Dispersion of powdered solids in viscous liquids is the result of the interaction between a complex flow and incompletely understood phenomena - rupture and erosion of solids - occurring at agglomerate length scales. Breakup of solid clusters in nonhomogeneous flows is studied by dynamic modeling. Complex how behavior is simulated by means of a chaotic flow; breakup is characterized by the 'fragmentation number', F alpha, which is the ratio of deforming viscous forces to resisting cohesive forces. A condition for rupture, F alpha > F alpha(sep), developed using a two fragment model cast in terms of a microstructural vector model, is presented. Clusters rupture and erode causing the population to evolve in space and time; conditions based on the magnitude of F alpha determine whether or not rupture occurs, and the probability of erosion. Results are analyzed by means of fragmentation theory. It is shown that the polydispersity is not constant, that the cluster size distribution resulting from dispersion is not self-similar, and that erosion in a nonhomogeneous flow leads to a wider size distribution than predicted by mean-field approaches. It is shown as well that regardless of the mixing, that the mass fraction of ultimate size clusters can be predicted by a polynomial relation derived via fragmentation theory and that the overall rates of erosion in both poorly mixed or well mixed flows can be described by a power law.