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Design of Flocculator - particle number and diameter

Design of Flocculator - particle number and diameter

(OP)
I'm currently working on a design for a mixing and flocculation facility (I'm a student) for a potable water treatment plant. I managed to desegn a fast mixer for mixing of coagulant but I'm having difficulties designing the slow mixers (for flocculation).

I want to calculate the reduction of number of particles over time in the unit operation I designed but for this I need the number of particles per unit volume(n) and their average diameter (d). I've got some influent details like FTU and SI but I that's it. I also need to have a realistic collision efficiency (a).

The equation I found for reduction of number of particles over time is: -dn/dt = (4*a*n^2*d^2*Gv) / 3

But I guess a more complete formula is: -dn/dt = (8*a*n*cv*Gv)/ PI

I also found these two formulas: n/no = e^(-ka*cv*Gv*t) (for flugflow) and n/no = 1/(1+ka*cv*Gv*t) for completely mixed systems

Gv = Velocity constant (already calculated)
cv = volumetric concentration derived from n and d
ka = no idea

I want to know a couple of things:
What does the ka value stand for?
What are realistic values for n and d for Meuse river water with a settling time of 3 months? Otherwise can I derive n and d from another parameter of my influent?
Wich one of the fomulas should I use?
What is a realistic collision efficiency rate (a)

By the way. I'll pobably design multiple flucculator following each other with reducing rotation speeds consecutive to reduce floc breaks.

RE: Design of Flocculator - particle number and diameter

(OP)
Thank you. This information certainly helps. Interesting research!

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