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Assuming an upward flow velocity of 1.2 mm/s, which used in the newer AguaClara plants, the diameter of floc that will roll-up was determined by using a root finding algorithm, and the plate settler spacing or tube diameter was plotted versus the minimum floc diameter. The minimum floc diameter corresponds to the minimum size of a floc particle that will roll up into the effluent; or the maximum size of a floc particle that the plate settler will prevent from going into the effluent.

Wiki Markup!Plate spacing vs floc diameter.png\|width=700px,align=centre!

Figure 2: Plate Spacing or Tube Diameter vs. Minimum Floc Diameter

The minimum floc diameter corresponds to the minimum size of particles that will still settle out of the tube and return to the floc blanket instead of going into the effluent.  With larger plate settler spacing, most floc roll-up could theroetically be eliminated.

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Figure 4: Floc Spacing vs. Floc Diameter

{latex}
\large
$$
d = d_0 \left( {{{18V_t \Phi \nu _{H_2 O} } \over {gd_0^2 }}{{\rho _{H_2 O} } \over {\rho _{Floc_0 } - \rho _{H_2 O} }}} \right)^{{1 \over {D_{Fractal} - 1}}}
$$
{latex}

The critical velocity model can be utilized to calculate the desired spacing to capture a floc particle of a particular size. The following equation results were summarized in Figure 5. Figure 5 represents the minimum spacing that will capture a floc particle with a particular settling velocity.

{latex}
\large
$$
S = V_{up} {{108\Phi \nu _{H_2 O} d^2 } \over {g\sin ^2 (\alpha )d_0^3 }}\left( {{{d_0 } \over d}} \right)^{D_{Fractal} } {{\rho _{H_2 O} } \over {\rho _{Floc_0 } - \rho _{H_2 O} }}
$$
{latex}

Where:

{latex}\large$$ alpha $${latex}

= The angle of the tube settler (60 degrees)

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