Recommendations
Based on the calculations associated with the critical velocity theory, the best way to avoid floc roll up is to maximize the plate settler spacing. Figure 1 shows the minimum plate settler spacing that will produce acceptable results. From the graph, it can be estimated that this diameter is approximately 5 mm. On the graph, this is the intersection of the minimum plate settler spacing that will produce acceptable performance and the specified AguaClara capture velocity.
Figure 1: Minimum Plate Settler Spacing vs. Capture Velocity
Figure 2 illustrates the minimum particle size that will roll up the plate settler plotted against plate settler spacing. The line at the order of magnitude of colloidal particle size shows that at a plate settler spacing of approximately 17 mm and a tube diameter of 23 mm there should theoretically be no floc roll up.
Figure 2: Plate Settler Spacing vs. Floc Diameter
Although the critical velocity theory suggests that larger plate settler spacing will produce the best results, the capture velocity theory suggests that failure will occurs with a larger plate settler spacing. Theoretically, at different terminal velocities (which can be converted to a particle diameter) either the capture velocity theory or the critical velocity
By comparing the size of floc particles that both the critical velocity theory and the capture velocity theory should theoretically filter out of the effluent, you can see which theory should govern the plate settler behavior. The equations relating the critical and capture velocity are as follows:
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h2. Recommendations Based on the calculations associated with the critical velocity theory, the best way to avoid floc roll up is to maximize the plate settler spacing. Figure 1 shows the minimum plate settler spacing that will produce acceptable results. From the graph, it can be estimated that this diameter is approximately 5 mm. !Minimum plate settler spacing v. Capture velocity.png|width=600px,align=centre! _Figure 1: Minimum Plate Settler Spacing vs. Capture Velocity_ \\ Figure 2 shows the minimum particle size that will roll up the plate settler plotted against plate settler spacing. The line at the order of magnitue of colloidal particle size shows that at a plate settler spacing of approximately 17 mm and a tube diameter of 23 mm there should theoretically be no floc roll up !Plate spacing vs floc diameter.png|width=600px,align=centre!\\ _Figure 2: Plate Settler Spacing vs. Floc Diameter_ Although the critical velocity theory suggests that larger plate settler spacing will produce the best results, the capture velocity theory (link) suggests that failure will occurs with a larger plate settler spacing. Theoretically, at different terminal velocities (which can be converted to a particle diameter) different theories will govern the behavior of the floc particles. By plotting the plant flow rates against the terminal settling velocity for both the critical and capture velocity theories (which can be converted into a particle size), you can see which theory should govern the plate settler behavior. The equations relating the critical and capture velocity are as follows: {latex} \large % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyuamaaBa % aaleaacaWGJbGaamOCaiaadMgacaWG0bGaamyAaiaadogacaWGHbGa % amiBaaqabaGccqGH9aqpdaWcaaqaaiabec8aWjaadofacaWGwbGaci % 4CaiaacMgacaGGUbGaeqiUde3aaWbaaSqabeaacaaIYaaaaaGcbaGa % aG4maiaaikdacaWGKbWaaSbaaSqaaiaaicdaaeqaaOWaaWbaaSqabe % aacaaIYaaaaOWaamWaaeaadaWcaaqaaiabgkHiTiaaigdacaaI4aGa % amOvaiabfA6agjabe27aUjabeg8aYnaaBaaaleaacaWGibGaaGOmai % aad+eaaeqaaaGcbaGaamizamaaDaaaleaacaaIWaaabaGaaGOmaaaa % kiaadEgacaGGOaGaeqyWdi3aaSbaaSqaaiaadIeacaaIYaGaam4taa % qabaGccqGHsislcqaHbpGCdaWgaaWcbaGaamOraiaadYgacaWGVbGa % am4yaaqabaGccaGGPaaaaaGaay5waiaaw2faamaaCaaaleqabaWaaS % aaaeaacaaIXaaabaGaamiramaaBaaameaacaWGgbGaamOCaiaadgga % caWGJbGaamiDaiaadggacaWGSbaabeaaliabgkHiTiaaigdaaaaaaa % aaaaa!732E! $$ Q_{critical} = {{\pi SV\sin \theta ^2 } \over {32d_0 ^2 \left[ {{{ - 18V\Phi \nu \rho _{H2O} } \over {d_0^2 g(\rho _{H2O} - \rho _{Floc} )}}} \right]^{{1 \over {D_{Fractal} - 1}}} }} $$ {latex} \\ \\ {latex} |
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\large
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$$
Q_{capture} = {{L\cos \theta + S\sin \theta } \over S}\left[ {\pi \left( {{S \over 2}} \right)^2 } \right]V
$$
{latex}
Where
S = Tube settler diameter (or spacing)
d0 = size of primary particles
V = upflow velocity
{latex} |
Where
S = Tube settler diameter (or spacing)
d0 = size of primary particles
V = Predicted Terminal Velocity
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% MathType!MTEF!2!1!+-
% feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuOPdyeaaa!3767!
$$
\Phi
$$
{latex}
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diameters. The predicted terminal settling velocity is a range from 5 to 100 meters per day. For each spacing, this is what is varied in order to get a range of flow rates to be tested in each ramp state experiment.
Figure 3 shows the difference between the 6.35 mm tube and the 23.8 mm tube in terms of what size particles the settler will prevent from going into the effluent. Roll-up will dominate effluent performance for these settling velocity ranges in 6.35 mm tube compared to 23.8 mm tube.
For the 23.8mm tube, the capture velocity theory governs the size of particles that settle out. Ramp State experiments are being done to confirm this. This goes along with the theory that there should be minimal to no floc roll up for tube settlers with larger diameters. If the capture velocity is governing the floc particles that end up in the effluent, then any floc roll up in the plate settler must be insignificant compared to the number of floc particles that the plate settler is not capturing. 
Figure 3: Plant Flow Rate vs. Terminal Velocity (Particle Size) for 6.35 mm tube and 23.8 mm tube
Based on this analysis, a larger tube would be more effective because the minimum size of particles that are settled out is larger. However, this theory needs to be tested, so the Ramp State Experiments are being run to try to match up experimental data to this theory.