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

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Abstract
If the solid constituent of a fluid saturated porous medium is assumed to be 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. The determination of these coefficients is therefore reduced to the solution of a boundary value problem for a viscous, compressible fluid. As an example, the pores have been assumed to be cylindrical. The motion of the fluid has been determined theoretically 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 obtained by Biot and by Hovem and Ingram. 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.

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