ABSTRACT
Dispersed systems are heterogeneous systems consisting of discrete inclusions of one phase suspended in a continuum of another phase. It is important to consider two length scales before treating dispersions and composites as a continuum. Velocity, pressure, velocity gradient, and stress all tend to fluctuate with time at any given location in the dispersed system; at some time the position is occupied by a particle and at another time, the same position may be occupied by the matrix. As volume averages of local fields are more convenient for analytical purposes as compared to ensemble averages, they are widely used in the development of constitutive equations for dispersed systems. It should be noted that the dipole strength, and hence the bulk stress in a dispersion, is symmetric only in the absence of externally applied torque on the particles.
