EVOLUTION OF GEOMETRIC STATISTICS

A model for the description of the geometry in multiphase mechanics is derived and studied. Equations for the rate of change of mean and Gauss curvature are derived. These coupled equations show that the evolution of these curvatures depend on the velocity of the interface normal to itself. Examples are given to show the utility of these equations. To apply these concepts to multiphase mechanical situations, an ensemble average is applied to the curvature equations. Equations for the evolution of the volume fraction and the interfacial area density are also derived. These equations also depend on the curvatures and the average interfacial velocity. Examples are given to show that these equations give a description of the geometry of multiphase mechanics that is superior to the present description, which describes the force between materials as depending on two geometric parameters, the volume fraction and the average radius of the dispersed material. These examples also suggest constitutive equations to descibe surface coalescence, and bubble breakup and coalescence.