Wave propagation in a dissipative poroelastic medium

Biot's theories on wave propagation in saturated porous solid consider the existence of three waves, i.e., two longitudinal waves and one transverse wave. This is true when the porous solid is saturated with a non-viscous fluid. But for the presence of viscosity in interstitial fluid, the propagation of an additional transverse wave is expected. So, in a porous solid saturated with viscous fluid, four attenuated waves should be propagating. Two of these are longitudinal/dilatational waves and other two are transverse/rotational waves. The additional fourth wave has a larger attenuation as compared to other three waves in the medium. Of the two transverse waves, it propagates with a smaller phase velocity and termed as slow S wave, analogous to the slow P wave of Biot's theories. The propagation velocities and attenuation coefficients of all the four waves vary, differently, with wave frequency as well as pore-fluid viscosity. The slow transverse wave travels faster with the increase of frequency and viscosity. However, this weak transverse wave slows down for a stronger fluid-solid coupling (both, bulk and shear).