Water Research 36 (2002) 1056–1066 Modeling coagulation kinetics incorporating fractal theories: comparison with observed data Du Gon Lee a , James S. Bonner b , Laurie S. Garton c, *, Andrew N.S. Ernest d , Robin L. Autenrieth a a Environmental and Water Resources Division, Civil Engineering Department, Texas A&M University, College Station, TX 77843-3136, USA b Conrad Blucher Institute for Surveying and Science, Texas A&M University Corpus Christi, 6300 Ocean Drive, Corpus Christi, TX 78412, USA c Texas Engineering Experiment Station, Texas A&M University, College Station, TX 77843-3126, USA d Environmental Engineering Department, Texas A&M University Kingsville, Kingsville, TX 78363, USA Received 1 November 1999; accepted 1 June 2001 Abstract There are currently four possible approaches in modeling coagulation kinetics: the traditional Euclidean rectilinear; the Euclidean curvilinear; the fractal rectilinear; and the fractal curvilinear. The fractal model includes the Euclidean caseasasubset.Theprimarypurposeofthisresearchistoinvestigatewhichoftherectilinearmodelsamongthesebest predicts the evolution of experimental observed particle size distribution (PSD). Using a fractal rectilinear model previously developed by the authors, model predictions were compared with a series of observed PSD data obtained from estuarine sediment particles in a 2m settling column, where the average velocity gradient (G)was20or40s 1 . Nonlinear parameter estimation was performed to estimate two free parameters for the fractal model (the fractal dimension, D F ; and the collision efficiency factor, a), and one free parameter (the collision efficiency factor, a) for the Euclidean model. Compared with the observed PSD, the simulation showed that the fractal rectilinear model was best, and that this model fit better for the larger size particles. The estimated D F was between 2.6 and 3.0. The research demonstrated that the a’s have multiple values for the same observed data, depending on the coagulation model used. This finding is significant because a is currently used as a single value based on the conventional Euclidean rectilinear model. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Coagulation; Euclidean; Fractal; Collision efficiency; Estuarine sediment particles 1. Introduction The traditional model for coagulation kinetics can be characterized as the Euclidean rectilinear model, in which is embedded two important assumptions: recti- linear motion and the coalesced sphere. In order to overcome the limitations associated with these assump- tions, two lines of theoretical improvement have emerged: curvilinear approach path and fractal aggre- gate geometry [1]. Fractal theories related to particle aggregates provide a new quantitative method to describe the structure of particle aggregates in various water systems. Previous research in this area includes fractal characterization of particles generated from wastewater treatment [2], bacterial and yeast aggregates from laboratory batch experiments [3], and phytoplank- tonaggregatesinasimulatedoceanicsystem[4].So,itis nowbelievedthatmostparticleaggregatesinnatureand engineered systems are fractal in their morphological structure. *Corresponding author. Tel.: +1-979-845-9775; fax: +1- 979-862-1185. E-mail address: lsgarton@tamu.edu (L.S. Garton). 0043-1354/02/$-see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII:S0043-1354(01)00281-0