Relation of Shear Stresses to Floc Strength
The ultimate goal of the design of the flocculation is to increase the size of the flocs. As described by the paper, Review of Floc Strength Bondage there are multiple ways to quantify the floc strength. The rate of floc growth may be written as the rate of collisions multiplied by an efficiency factor α subtracted by the Rate of break up.
R_floc=αR_col-R_br
The rate of collisions and break up depends on the size of the floc characterized by its diameter. The R_br simply depends on the shear stress of the fluid and the strength of the floc. By using estimates from literature sources (above), and the calculated shear stress values, the maximum floc value can be quantified.
Alternatively, the maximum diameter (d) can be expressed in terms of the floc strength co-efficient (C), the average velocity gradient (s-1) and the stable floc size exponent (γ).
d=CG^-γ
Logarithmic regression can be completed experientally to detemine the appropriate coefficients for the flocs. (typicall y=.5)