Flocculation model of cohesive sediment using variable fractal dimension

Abstract

A new flocculation model using variable fractal dimension is proposed and validated with several experimental data and an existing model. The proposed model consists of two processes: aggregation and breakup due to flow turbulence. For aggregation process, the aggregate structure is considered to have the characteristic of self-similarity, the main concept of fractal theory. Under this assumption, a variable fractal dimension instead of a fixed one adopted by previous studies is utilized here for general cohesive sediment transport. For breakup, similar concept is adopted in a more empirical manner because breakup is too abrupt to entirely apply the concept of variable fractal dimension. By a linear combination of the formulations for aggregation and breakup processes, a flocculation model which can describe the temporal evolution of floc size is obtained. Flocculation model using variable fractal dimension is capable of predicting equilibrium floc size when compared with several experimental data sets using different types of mud provided that empirical coefficients are calibrated. Through model-data comparison with Manning and Dyer (Marine Geology 160:147-170, 1999), it is also clear that some of the empirical coefficients may depend on sediment concentration. Model results for the temporal evolution of floc size are less satisfactory, despite model results shows a more smooth "S-curve" for the temporal evolution of floc size as compared with the previous model using fixed fractal dimension. The proposed model is limited to mono-size of primary particle and dilute flow condition. These other features shall be investigated as future work.

Stochastic Flocculation Model for Cohesive Sediment Suspended in Water

“…From the simulation results, it is clearly established that a new FGM from Son and Hsu [1] has the capability to replicate the temporal evolution of floc size as well as the equilibrium floc size. In addition, from comparison with results calculated by models developed by Son and Hsu [7] and Winterwerp [8], it is also concluded that both the variable fractal dimension and the variable yield strength of flocs are critical to modeling the flocculation process. Son and Hsu [25] develop a sediment transport model for cohesive sediment and incorporate it into FGMs from Winterwerp [8], Son and Hsu [7], and Son and Hsu [1].…”

“…It has been concluded in many studies that turbulent shear is the dominant mechanism of suspended sediment collisions (e.g., [5,6]). Moreover, turbulent shear is considered as the main mechanism of floc breakup (e.g., [1,7,8]). Many laboratory studies on the effects of turbulent shear have been conducted utilizing a mixing tank and Couette viscometer in order to control the intensity of turbulent shear (e.g., [9][10][11][12]).…”

“…However, many studies show that the fractal dimension of natural flocs is variable (e.g., [20,21]). Based on Levich [19] and Khelifa and Hill [20], Son and Hsu [7] improved Winterwerp's FGM [8] by adopting an empirical equation with a variable fractal dimension. However, neither Son and Hsu [7] nor Winterwerp [8] appropriately address the temporal evolution of floc size, although both calculate the equilibrium floc size under constant turbulence intensity conditions.…”

“…Based on Levich [19] and Khelifa and Hill [20], Son and Hsu [7] improved Winterwerp's FGM [8] by adopting an empirical equation with a variable fractal dimension. However, neither Son and Hsu [7] nor Winterwerp [8] appropriately address the temporal evolution of floc size, although both calculate the equilibrium floc size under constant turbulence intensity conditions. Son and Hsu [1] further theoretically and mathematically derive an equation for the yield strength of flocs, which depends on the floc size and fractal dimension.…”

“…The equation is similar to an empirical equation from Sonntag and Russel [22] when one empirical parameter, r, is set to be about 0.7 (see [1] for more details). By incorporating this equation with a FGM from Son and Hsu [7], Son and Hsu [1] propose a new FGM using a variable fractal dimension and yield strength. The model from Son and Hsu [1] has been validated with laboratory experiments by Spice et al [23] and Burban et al [24].…”