The conservation equations for dilute sprays

A natural question that arises in the preceding analysis is What really determines the parameters Xj and, which were treated as known quantities Both of these quantities depend on the interaction of the spray with the gas 

Consideration will be restricted to dilute sprays, so that the statistical fluctuations in the flow, which are induced by the random motion of individual particles, may be neglected. Therefore, our objective is to obtain the hydrodynamic equations for the (local) average properties of the gas. These equations will be derived by phenomenological reasoning and will be shown to be equivalent to the ordinary equations of fluid dynamics, with suitably added source terms accounting for the average effect of the spray. For the sake of generality, allowance will be made for M different kinds of droplets and N different chemical species in the gas. 

---