This paper analyses the influence of activated sludge technologies on the Particle Size Distribution (PSD) of urban wastewater treatment plants operating under real conditions. The activated sludge treatment systems selected for the analysis are the most widely used in wastewater treatment installations: (a) double step activated sludge, (b) medium load activated sludge, (c) prolonged aeration, and (d) membrane bioreactors The main quality parameters (suspended solids, turbidity, and COD) and PSD in the influent and effluent of each different activated sludge treatment were analyzed during 1 year. The PSD was fitted using the power law (\documentclass[12pt]{minimal}
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\begin{document}$$ n\left( {{d_{\text{P}}}} \right) = \frac{{\partial {\text{N}}\left( {{d_{\text{p}}}} \right)}}{{\partial {d_{\text{p}}}}} = A \cdot d_{\text{p}}^{{ - b \cdot {\text{Log}}\left( {{d_{\text{p}}}} \right)}} $$\end{document}) obtaining coefficients A and b to define the particle distribution. Mathematical correlations between this coefficients and the rest of parameters studied were found \documentclass[12pt]{minimal}
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\begin{document}$$ \left( {\matrix{ {{\text{SS}} = {0}{.0126} \cdot {A^{{{0}{.781}}}},} &{{\text{Turbidity}} = 15.5814 + 1.164 \cdot {{10}^3} \cdot A{,}} &{{\text{COD}} = \frac{{1}}{{{0}{.0133} + \cdot \frac{{{49}{.85}}}{\text{A}}}}} \\ }<!end array> } \right) $$\end{document}. The relation with the average particle size by mass was also found, (\documentclass[12pt]{minimal}
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\begin{document}$$ {d_{\text{pma}}} = - 11.6502 + \frac{{50.4265}}{b} $$\end{document}). Moreover, a relation between PSD and the particle elimination efficiency of the secondary treatment was study, (\documentclass[12pt]{minimal}
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\begin{document}$$ \eta = 0.1434 - \frac{{0.5602}}{{{A_{\text{rel}}}}} + \frac{{0.7490}}{{{b_{\text{rel}}}}} $$\end{document}). Finally, the particulate matter nature was assessed by SEM-EDX. It can be concluded that membrane bioreactor is the technology that produces the best water quality effluent due to physic process of particle separation by ultrafiltration membrane technology.
