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PDF, 3.7Mb - G-CSC Home

PDF, 3.7Mb - G-CSC Home

Phenomena in the

Phenomena in the CrystallizerFluid dynamics:polydisperse suspensionturbulencesedimentationtransport of the dissolved substancetemperature/heating/coolingPopulation dynamics:growthbreakage (splitting)nucleationdissolvingCrystallization – p.4/20

The PopulationNumber density F(t,ξ): number of particles withξ l i ≤ ξ i ≤ ξ u i (1 ≤ i ≤ N) at time t is ∫ ξ u 1ξ l 1· · ·∫ ξ u Nξ l NF(t,ξ)dξ.Growth and breakage:∫F t + ∇ ξ · (w(c,ξ)F) = −δ(ξ)F + k(ξ,ζ)δ(ζ)F(t,ζ)dζ,} {{ }ΩGrowth} {{ }Splittingξ ∈ Ω = [ξ1 min ,ξ1 max ] × · · · × [ξNmin,ξmaxN ],w: the growth rate, δ: the splitting rate.Balance of the dissolved substance:∫c t = − a(ζ,c,F)F(t,ζ)dζΩCrystallization – p.5/20

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