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 $\tilde{ K}(\omega)$.
Categories: cond-mat.dis-nn