VOLUME AVERAGING OF SLIGHTLY NONHOMOGENEOUS SUSPENSIONS

We consider the problem of volume averaging in a two-phase dispersed s ystem with non-uniform bulk fields, for instance suspensions with grad ients of the particle concentration. We limit ourselves to slightly no n-homogeneous suspensions for which the scale of macroscopic variation is much larger than the particle distance and we look for the average of quantities which vanish everywhere except inside the particles or at the interfaces. The results appear as a multipolar expansion remini scent of the one developed by Lorenz for electromagnetic media. We che ck these results in some simple situations and use them to define the average stress and average interphase force in a suspension with small non-uniformities.