Theory of sound propagation through a fluidic medium with suspended clay and silt particles having the general characteristics of mud

Abstract

Work presented at previous meetings and in various publications for propagation of sound through mud continues with a theory that simultaneously takes into account viscous flow past both suspended clay and silt particles. Why silt particles do not settle under the action of gravity to the bottom of the layer is explained because (1) the clay particles adhere together in a flocculated card-house configuration and (2) the silt particles are trapped in the clay matrix. The conjecture is defended that the clay matrix and the silt particles move in lock-step under the influence of an incident sound wave. Neighboring particles of different sizes move with the same velocity amplitude, although they are subjected to different viscous forces. The theories of Stokes, Happel, and Brenner are used to calculate viscous forces at low frequencies for particles of different shapes, with the clay particles idealized as thin platelets and the silt particles idealized as spheroids with different eccentricities and random orientations. The forces on the clay particles continue to be given by the low frequency approximation for all frequencies of interest, and the deviations from Stokes's low frequency law are taken to be what corresponds to a sphere with the equivalent radius. The size distributions of the particles are taken from existing data. Modified fluid dynamic equations are derived using basic principles. The attenuation is shown to vary as frequency squared at low frequencies and as the square root of frequency for higher frequencies.