Acoustic flow in porous media

Abstract

We calculate the steady acoustic flow-The steady drift of fluid mass or acoustic streaming appearing along the path of an acoustic stimulus-in porous media. In particular we suggest a mechanism to explain acoustic contributions to mass transport in porous media at geological unit operation and lab-on-A-chip length scales. We study several cases of steady acoustic flow for a planar acoustic wave whose wavelength is large compared with the pore size. We commence our analysis at the ideal limit of same acoustic properties in the solid and fluid. The effective flow may then be treated intuitively according to the Darcy equation for flow through porous media in addition to a correction for the average azimuth of the pores compared with the acoustic path. We further consider the framework of a rigid porous frame where the presence of a flow forcing mechanism resulting from the viscous dissipation of the acoustic wave at the solid surface of the pores hinders the intuitive application of the Darcy equation. However we show that the steady acoustic flow in this case may be written as a quasi-Darcy-Type equation. The analysis is conducted by a detailed calculation of the transport of mass through cylindrical pores of similar size but arbitrary azimuth compared with the acoustic path. We consider large medium and small pore diameter limits relative to the viscous penetration length of the acoustic wave near the pore surface.