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. +(BrieflyOn explainthe againgraph, how this is estimated.)+ the intersection of the minimum plate settler spacing that will produce acceptable performance and the specified AguaClara capture velocity.
!Minimum plate settler spacing v. Capture velocity.png|width=600px,align=centre!
_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. +(Put this in the figure. Comment about what this means for performance in the paragraph above.)+\\
!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) +(was a link supposed to be put here?)+ suggests that failure will occurs with a larger plate settler spacing. Theoretically, at different terminal velocities (which can be converted to a particle diameter) differenteither theoriesthe willcapture governvelocity thetheory behavioror of the floc particles +(what do you mean by different theories?)+.critical velocity
By plottingcomparing the size plantof floc flowparticles ratesthat againstboth the terminal settlingcritical velocity fortheory bothand the critical and capture velocity theories +(???)+ (which can be converted into a particle size)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:
{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}
\large
% MathType!MTEF!2!1!+-
% feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyuamaaBa
% aaleaacaWGJbGaamyyaiaadchacaWG0bGaamyDaiaadkhacaWGLbaa
% beaakiabg2da9maalaaabaGaamitaiGacogacaGGVbGaai4CaiabeI
% 7aXjabgUcaRiaadofaciGGZbGaaiyAaiaac6gacqaH4oqCaeaacaWG
% tbaaamaadmaabaGaeqiWda3aaeWaaeaadaWcaaqaaiaadofaaeaaca
% aIYaaaaaGaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaOGaay5w
% aiaaw2faaiaadAfaaaa!53CA!
$$
Q_{capture} = {{L\cos \theta + S\sin \theta } \over S}\left[ {\pi \left( {{S \over 2}} \right)^2 } \right]V
$$
{latex}
Where
S = Tube settler diameter (or spacing)
d0 = size of primary particles
V = upflowPredicted Terminal velocityVelocity
{latex}
\large
% MathType!MTEF!2!1!+-
% feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuOPdyeaaa!3767!
$$
\Phi
$$
{latex}
= Shape Factor
V = Predicted Terminal Settling Velocity
\\
Since, with our experiments, all of these variables will be held constant except for the spacing, we can analyze these relationships between critical and capture velocity theories for different tube diameters. +(Be more specific here. What specific parameters are you varying? Are you trying to confirm that the spacing you calculate in theory will predict performance?)+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 +(What difference? Inin terms of what way?)+. Forsize particles the 6.35mm tube, the critical velocity theory should entirely govern the effluent turbidity produced from experiments with this tube size. +(Say it more succinctly that rollsettler 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. +(Does it govern it? Is this theory still valid?)+ 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. +(This sentence is vague. Be more specific about what you are accomplishing here.)+
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. !6.35mm Terminal Velocity vs Plant Flow Rate.png|width=400px,align=left! !23.8mm Terminal Velocity vs plant Flow rate.png|width=400px,align=right!\\
\\
\\
_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|PSS Fall 2009 Ramp State Experiment] are being run to try to match up experimental data to this theory. | 