Propagation of Elastic Waves in a Gas-Filled Poroelastic Medium: The Influence of the Boundary Conditions

Abstract

We consider the propagation of elastic waves in gas-filled porous media at small but non-zero values of Knudsen numbers $$ {\text{Kn}} $$ , where $$ {\text{Kn}} = \lambda /l $$ , $$ \lambda $$ is the mean free path of gas molecules; $$ l $$ is the characteristic size of inclusion (the so-called slip regime). In this case, it is possible to apply the classic equations of hydrodynamics with modified boundary conditions at solid walls. We have assumed that the gas molecules distribution function is satisfied at the modified Maxwell boundary conditions (Struchtrup 2013; Mohammadzadeh and Struchtrup 2015). We have obtained the expressions for drag and added mass coefficients for the Biot equations of poroelasticity for a system of randomly oriented gas-filled cylindrical capillaries. Our calculations have shown that the drag and added mass coefficients depend considerably on the Knudsen number and the properties of the surface. The influence of the interfacial slip effect on the velocities of the compressional wave of the first kind and shear wave is small, but the velocity and attenuation of the compressional wave of the second kind are considerably influenced by this effect. The results obtained show the fundamental possibility of the determination of the accommodation coefficient by measuring the velocity of the compressional wave of the second kind for different values of the Knudsen number.