Experimental characterization of air-saturated porous material via low-frequencies ultrasonic transmitted waves

Abstract

An improved acoustic method is proposed for measuring the tortuosity and the viscous and thermal characteristic lengths of air-saturated porous materials via low-frequency ultrasonic transmitted waves (70 kHz–110 kHz). The equivalent fluid model is considered. The interaction between the saturated fluid and the structure is taken into account in two frequency response factors: the dynamic tortuosity of the medium and the dynamic compressibility of the air which are described by their high-frequency expansion in powers of the viscous and thermal skin depth, either limiting the expansion to the first two leading terms or the first three leading terms with the introduction of two new viscous and thermal shape factors. These two new factors play an important role in stabilizing and improving the inverted parameters of the tortuosity and the viscous and thermal characteristic lengths in the frequency band considered. The inverse problem is solved numerically in the frequency domain by minimizing the spectrum of simulated and experimental transmitted signals. Optimized parameters of tortuosity, viscous and thermal characteristic lengths, and viscous and thermal shape factors are obtained simultaneously. The tests are carried out with three samples of plastic foam. The results obtained by the two procedures are discussed and compared to those given in the literature.

Static airflow resistivity association law of a multilayer rigid porous material

“…To specify the frequency regime, one must compare the viscous skin thickness 𝛿(𝜔) = √2𝜂/𝜔𝜌 0 (η: fluid viscosity, ω: angular frequency) at a given frequency with the characteristic radius of the pore r. If δ << r, one is in the high frequency domain. [7,33]; otherwise, If δ > r, one is in the low frequency domain. In Darcy's regime [30,32] (very low-frequency approximation), the expressions of the response factors 𝛼(𝜔) and 𝛽(𝜔) when ω → 0 are given by the relations [30,32]:…”

Impact of the physical parameters describing the rigid porous materials on the reflected low-frequency ultrasonic wave at oblique incidence

“…, where is the density of the saturating fluid, η is the viscosity, the pulsation frequency, the Prandtl number). At low ultrasonic frequencies, the corrected dynamic tortuosity α(ω) and dynamic compressibility β(ω) are expressed as follows [4]:…”

“…The viscous and thermal characteristic lengths and ′ were introduced by Johnson and Allard [1][2][3]. Another important parameter is the dimensionless factor introduced by Sadouki [4], which characterizes the correction for the viscous skin depth in the low-frequency regime of ultrasonic waves near the tube surface. The velocity distribution near the surface is significantly disturbed by the viscous forces generated by the motionless frame, making ξ a relevant factor to consider.…”

“…The model was refined by introducing viscous and thermal form factors (ξ and ξ') to fit the ultrasonic low-frequency limit. These two form factors played a crucial role in stabilizing and improving the values of tortuosity, viscous, and thermal characteristic lengths in the transmitted signals [4]. Previous studies [5,6] have been conducted to demonstrate the impact of these parameters on normally transmitted and reflected signals in the low-frequency ultrasound regime.…”

Analytical Modeling of a Transmission Coefficient for Ultrasonic Waves in Human Cancellous Bone

“…Ultrasonic wave propagation complexity in bones arises from factors such as saturating fluid properties [5], solid phase mechanical characteristics [6], anisotropy [7], and macroscopic structural parameters like porosity, tortuosity, and viscous characteristic length [7,8]. Developing a comprehensive theoretical model, such as Biot theory modified by Johnson, is crucial to address this complexity [9,10], aiding the solution of the inverse problem [4,[11][12][13] and enabling extraction of bone's physical and mechanical properties from ultrasonic measurements.…”