A Hydrodynamic and Surface Coverage Model Capable of Predicting Settled Effluent Turbidity Subsequent to Hydraulic Flocculation

William H. Pennock, Monroe L. Weber-Shirk, Leonard W. Lion

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


A widely applicable hydraulic flocculator design model would facilitate increased adoption of this sustainable technology. To this end, the authors previously proposed rate equations for the removal of nonsettleable aggregates in hydraulic flocculators (Pennock et al.). This work continues the prior effort by developing two models for coupled flocculation/sedimentation performance. The first model describes settled effluent turbidity for flocculators where the relative velocities between particles are dominated by viscous forces (e.g., laminar flows). Similarly, the second model applies where inertial forces dominate. Predictions of these models were compared with laboratory-scale flocculation/sedimentation data obtained from both a laminar- and a turbulent-flow flocculator. The viscous equation fit data from the laminar flow flocculator well. For the turbulent flocculator, both models gave good fits of the data, but the inertial model performed slightly better. The similarity of the two models under the experimental constraints explains this result, and further study in different conditions is needed to delineate the applicability of the models in turbulent flocculation. Given the similarity between the models and that the product of the mean fluid velocity gradient applicable to laminar flow (Ḡ) and hydraulic residence time (θ), Ḡ(θ), has historically been used in flocculator design, it is recommended that the viscous flocculation model introduced in this article be used. The new flocculation models have a single adjustable parameter and, in addition to being able to predict settled effluent turbidity from coagulant dose, also provide reasonable estimates of flocculator design parameters from first principles and dimensional analysis.

Original languageEnglish (US)
Pages (from-to)1273-1285
Number of pages13
JournalEnvironmental Engineering Science
Issue number12
StatePublished - Dec 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Environmental Chemistry
  • Waste Management and Disposal
  • Pollution


  • Lagrangian performance model
  • polyaluminum chloride precipitate nanoparticles
  • settled water turbidity
  • sustainable drinking water treatment
  • turbulent flow


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