Linear dynamics of double porosity and dual-permeability materials. Governing equations and acoustic attenuation.
For the purpose of understanding the acoustic attenuation of double-porosity composites, the key macroscopic equations are those controlling the fluid transport.
Two types of fluid transport are present in double porosity dual-permeability materials:
The scalar transport that occurs between the two phases can produce large amounts of wave-induced attenuation. The scalar transport equation is derived using volume-averaging arguments and the frequency dependence of the transport coefficient is obtained.
The dual-permeability vector Darcy law that is obtained allows for fluid flux across each phase individually and is shown to have a symmetric permeability matrix. The nature of the cross coupling between the flow in each phase is also discussed.Physical Review E 68, 036604