General equation of change for a particle population

Particle separation devices, aerosol/hydrosol separation in granular media, crystallization and precipitation devices generally involve a size-distributed particle population. 

The notion of a size-distributed particle population was introduced in Section 2.4 via a particle size density function/(rp) the quantity/(rp)drp represents the fraction of particles in the size range of Vp to Vp + dVp in a unit fluid volume. It is also the probability of finding a particle having a size in the size range Vp to Vp + dVp in a unit fluid volume. 

We will determine the contribution of each of these categories now to the overall balance in the number of particles  

Open separators bulk flow parallel to force and CSTSs 

Dividing by (AxAyAz) and allowing the individual dimensions Ax, Ay and Az to shrink to zero in the limit, we get the population balance equation (PBE) in cartesian coordinates  

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To provide an elementary background on separation systems where particles are present in a fluid and particle motion is important for separation, the equations of motion of a particle in a fluid are provided next these are also called trajectory equations. These equations have been followed by a general equation of change for a particle population, the population balance equation. Analysis of a CSTS for particulate systems is considered at the end of this section. 

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