Acoustofluidic equations governing fluid-elastic media with suspended particles and shear elastic properties

Abstract

Understanding physics of complex media is generally helped by one's having a complete set of partial differential equations that govern the motion and interactions within the media. A single scalar wave equation is usually not sufficient for understanding all the acoustic properties of interest. An example of such a set of equations are those developed by M. A. Biot (1956) for low frequency propagation of compressional, shear, and other waves in poroelastic media. An analogous set of equations is here developed for a medium that has three primary phases—(1) a fluid, (2) a gossamer array of thin platelets held together by van-der-Waals forces, and (3) a disperse and somewhat random array of larger solid particles held in suspension by the gossamer array. Marine sediment mud is one example of such a medium. Because of the gossamer array. the medium resists static shear, and its compressibility is primarily caused by the fluid. Using various physical principles, one can formulate different elastical-mechanical equations for each of the three phases, or even for subcategories of the phases (such as for suspended particles within different size ranges). The phases interact via different physical mechanisms, such as viscous forces exerted by the fluid on the suspended particles. Examples are given for the use of these equations and of their implications. [This material is based upon research supported by, or in part by, the U. S. Office of Naval Research under award numbers N00014-15-2039, N00014-18-1-2439, and N00014-19-1-2636.]