Kinematic waves in a liquefied paste

Paste means a dense mass of small unconsolidated (i.e., not joined together) solid particles with the pore-spaces completely filled with either gas or liquid. Liquefaction, here, means the conversion of its nature from that of a solid to that of a fluid by the application of mechanical motion; it can have, individually, either industrial applications or catastrophic consequences. The range of volume concentrations of the solid is very narrow in the liquefied state, and the liquefaction process requires that the mechanical motions be of relatively large amplitude and low frequency. The actual mechanism of the process is obscure; one is postulated here. It involves kinematic travelling waves, one in each phase, that do not utilize elastic processes, the energy and pressure amplitudes being much less than elastic dilatational waves would entail. Coupling between the waves is by conservative (inertial) forces and the dilatational phenomenon in each arises from the longitudinal spacing of the particles. The mass of each particle is its virtual mass. A plane sinusoidal wave is considered and expressions for wave velocity, phase constant, stress and concentration (as well as quantities analogous to “elasticity” and “elastic condensation”) are deduced. Some measured values of wave velocity and pressure amplitudes are reported and discussed in the light of the hypothesis.