On the drag and virtual mass coefficients in Biot's equations

Consider a hypothetical experiment in which the solid constituent of a fluid-saturated porous medium is subjected to a uniform oscillatory motion. Biot's equations can be solved for the drag and virtual mass coefficients in terms of the resulting oscillatory motion of the fluid. Assuming the pores to be cylindrical, the motion of the fluid has been determined by subjecting the wall of a cylinder of viscous compressible fluid to a uniform oscillatory motion and averaging the resulting fluid displacement over the volume of the cylinder. Motions parallel to and normal to the axis of the cylinder have been considered. In the case of motion parallel to the cylinder axis, the obtained coefficients are equivalent to those derived by Biot [J. Acoust. Soc. Am. 28, 179–191 (1956)] and Hovem and Ingram [J. Acoust. Soc. Am. 66, 1807–1812 (1979)]. By superimposing the parallel and normal cases, the coefficients for cylindrical pores at an arbitrary angle to the propagation direction have been obtained. Then, by averaging with respect to the angle, the coefficients have been determined for a material containing pores of random orientation. [Work supported by the ONR.]