testing porous materials enable the characterization of the behaviour of the porous matrix when subjected to an acoustic wave, without consideration to energetic quantities. Here, this paper presents two novel measurement techniques allowing for the experimental quantification of the power dissipated within the porous material, by making an explicit distinction between thermal relaxation and viscous dissipation effects. The study involves a model to quantify the viscous and thermal energetic behaviours from which analytical expressions guiding the elaboration of the proposed experimental techniques are derived, and finally validated through experimental data. Experimental tests have been carried out on three different samples (polyester fibers, wire mesh and triangular pores sample) largely used both in acoustic and thermoacoustic fields. The experimental data compared with the theoretical prediction for each sample allow to validate the measurement methodologies. By bridging theoretical modelling with experimental validation, this work contributes to the broader understanding and utilization of porous materials in energy conversion applications.

This article presents an improved and extended modeling approach for acoustic wave propagation in rigid porous materials, focusing on examples, such as plastic foams used for noise reduction in automotive applications. We demonstrate that the classical model (Johnson-Champoux-Allard) in the asymptotic high-frequency limit, widely employed in the literature, fails to accurately reconstruct the transmitted acoustic signal through high absorbent porous materials characterized by significant wave attenuation. The study focuses on the airborne ultrasonic frequency range (30–200 kHz). To address this limitation, we introduce new non-acoustic parameters Σ and V for viscous effects, and Σ′ and V′ for thermal effects, with surface and volumetric dimensions, respectively, allowing for the reconstruction of the transmitted signal and accurate modeling of the pronounced acoustic attenuation within the material. These parameters are incorporated into the expansion on skin depths of the dynamic tortuosity α(ω) and thermal tortuosity α′ (ω) response functions, which describe the inertial-viscous and thermal interactions between the fluid and the solid, respectively. This novel modeling approach enables a more comprehensive study of high attenuating porous media, which are crucial for effective noise reduction. Additionally, it opens up new possibilities for characterization beyond the capabilities of current models.

This work is concerned with the multiscale prediction of the transport properties associated with thermocompressed materials as recycled cotton felts bonded with petro-sourced fibers (Co-PET/PET).First, a geometric characterization is performed on the studied sample using scanning electron microscopy to identify the main microstructural descriptors (fiber angular orientation, fiber diameter polydiversity).Second, two representative volume elements (RVEs) of the sample are built: one for estimating the low-frequency transport parameters and one for estimating the the high-frequency transport parameters.Each RVE is built with rectilinear fibers parameterized by the probability density function of the fiber orientation and an appropriate weighted diameter.For the low-frequency RVE, a volume-weighted mean diameter is used, and an inverse volume-weighted mean diameter is used for the high-frequency RVE.These two RVEs make it possible to estimate the transport parameters in low and high frequency asymptotic behaviors using numerical homogenization methods.Finally, the estimated transport parameters are successfully compared to experimental measurements.The results demonstrate the role of the diameter polydispersity on the transport properties of random fibrous structures.

This research examines ultrasonic wave propagation in air-saturated plastic foams used for noise pollution reduction, questioning the effectiveness of current models such as the well known Johnson-Champoux-Allard model at high frequencies. These foams present a challenge for existing models to accurately depict visco-inertial and thermal interactions within their pores. The study highlights the model's failure to align experimental results with theoretical predictions. It introduces novel parameters denoted as Σ and V for viscous effects, and Σ′ and V ′ for thermal effects, to improve the representation of fluid-sturcture interactions. These parameters suggest a more significant boundary layer effect within the pores than previously considered. This approach aims to provide additional physical context for the principles governing the behavior of highly attenuating porous media and to explore new avenues for material characterization that surpass the limitations of existing models.

This study investigates the influence of pore size polydispersity on the acoustic behavior of high-porosity solid foams using numerical simulations. The effect of the size of the periodic unit cell (PUC) on the transport parameters is first examined. It is found that the size of the PUC required for properly estimating the acoustic properties of random foams depends on both the analyzed transport parameter(s) and level of polydispersity. Assuming identical and constant aperture ratio of membranes, the results indicate that (i) the viscous permeability is a reliable indicator regarding the size of the PUC (a more constraining property than the other transport parameters), and (ii) high-polydispersity foams require a larger number of pores in the PUC to achieve convergence with respect to morphological characteristics and acoustic properties. The influence of polydispersity on dimensionless transport parameters is then analyzed. It is found that polydispersity has a negligible effect on the high-frequency tortuosity but induces substantial variations in the remaining macroscopic parameters. Simulations further show that the ratio of the dimensionless transport parameters does not depend on membrane aperture ratio. This important result allows us to propose a fast method to estimate the acoustic properties of a random foam from the transport parameters of monodisperse foams with different pore sizes, for each studied transport parameter. The proposed method is finally employed to characterize the pore size and polydispersity in two real foams (with and without membranes), solving an inverse problem.

Melamine foam, categorized as an open-cell foam structure, absorbs sound through its three-dimensional network of thin struts. The pore size polydispersity within the open-cell melamine microstructure is evidenced from a top-down approach and confirmed by scanning electron microscope (SEM)-image analysis. The remarkable ability of melamine foams to mitigate sound energy is attributed to the pore size distribution, which encompasses co-existing pores of distinct characteristic sizes. Consequently, low-frequency and high-frequency fluid flows will follow different paths within the pore structure. A poly-sized model, which provides a connection between microstructure polydispersity and macroscopic properties, is successfully applied to three different melamine foams. This work highlights the significance and implications of polydispersity effects on the acoustic behavior of open-cell foams.

The multi-scale asymptotic method provides a separate description of the viscous and thermal response functions governing acoustic waves propagation through porous materials.However, these response functions are inherently interdependent for simple porous structures such as slits or tubestheir determination being directly influenced by the microstructural features of the geometry.This study aims to identify, characterize, and realize a microgeometry providing the ability to independently modify the viscous and thermal behaviours.A relative autonomy in the control of these phenomena would make it possible to regulate energy conversion processes within the structure, which can be either dissipative (e.g., sound absorption) or generative (e.g., thermoacoustic gain).Among the various microgeometries, cellular solids made by an assembly of cells with solid edges or faces, packed together so that they fill space, emerge as promising candidates for achieving such a goal.Within the interconnected cells (pores), the viscous losses are governed by the aperture sizes of the faces (throat section).On the other hand, the thermal exchanges are closely related to the interface between the fluid and the solid and consequently to the dimensions of the cells.The identified microstructure is a typical Kelvin cell-based geometry, modified to account for manufacturing constraints, and characterized by faces with well-defined opening ratio and thickness.This work presents a model, experimentally validated, to predict the transport parameters of such cellular solids.It provides a valuable tool for designing microstructures having the attributes to independently tune thermal and viscous effects for specific application requirements.

Bài báo trình bày kết quả phát triển vật liệu composite mới nguồn gốc tự nhiên trên cơ sở nhựa epoxy resorcinol sinh học – diatomite bằng quy trình xanh hai giai đoạn dựa trên đặc tính “sống” của sự trùng hợp cation. Bao gồm sự khởi đầu phản ứng bằng ánh sáng và sau đó là sự hóa rắn không cần ánh sáng dưới tác dụng nhiệt, quy trình này cho phép thu được các composite epoxy-diatomite dày và không trong suốt mà không cần dùng bất cứ dung môi hay chất hóa rắn gốc amine nguy hại nào. Các ảnh hưởng của hàm lượng diatomite đối với các tính chất cơ học và phản ứng với lửa của những composite này đã được khảo sát. Trên cơ sở đánh giá các tính chất này, composite thu được với diatomite chiếm 40% khối lượng được xem như composite tối ưu. Composite này có mô đun uốn là 3,6 MPa và ứng xử làm chậm cháy đáng chú ý với đỉnh tốc độ tỏa nhiệt (peak of Heat Release Rate - pHRR) 132 W/g và tổng lượng tỏa nhiệt 6 kJ/g ghi nhận được trong phân tích nhiệt lượng kế dòng đốt cháy nhiệt phân (Pyrolysis Combustion Flow Calorimetry - PCFC).

Thermoacoustic technology can play a significant role in the development of renewable energies. Thermoacoustic engines and heat pumps (or refrigerators) are however characterized by a low efficiency attributed to suboptimal components. The core of these devices is a porous material, named stack (or regenerator), in which thermoacoustic conversion takes place. The most frequently used stack in the literature remains the wire mesh, although there is still a lack of formulation for the corresponding thermoviscous response functions. Essentially, all the dynamic thermal and viscous behaviors of a porous structure can be derived thanks to the Johnson-Champoux-Allard-Lafarge (JCAL) semi-phenomenological model, where transport parameters provide input information on the macroscopic level to the model. Here, we report a set of structure–property correlations between the transport parameters of the stack and the geometrical features of the wire mesh obtained from first-principles calculations. Validation of the model is carried out by means of experimental measurements performed on three different specimens. Our results show that the knowledge of the termoviscous functions for the wire mesh allows drawing preliminary considerations on the thermoacoustic efficiency of the stack, without needing to consider a full numerical simulation of the entire device.

The distribution of fiber diameters plays a crucial role in the transport and sound absorbing properties of a three-dimensional random fibrous (3D-RF) composites. Conventionally, volume-weighted averaging of fiber diameters has been utilized as an appropriate microstructural descriptor to predict the static viscous permeability of 3D-RF composites. However, the long wavelength acoustical properties of a 3D-RF composites are also sensitive to the smallest fibers, this is particularly true in the high-frequency regime. In our recent research, we demonstrated that an inverse volume-weighted averaging of fiber diameters can effectively serve as a complementary microstructural descriptor to capture the high-frequency behavior of polydisperse fibrous media. In the present work, we review the identification of two representative volume elements (RVEs) which relies on the reconstruction of 3D-RF composites having volume-weighted and inverse-volume weighted averaged fiber diameters, respectively in the low-frequency and high frequency regimes. We examine the implication of such a weighting procedure on the transport and sound absorbing properties of polydisperse fibrous media, highlighting their potential advantages. Furthermore, we discuss the challenges associated with this research field. Finally, we provide a brief perspective of the future directions and opportunities for advancing this area of study, aiming to overcome challenges and extend the benefits of employing polydispersity as a new lever for the optimization of 3D-RF composites in sound-absorbing materials.

This work aims at studying the mechanical and acoustic behaviours of a new bio-based porous epoxy resin obtained by a "green" adapted combination of the cationic photopolymerization and the porogen leaching technique. This new kind of material generally possesses interconnected complex morphology and it would be useful to consider this feature in a model. In this study, the effective properties of the material were estimated by using the asymptotic homogenization method. Four types of ordered pore arrangements together with systematic variations of the porosity and the pore size have been studied. Based on the results of these investigations, a subtle relation between the microstructure and mechanical/acoustic properties has been established. The estimated equivalent dynamic density and equivalent dynamic bulk modulus were compared with experimental results obtained by conducting the three-microphone impedance tube testing. The processing parameters of material elaboration could be adjusted so that the obtained porous material would possess the best sound absorption performance.

Porous materials are an excellent way to increase the power that an oscillating flow can exchange with a solid surface. They can be used to dissipate sound wave power or, as in the last decades, they were also employed to convert thermal power into sound power or vice versa (thermoacoustic devices). In both cases, it is crucial to understand how the geometrical characteristics of the solid skeleton influence the frequency-dependent viscous and thermal power exchanges inside the porous structure. In this study, we note that two representative frequencies of viscous and thermal phenomena, respectively, define frequency bands characterized by different power exchanges. For a porous material with simple microgeometry, such as uniform cross-sectional pores, the hydraulic radius and the porosity allow to univocally assess the viscous and thermal exchange in the different behavioural frequency regions, while, in the case of complex microstructure of a porous material, more parameters are involved. In this work, the semi-phenomenological Johnson-Champoux-Allard-Lafarge model is used to characterize a generic porous material through its own six input transport parameters. Here, it is shown that these parameters can also be of valuable interest to better understand power exchanges before and after the viscous and thermal representative frequency. The findings of this study suggest how the geometrical descriptors characterizing the microstructure of the porous material can be tuned to improve its power exchange performance.