Stochastic Flocculation Model for Cohesive Sediment Suspended in Water

Abstract

Existing flocculation models for cohesive sediments are classified into two groups: population balance equation models (PBE) and floc growth models. An FGM ensures mass conservation in a closed system. However, an FGM determines only the average size of flocs, whereas a PBE has the capability to calculate a size distribution of flocs. A new stochastic approach to model the flocculation process is theoretically developed and incorporated into a deterministic FGM in this study in order to calculate a size distribution of flocs as well as the average size. A log-normal distribution is used to generate random numbers based on previous laboratory experiments. The new stochastic flocculation model is tested with three laboratory experiment results. It was found and validated with measured data that the new stochastic flocculation model has the capability to replicate a size distribution of flocs reasonably well under different sediment and carrier flow conditions. Three more distributions (normal; Pearson type 3; and generalized extreme value distributions) were also tested. From the comparison with results of different distribution functions, it is shown that a stochastic FGM using a log-normal distribution has a comparative advantage in terms of simplicity and accuracy.

Rheological and Flocculation Analysis of Microfibrillated Cellulose Suspension Using Optical Coherence Tomography

“…The (length-weighted) distribution of floc dimensions, in both radial and axial directions, was then computed for every image in the sequence as the run-length distributions (see Figure 6). The floc size distributions were log-normal, which are typical for fibers [32,33] and many other flocculating particles [34,35]. Determined distributions were finally averaged to obtain the length weighted average floc sizes.…”

A Simple Explicit Expression for the Flocculation Dynamics Modeling of Cohesive Sediment Based on Entropy Considerations

“…The Shannon entropy quantitatively measures the mean uncertainty associated with a probability distribution of a random variable. Consider the characteristic floc size D, during the flocculation process as a continuous random variable [48,49]. The objective of this study is to derive the characteristic floc size as a function of flocculation time, t. For simplicity, we let the excess floc size,D(t), be defined asD…”

Flocculation of suspended cohesive particles in homogeneous isotropic turbulence

“…Based on the early pioneering work by Levich (1962), several of these investigations have employed a population balance approach to formulate models for the temporal floc evolution (Winterwerp 1998; Maggi et al. 2007; Son & Hsu 2008, 2009; Shin, Son & Lee 2015). Alternative approaches based on the classical work by Smoluchowski (1918) propose statistical collision equations (Ives & Bhole 1973; Yang et al.…”