Influence of dynamic tortuosity and compressibility on the propagation of transient waves in porous media

Transient Acoustic Wave Propagation in Porous Media

“…This parameter appears naturally at the reflection and transmission of an acoustic wave through a slice of porous material. The solution of the wave equation (13) is given by the Green function G of the porous medium [3,18], defined by:…”

“…Extensions of Pride-Lafarge (6,8) are expressed in the time domain [3] using the definition of fractional derivative:…”

“…Since the coefficient C exchange rate, the coefficients c ′ and Δ given by equation ((17, 18) also change. With extensions of Pride-Lafarge, the coefficient Δ 2 can be negative [3], it gives:…”

“…Using expressions (26 and 27) and analytical calculations given in [3], we obtain the solution of the wave equation when Δ 2 is negative:…”

“…In medicine, the characterization of porous media such as trabecular bone, is useful for diagnosing osteoporosis, bone disease that is manifested by the deterioration of bone microarchitecture. Acoustic characterization of materials is often achieved by measuring the attenuation coefficient and phase velocity in the frequency domain [1] or by solving the direct and inverse problems directly in the time domain [2][3][4]. The attractive feature of a time domain based approach is that the analysis is naturally limited by the finite duration of ultrasonic pressures and is consequently the most appropriate approach for the transient signal.…”