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Acoustic attenuation.

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:


  • A scalar transport that occurs entirely within each averaging volume and that accounts for the rate at which fluid is exchanged between porous phase 1 and porous phase 2 when there is a difference in the average fluid pressure between the two phases and
  • A vector transport that accounts for fluid flux across an averaging region when there are macroscopic fluid-pressure gradients present. 


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