Multiphase systems, such as sprays and aerosols, are characterized by the existence of a continuous primary phase and a disperse secondary phase. The interaction between the two phases and/or the chemical reactions can affect both composition and characteristic velocity of the primary and secondary phases, as well as the size distribution of the secondary phase. In order to describe these systems, the continuity, mass balance and momentum balance equations as well as additional equations for turbulence, must be solved. Nevertheless if there is the need to account for the evolution of the secondary phase because of continuous and discrete events the population balance equation must be solved. In this work two very efficient ways to cope with these issues will be presented. In particular the use of the quadrature method of moments coupled with the mixture multiphase model, and the multi-fluid model will be presented and discussed.

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