Capillary forces in the acoustics of patchy-saturated porous media

TL;DR

This paper extends the linearized acoustic theory for porous media saturated with two fluids by incorporating capillary effects, showing how membrane surface tension influences the frequency-dependent bulk modulus.

Contribution

It introduces a generalized model that accounts for pressure discontinuities due to capillary forces, modifying the low-frequency behavior of the bulk modulus in porous media.

Findings

Bulk modulus depends on membrane surface tension and fluid topology.

Capillary stiffness effects can be incorporated by renormalizing low-frequency coefficients.

Frequency-dependent behavior similar to zero-membrane stiffness case for long wavelengths.

Abstract

A linearized theory of the acoustics of porous elastic formations, such as rocks, saturated with two different viscous fluids is generalized to take into account a pressure discontinuity across the fluid boundaries. The latter can arise due to the surface tension of the membrane separating the fluids. We show that the frequency-dependent bulk modulus $\tilde{K}(\omega)$ for wave lengths longer than the characteristic structural dimensions of the fluid patches has a similar analytic behavior as in the case of a vanishing membrane stiffness and depends on the same parameters of the fluid-distribution topology. The effect of the capillary stiffness can be accounted by renormalizing the coefficients of the leading terms in the low-frequency asymptotic of $\tilde{K}(\omega)$.