Net flow of compressible viscous liquids induced by travelling waves in porous media

The influence of ultrasonic radiation on the flow of a liquid through a por ous medium is analyzed. The analysis is based on a mechanism proposed by Ga niev et al. according to which ultrasonic radiation deforms the walls of th e pores in the shape of travelling transversal waves. Like in peristaltic p umping, the travelling transversal wave induces a net flow of the liquid in side the pore. In this article, the wave amplitude is related to the power output of an acoustic source, while the wave speed is expressed in terms of the shear modulus of the porous medium. The viscosity as well as the compr essibility of the liquid are taken into account. The Navier-Stokes equation s for an axisymmetric cylindrical pore are solved by means of a perturbatio n analysis, in which the ratio of the wave amplitude to the radius of the p ore is the small parameter. In the second-order approximation a net flow in duced by the travelling wave is found. For various values of the compressib ility of the liquid, the Reynolds number and the frequency of the wave, the net how rate is calculated. The calculations disclose that the compressibi lity of the liquid has a strong influence on the net flow induced. Furtherm ore, by a comparison with the flow induced by the pressure gradient in an o il reservoir, the net flow induced by a travelling wave can not be neglecte d, although it is a second-order effect.