Acoustic flow in porous media

We calculate the acoustic flow – the steady drift of fluid mass to appear due to the convection of momentum along the path of an acoustic wave – in a porous medium. In particular, we suggest a mechanism to explain observations of acoustic contributions to mass transport in porous media at geological, unit operation, and lab on a chip length scales. We study three limits for the case of an acoustic planar wave (that is, sound or ultrasound waves) whose wavelength is large compared to the pore size. We commence our analysis at the ideal limit of similar acoustic properties in the solid and fluid. The acoustic flow may then be treated according with the Darcy theory for flow through porous media in addition to a correction for the average azimuth of the pores compared to the acoustic path. The two other limits are taken within the framework of a rigid porous frame. The presence of a flow forcing mechanism to result from the viscous dissipation of the acoustic wave at the solid surface of the pores in this case hinders the direct use of the Darcy theory. The analysis is conducted by a detailed calculation of the convective transport of mass through cylindrical pores of similar size but arbitrary inclination, where we consider large and medium to small pore diameter limits.