We study the wave properties at a fluid/porousmedium interface by using newly derived closed-form expressions for the reflection and transmission coefficients. We illustrate the usefulness of these relatively simple expressions by applying them to a water/porousmedium interface (with open-pore or sealed-pore boundary conditions), where the porous medium consists of (1) a water-saturated clay/silt layer, (2) a water-saturated sand layer, (3) an air-filled clay/silt layer, or (4) an airfilled sand layer. We observe in the frequency range 5 Hz-20 kHz that the fast P-wave and S-wave velocities in the four porous materials are indistinguishable from the corresponding frequency-independent ones calculated using Gassmann relations. Consequently, for these frequencies we would expect the reflection and transmission coefficients for the four water/porous-medium interfaces to be similar to the ones for corresponding interfaces between water and effective elastic media (described by Gassmann wave velocities). This expectation is not fulfilled in the case of an interface between water and an air-filled porous layer with open pores. A close examination of the expressions for the reflection and transmission coefficients shows that this unexpected result is because of the large density difference between water and air.
In this study a general bead-spring model is used for predicting some rheological properties of a cubic bead-spring structure of arbitrary size immersed in a Newtonian solvent. The topology of this bead-spring structure is based upon the well-known cubic crystals (SC, BCC or FCC) and it consists of equal Hookean springs and beads with equal friction coefficients, while hydrodynamic interaction is not included. An appropriate combination of the equations of motion, the expression for the stress tensor and the equation of continuity leads to an explicit constitutive equation with three sets of relaxation times belonging to the three types of bead-spring cubes (SC, BCC or FCC). For small-amplitude oscillatory shear flow it is found that the three relaxation spectra, which are significantly different, result in dynamic moduli which differ mainly in one aspect: the characteristic SC, BCC and FCC time scales are different. The BCC and FCC time scales can be obtained by multiplication of the SC time scale by the ratios M sc /M bcc and M sc /M fcc respectively, where M sc , M bcc and M fcc denote the number of springs in the three types of cubic bead-spring structures.
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