Population Balance Equation
The population balance equation describes the balance of particles in a population. A discretized formulation is implemented across a number of different size intervals i according to
(3-151)
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ni is the number density in a specific size interval (SI unit: 1/m4)
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Gi is the growth rate (SI unit: m/s)
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Li is the end-point size of interval i (SI unit: m)
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L0 is the smallest size solved for (SI unit: m)
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B is the nucleation rate (SI unit: 1/m3/s)
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Bagg,i is the aggregation birth term (SI unit: 1/m4/s)
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Dagg,i is the aggregation death term (SI unit: 1/m4/s)
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Bbreak,i is the breakage birth term (SI unit: 1/m4/s)
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Dbreak,i is the breakage death term (SI unit: 1/m4/s)
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Si is an additional source term (SI unit: 1/m4/s)
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Ji is the diffusive mass flux vector (SI unit: 1/m3/s)
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u is the velocity vector (SI unit: m/s)
In the above equation, δ is the Dirac delta function. The diffusive flux, Ji, is written as
(3-152)
where Di (SI unit: m2/s) is the diffusion coefficient for particles in size interval i.