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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

If you open the textbook (unknown), you answers are probably there.

Other textbooks such as Water Supply and Pollution Control by Mark Hammer have examples of these calculations.

Ka is the aggregation coefficient

http://www.ecs.umass.edu/cee/reckhow/courses/371/3...

### RE: Design of Flocculator - particle number and diameter

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

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