Aggregation moment source term

As it is possible to see, the drift term has disappeared since the continuous growth of particle size does not change the total number concentration (if Gl > 0). However, N is influenced by the rate of formation of particles (e.g. nucleation), and the rates of aggregation and breakage, which cause appearance and disappearance of particles. These processes are all contained in the source term /tL.o The third-order moment mL,3 is related to the fraction of volume occupied by particles with respect to the suspending fluid and can be easily found fromEq. (2.18) ... 

Note that the sign of the source term will depend on whether particles are created or destroyed in the system. Note also that the spatial transport term in Eq. (4.46) will generally not be closed unless, for example, all particles have identical velocities. The transport equation in Eq. (4.46) is mainly used for systems with particle aggregation and breakage (i.e. when N(t, x) is not constant). In such cases, it will typically be coupled to a system of moment-transport equations involving higher-order moments. 

In the case of aggregation, when the internal coordinate f is purely additive during one aggregation event, the PBE has the source term given in Eq. (7.9) and the evolution equation for the moment of order k is... 

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