Wave equation in non-integer-dimensional porous media

Abstract

Over some range of scales, porous media display properties of fractals. It particular both pore sizes and pore-interfaces exhibit the fractal characteristics. One of the fascinating interests of fractals is their capability to model objects with complicate structure. This is due to an important property of fractal objects that their structure is characterized by a small number of parameters. One of them is the fractal dimension which tells how the fractal fills the space in which it lies. Very early, fractal concept has been incorporated in the study of porous media to investigate various phenomena as flow in porous media, pores and fractures of geological media. We present generalized Biot's wave equations for a fractional dimensional system of 3-spatial coordinates used as an effective description of porous media. Some specific examples are given as an application of this model.

Transient Acoustic Wave Propagation in Non-Integer-Dimensional Rigid Porous Media

“…Modeling of acoustic propagation in in non-integer-dimensional porous media was initiated by Depollier et al (2008) using the Stillinger (1977), Palmer-Stavrinou (2004) formalism. In this work, we develop a temporal model for the propagation of ultrasonic waves in non-integer-dimensional rigid porous medium.…”