Electrochemical basis of the card-house model of mud and its acoustical implications

Abstract

A basic mud model contains thin mineral (kaolinite and smectite) particles, roughly hexagonally shaped platelets, with diameters typically 1 micron. Isomorphous substitution causes each platelet to carry a net negative charge per unit area. Because the ions in the surrounding water respond so that there is a net positive charge on both sides of the platelet, each platelet is modeled as a sheet of longitudinal electric quadrupoles aligned perpendicular to the surface. The electrical interaction between platelets is responsible for the card-house structure, whereby the edge of one platelet touches a central line along the surface of another platelet, with the platelets being at right angles to each other. When the perpendicular arrangement is perturbed, a restoring torque attempts to return the platelets to their original state. Electrostatic analysis is used to explain why the restoring torque is formally singular at the joining line when one platelet is slightly tilted from perpendicular. This singularity requires imposition of the cantilever boundary condition in order to consider the shear resistance of mud, with each platelet bending as an elastic plate. Estimated shear speed is shown to be consistent with observations. © 2013 Acoustical Society of America.