Some Mathematical and Physical Aspects of Continuum Models for the Motion of Granular Materials

Publisher Summary This chapter discusses some mathematical and physical aspects of continuum models for the motion of granular materials and describes some problems associated with the formulation and solution of differential equations of motion for a continuum model of a granular material. In many practical situations, the flow of a granular material is strongly influenced by drag forces, resulting from relative motion of the solid material and the fluid that occupies its interstices. This is known to influence the discharge rate of fine particles from a hopper and is a dominant factor in determining the behavior of systems such as fluidized beds, pneumatic transport lines, and standpipes. A convenient geometric representation of the state of stress at any point is provided by the Mohr construction. For a material, which is about to yield or is yielding slowly enough that inertial effects can be ignored, the components of force balance yield a pair of partial differential equations in the three elements of the stress tensor. The equations are closed by the algebraic relation between the elements of the stress tensor provided by the Coulomb yield condition.