If the mass fraction of the dispersed phase is small, then one-way coupling between the phases is a reasonable assumption; that is, the dynamics of the particle phase are affected by the carrier phase, but the reverse is not the case. However, if the mass fraction of the dispersed phase is large, the interaction of the dynamics between the two phases must be considered - this is two-way coupling.
A problem with the Lagrangian treatment of the dispersed phase is that once the number of particles becomes large, it may require a prohibitive amount of computational power to track a sufficiently large sample of particles required for statistical convergence. In addition, if the particles are sufficiently light, they behave essentially like a second fluid. In this case, an Eulerian treatment of the dispersed phase is sensible.