ANSYS FLUENT 12.0 Population Balance Module Manual - 2.2 The Population Balance Equation (PBE)

2.2 The Population Balance Equation (PBE)

Assuming that $\phi$ is the particle volume, the transport equation for the number density function is given as

$\frac{\partial}{\partial t}[n(V,t)]+\nabla \cdot [\vec{u}n(V... ...\nabla_{\rm v} \cdot [G_{\rm v}n(V,t)]}_{\mbox{Growth term}} =$

$\underbrace{\frac{1}{2}\int_0^V a(V-V^\prime, V^\prime) n(V-... ...,t) n(V^\prime,t) dV^\prime}_{\mbox{Death due to Aggregation}}$

$\; \; + \underbrace{\int_{\Omega_{\rm v}} p g(V^\prime)\beta... ...\; \; - \underbrace{g(V)n(V,t)}_{\mbox{Death due to Breakage}}$

(2.2-1)

The boundary and initial conditions are given by

$n(V,t=0)=n_{\rm v}; \;\;\; n(V=0,t)G_{\rm v} = \dot{n}_0$

(2.2-2)

where $\dot{n}_0$ is the nucleation rate in particles/m -s.

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