ISSN 1063-7710, Acoustical Physics, 2007, Vol. 53, No. 2, pp. 213–216. © Pleiades Publishing, Ltd., 2007. Original Russian Text © M.G. Markov, 2007, published in Akusticheskiœ Zhurnal, 2007, Vol. 53, No. 2, pp. 249–253. 213 INTRODUCTION At present, the acoustics of fluid-saturated porous media is one of the most rapidly progressing branches of the mechanics of multiphase systems. Its theoretical foundations were laid by Frenkel and Biot [1, 2]. The basic statement of the Frenkel–Biot theory concerning the presence of two types of longitudinal waves (of the first and second kinds) in a fluid-saturated porous medium was confirmed experimentally [3, 4], while the theoretical results have received further development in a number of monographs [5–8] and in numerous scien- tific papers. As a rule, equations for describing a fluid-saturated porous medium are constructed by applying the equa- tions of the elasticity theory and the Navier–Stokes equation at the microscopic level with the continuity conditions for the velocities at interfaces and with a subsequent averaging. An attempt to consider a possi- ble boundary slip between the solid and fluid phases was made in [9, 10]. For the interfacial slip velocity, an empirical expression was proposed. According to this expression, the slip velocity strongly depends on fre- quency and tends to zero in both low- and high-fre- quency bands. The existence of an interfacial slip was confirmed experimentally for liquids [11] and gases [12]. However, there are reasons to believe that such a slip is possible in the low-frequency band as well, and that, at least for gases, the problem can be solved with reasonable accuracy by using the methods of statistical mechanics or molecular dynamics. In practice, a flow with a slip can be realized, e.g., in laboratory studies of rocks, oil, and gas collectors. In this paper, theoretical results [13] for the isother- mal slip factor are used to calculate the drag coefficient and the virtual mass coefficient involved in equations of the acoustics of a fluid-saturated porous medium and to estimate the effect of the interfacial slip on the kine- matic and dynamic parameters of elastic waves. CALCULATION OF THE DRAG AND VIRTUAL MASS COEFFICIENTS IN THE EQUATIONS OF A FLUID-SATURATED POROUS MEDIUM The calculation is carried out using the method pro- posed in [14, 15]. The dynamic equations of a fluid-sat- urated porous medium have the form (1) where U and U f are the displacement vectors of the skeleton and the fluid in the pores, respectively; ρ s and ρ f are the densities of the elastic skeleton and the fluid; T and T f are the stress tensors in the elastic skeleton and the fluid; ϕ is the porosity; and b and c are the drag coefficient and the virtual mass coefficient, respec- tively. ρ s 1 ϕ – ( ) U ˙˙ ∂ x T b U ˙ f U ˙ – ( ) c U ˙˙ f U ˙˙ – ( ) , + + = ρ f 1 ϕ – ( ) U ˙˙ f ∂ x T f b U ˙ f U ˙ – ( ) – c U ˙˙ f U ˙˙ – ( ) , – = Effect of Interfacial Slip on the Kinematic and Dynamic Parameters of Elastic Waves in a Fluid-Saturated Porous Medium M. G. Markov Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, CP 07730, México, DF e-mail: mmarkov@imp.mx Received March 16, 2005 Abstract—The method proposed by Bedford, Costley, and Stern (in 1984) is used to derive the expressions for the drag and virtual mass coefficients involved in the equations of the acoustics of fluid-saturated porous media taking into account the interfacial slip. Special consideration is given to the case of gas-filled pores, which allows one to obtain the expression for the isothermal slip factor in an explicit form by solving the Boltzmann kinetic equation. It is shown that, for longitudinal waves of the first kind and transverse waves, the effect of the interfacial slip on their velocities is small. The presence of the interfacial slip leads to an increase in the atten- uation coefficients of these waves, but the corresponding calculated values prove to be much smaller than the measured ones. For the longitudinal waves of the second kind, the effect of the interfacial slip on their kinematic and dynamic parameters is considerable and can be estimated experimentally. PACS numbers: 43.20.Jr, 47.27.Lx DOI: 10.1134/S1063771007020157 ACOUSTICS OF STRUCTURALLY INHOMOGENEOUS SOLID MEDIA. GEOLOGICAL ACOUSTICS