Poroacoustic acceleration waves in a Jordan–Darcy–Cattaneo material

Poroacoustic waves under a mixture-theoretic based reformulation of the Jordan–Darcy–Cattaneo model

“…In 2013, Ciarletta et al [1] investigated poroacoustic acceleration waves in fluids that saturate a class of porous solids that are both rigid and admit porosity values in the range 0.1 χ 0.4, where we note that, in general, χ ∈ (0, 1). In such media, the authors of Ref.…”

“…In such media, the authors of Ref. [1] contend, poroacoustic propagation is more accurately modeled not by the conventional 'Darcy-Jordan model' (DJM) [2,3], but instead by the following first order system, which they term the 'Jordan-Darcy-Cattaneo' (JDC) model:…”

“…In Sys. (1), υ = v − v s /χ , where v = (u, v, w) is the intrinsic average velocity of the fluid [4,Section 1.3] and v s is the velocity 1 of the solid matrix; ϱ(> 0) is the mass density of the fluid; P is a pressure; µ(> 0) is the shear viscosity; K (> 0) is the permeability; τ (> 0), the relaxation time parameter, distinguishes Eq. (1b) from Darcy's law in that letting τ → 0 reduces the former to the latter; D/Dt denotes the material derivative operator; and D/Dt, the Lie derivative operator of 'Christov-Morro' theory [6][7][8], becomes in the present setting (see Ref.…”

“…(1b) from Darcy's law in that letting τ → 0 reduces the former to the latter; D/Dt denotes the material derivative operator; and D/Dt, the Lie derivative operator of 'Christov-Morro' theory [6][7][8], becomes in the present setting (see Ref. [1,Eq. (5)…”

“…Throughout their analysis, Ciarletta et al [1] tacitly regard Eq. (1b) not as a constitutive relation for the drag force but, rather, as the momentum equation for the fluid phase; and indeed, its form echoes that of the DJM, as can be seen by reexpressing Eq.…”