# Flocculation and transport of cohesive sediment

5 TABLE OF CONTENTS

page

ACKNOWLEDGMENTS...............................................................................................................4

LIST OF TABLES...........................................................................................................................7

LIST OF FIGURES.........................................................................................................................8

LIST OF ABBREVIATIONS........................................................................................................13

ABSTRACT...................................................................................................................................17 CHAP TER 1 INTRODUCTION..................................................................................................................19

1.1 Significance of Study on Cohesive Sediment Transport..................................................19

1.2 Objectives of This Study..................................................................................................20

1.3 Terminology.....................................................................................................................21

1.4 Outline of Presentation.....................................................................................................23

2 LITERATURE REVIEW.......................................................................................................25

2.1 Studies on Flocculation and Yield Strength of Floc.........................................................25

2.2 Sediment Transport Modeling..........................................................................................29

3 STUDY ON PROPERTIES OF COHESIVE SEDIMENT....................................................32

3.1 General Properties of Cohesive Sediment........................................................................32

3.2 Fractal Dimension.............................................................................................................35

3.3 Flocculation Process.........................................................................................................39

4 MODELING FLOCCULATION OF COHESIVE SEDIMENT...........................................42

4.1 Overview on Flocculation Modeling................................................................................42

4.2 Lagrangian Flocculation Models......................................................................................44

4.2.1 Winterwerp’s Flocculation Model..........................................................................44

4.2.2 Flocculation Model Using a Variable Fractal Dimension......................................48

4.2.3 Flocculation Model Using a Variable Fractal Dimension and Variable Yield Strength........................................................................................................................56

4.3 Investigation of Flocculation Models...............................................................................62

4.3.1 Application of FM A and FM B.............................................................................62

4.3.2 Application of FM C and FM D.............................................................................81

5 MODELING TRANSPORT OF COHESIVE SEDIMENT.................................................101

5.1 Governing Equations for Flow Momentum and Concentration.....................................101

6 5.2 Flow Turbulence.............................................................................................................104

5.3 Bottom Boundary Conditions.........................................................................................106

5.4 Flow Forcing for Tidal and Unsteady Flow Condition..................................................107

5.5 Preliminary Tests............................................................................................................108

6 MODEL APPLICATION TO EMS/DOLLARD ESTUARY..............................................117

6.1 In-situ Measurement in Ems/Dollard Estuary................................................................117

6.2 Calibration of Models.....................................................................................................119

6.3 Investigation of Sediment Transport Model...................................................................127

7 SUMMARY, CONCLUSIONS AND REMARKS..............................................................172

7.1 Summary and Conclusion...............................................................................................172

7.2 Concluding Remarks for Future Study...........................................................................176

APPENDIX DERIVATION OF EQUATION 4-24...............................................................178

LIST OF REFERENCES.............................................................................................................181

BIOGRAPHICAL SKETCH.......................................................................................................190

7 LIST OF TABLES Table page

3-1 Intensity of cohesion according to size of sedim ent (Mehta and Li, 1997).......................34

3-2 Classification of sediment by size......................................................................................34

3-3 Properties of clay minerals.................................................................................................34

3-4 Cation exchange capacity of clay minerals........................................................................35

4-1 Experiment values and parameters of flocculation models...............................................55

4-2 Summary of flocculation models used in this study..........................................................61

4-3 Empirical parameters of the flocculation models used for experiment of Spicer et al. (1998).................................................................................................................................88

4-4 Empirical parameters of the flocculation models used for experiment of Biggs and Lant (2000).........................................................................................................................88

4-5 Experimental conditions of Burban et al. (1989)...............................................................92

4-6 Empirical parameters of the flocculation models used for experiment of Burban et al. (1989).................................................................................................................................92

5-1 Numerical coefficients adopted for the eddy viscosity and k-ε equations.......................106

6-1 Sediment transport models combined with or without flocculation models....................121

6-2 Assumed values and calibrated coefficients of FMs........................................................126

6-3 Calibrated values of empirical coefficients for the critical shear stress...........................128

8 LIST OF FIGURES Figure page

3-1 Example of definition of fractal dimension.......................................................................37

3-2 Example of two same sized aggregates having different fractal dimensions. A) F=3.0 and B) F=2.5......................................................................................................................38

3-3 Schematic sketch of floc structure due to flocculation process.........................................40

3-4 Conceptual diagram for effect of turbulent shear and concentration on floc size (Dyer, 1989)..................................................................................................................................41

4-1 Evolutions of F n (X) with X for three experiments and values of p and q. A) p = 1.0, q = 0.5, B) q = 0.5, and C) p = 1.0........................................................................................54

4-2 Model results with different initial floc sizes (4, 10, 20, 40, 60 and 80 μm).....................55

4-3 Experimental results of equilibrium floc size reported by Bouyer et al. (2004) and modeled results of FM A and FM B for several dissipation parameters...........................64

4-4 Experimental results of equilibrium floc size measured by Biggs and Lant (2000) and model results of FM A and FM B for several dissipation parameters...............................65

4-5 Temporal evolution of floc size measured by Biggs and Lant (2000) and calculated by FM A for the case of G=19.4 s -1 . Three curves represent model results using different sets of k ’ A and k ’ B .................................................................................................68

4-6 Temporal evolution of floc size measured by Biggs and Lant (2000) and calculated by FM B for the case of G=19.4 s -1 . Three curves represent model results using different sets of k ’ A and k ’ B .................................................................................................69

4-7 Temporal evolution of floc size measured by Biggs and Lant (2000) and calculated by FM A for the case of G=19.4 s -1 . Three curves represent model results using different sets of p and q......................................................................................................70

4-8 Temporal evolution of floc size measured by Biggs and Lant (2000) and calculated by FM B for the case of G=19.4 s -1 . Three curves represent model results using different sets of p and q......................................................................................................71

4-9 Change of the fractal dimension of FM B with time for the case of G=19.4 s -1 ................72

4-10 Comparison of two flocculation models, FM A and FM B, for T71 experiment of Delft Hydraulics.................................................................................................................73

4-11 Comparison of two flocculation models, FM A and FM B, for T69 experiment of Delft Hydraulics.................................................................................................................74

9 4-12 Comparison of two flocculation models, FM A and FM B, for T73 experiment of Delft Hydraulics.................................................................................................................75

4-13 Equilibrium floc sizes due to different dissipation parameters measured by Manning and Dyer (1999) and the calculated results of FM A and FM B for c=120 mg/l...............77

4-14 Equilibrium floc sizes due to different dissipation parameters measured by Manning and Dyer (1999) and the calculated results of FM A and FM B for c=160 mg/l...............78

4-15 Experimental result of Spicer et al. (1998) and model results of FM C............................85

4-16 Experimental result of Spicer et al. (1998) and model results of FM D............................86

4-17 Experimental result of Spicer et al. (1998) and model results of FM A and FM B...........87

4-18 Experimental result of Biggs and Lant (2000) and model results of FM C.......................89

4-19 Experimental result of Biggs and Lant (2000) and model results of FM D......................90

4-20 Experimental result of Biggs and Lant (2000) and model results of FM A and FM B.....91

4-21 Experimental results of case B12 of Burban et al. (1989) and model results of FM C and FM D...........................................................................................................................96

4-22 Experimental results of case B12 of Burban et al. (1989) and model results FM A, FM B, and FM C................................................................................................................97

4-23 Experimental results of case B4 of Burban et al. (1989) and model results of FM C and FM D...........................................................................................................................98

4-24 Experimental results of case B4 of Burban et al. (1989) and model results FM A, FM B, and FM C.......................................................................................................................99

4-25 Temporal evolution of floc size simulated by FM A combined with a variable yield strength.............................................................................................................................100

5-1 Definition of coordinate system.......................................................................................101

5-2 Depth-averaged flow velocity and water depth used to test the sediment transport model. A) The depth-averaged flow velocity and B) the water depth.............................111

5-3 Mass concentration calculated by sediment transport model combined with FM C using two types of concentrations....................................................................................112

5-4 Volumetric concentration calculated by sediment transport model combined with FM C using two types of concentrations................................................................................113

5-5 Velocity calculated by sediment transport model combined with FM C using two types of concentrations....................................................................................................114

10 5-6 Mass concentration calculated by sediment transport model combined with FM C using one type of concentration.......................................................................................115

5-7 Volumetric concentration calculated by sediment transport model combined with FM C using one type of concentration...................................................................................116

6-1 The Ems/Dollard estuary and the measuring pole equipped with a rigid frame for in- situ measurement (van der Ham et al., 2001)..................................................................118

6-2 Time evolution of floc sizes simulated by FMs combined with sediment transport model................................................................................................................................122

6-3 Time evolution of fractal dimensions simulated by FMs combined with sediment transport model................................................................................................................123

6-4 Time evolution of densities simulated by FMs combined with sediment transport model................................................................................................................................124

6-5 Time evolution of settling velocities simulated by FMs combined with sediment transport model................................................................................................................125

6-6 Velocities measured and calculated by CMC at 1.0 m....................................................129

6-7 Velocities measured and calculated by CMB at 1.0 m....................................................130

6-8 Velocities measured and calculated by CMA at 1.0 m....................................................131

6-9 Velocities measured and calculated by CMN at 1.0 m....................................................132

6-10 Measured mass concentrations and mass concentrations calculated by CMC using a variable fractal dimension and yield strength..................................................................133

6-11 Measured mass concentrations and mass concentrations calculated by CMB using a variable fractal dimension and a constant yield strength.................................................134

6-12 Measured mass concentrations and mass concentrations calculated by CMA using a constant fractal dimension and yield strength..................................................................135

6-13 Measured mass concentrations and mass concentrations calculated by CMN using constant floc size and density..........................................................................................136

6-14 Measured and simulated mass concentration profiles.....................................................137

6-15 Settling velocities of floc and dissipation parameter at 0.5 m, 1.0 m, and 1.5 m above the bottom calculated by CMC. A) settling velocity and B) dissipation parameter........140

6-16 Mass concentrations at 0.3 m and 0.7 m calculated by CMC using the constant c τ

and the variable c τ ...........................................................................................................142

11 6-17 The bottom stress (dotted lines) and the critical shear stress (solid lines) calculated by CMC............................................................................................................................143

6-18 The bottom stress (dotted lines) and the critical shear stress (solid lines) calculated by CMB............................................................................................................................144

6-19 The bottom stress (dotted lines) and the critical shear stress (solid lines) calculated by CMA...........................................................................................................................145

6-20 The bottom stress (dotted lines) and the critical shear stress (solid lines) calculated by CMN...........................................................................................................................146

6-21 Vertical profiles of size, settling velocity, and mass concentration of floc calculated by CMC and CMB at t=14.6 hr. The velocity at t=14.6 hr is around zero......................148

6-22 Vertical profiles of size, settling velocity, and mass concentration of floc calculated by CMC and CMB at t=18.0 hr. The velocity at t=18.0 is at the peak............................149

6-23 Simulated volumetric concentration profiles. Solid and dotted lines represent simulation results of CMC and CMN..............................................................................151

6-24 Settling velocity plotted as function of floc size..............................................................153

6-25 Relationship between settling velocity and mass concentration calculated by CMC......154

6-26 Relationship between settling velocity and dissipation parameter (G) calculated by CMC.................................................................................................................................157

6-27 Relationship between floc size and mass concentration calculated by CMC..................158

6-28 Relationship between settling velocity and volumetric concentration calculated by CMC.................................................................................................................................159

6-29 Relationship between settling velocity and density of floc calculated by CMC.............161

6-30 Relationship between settling velocity and mass concentration calculated by CMB......162

6-31 Relationship between settling velocity and dissipation parameter (G) calculated by CMB.................................................................................................................................163

6-32 Relationship between floc size and mass concentration calculated by CMB..................164

6-33 Relationship between settling velocity and volumetric concentration calculated by CMB.................................................................................................................................165

6-34 Relationship between settling velocity and density of floc calculated by CMB.............166

6-35 Relationship between settling velocity and density of floc calculated by CMA.............168

12 6-36 Mass concentration calculated by CMC without damping effect of density stratification.....................................................................................................................169

6-37 Mass concentration calculated by CMC with c σ =1.0.....................................................171

A-1 Schematic description on adopting the mensuration by parts for Eq. A-1......................179

A-2 Schematic description on adopting the mensuration by parts for Eq. A-3......................180

13 LIST OF ABBREVIATIONS a Empirical coefficient for breakup process B 1 Empirical parameter for yield stress of floc [N] B 2 Empirical parameter for yield strength of floc [N] c Mass concentration [kg/m 3 ] 1 C ε , 2 C ε , 3 C ε Numerical parameter C μ Numerical parameter CMA Sediment transport model combined with FM A CMB Sediment transport model combined with FM B CMC Sediment transport model combined with FM C CMN Sediment transport model without flocculation model d Size of primary particle [m]

D Size of floc [m or μ m] D 0 Initial floc size [m or μ m] D e

Equilibrium floc size [m or μ m]

f c D Characteristic size of floc [m or μ m] e b , e c , e d

Efficiency parameter E Erosion flux f s Shape factor F Three-dimensional fractal dimension of floc F c Characteristic fractal dimension F c,p Cohesive force of primary particle [N] F n Function for equilibrium floc size F y Yield strength of floc [N] FM Flocculation model

14 FM A Flocculation model using constant fractal dimension and constant yield strength FM B Flocculation model using variable fractal dimension and constant yield strength FM C Flocculation model using variable fractal dimension and variable yield strength theoretically derived FM D Flocculation model using variable fractal dimension and variable yield strength empirically proposed by Sonntag and Russel (1987) G Dissipation parameter (Shear rate) [s -1 ] h Water depth [m]

k Turbulent kinetic energy [m 2 /s 2 ] ' A k Empirical dimensionless coefficient for aggregation process ' B k Empirical dimensionless coefficient for breakup process M Total eroded mass [kg] n Number of flocs per unit volume N Number of primary particles within a floc N rup

Number of primary particles in the plane of rupture

N turb

Rate of collision of particles due to turbulent flow p Empirical coefficient for breakup process q Empirical coefficient for breakup process r Empirical parameter for y τ

s s Specific gravity of primary particle t Time [s] T rel Relaxation time [s] T L Turbulent eddy time scale [s] u x -direction flow velocity [m/s] u τ Total bottom friction velocity [m/s]

15 U Computed depth-averaged x -direction flow velocity [m/s] U 0 Desired depth-averaged x -direction flow velocity [m/s] v y -direction flow velocity [m/s] V Computed depth-averaged y -direction flow velocity [m/s] V 0

Desired depth-averaged y -direction flow velocity [m/s] W s Settling velocity [m/s] X Ratio of the equilibrium floc size to primary particle size α Empirical coefficient for variable fractal dimension s α Slope of the bottom 1 α , 2 α , 3 α Empirical parameter for variable critical stress β Empirical coefficient for variable fractal dimension e β Empirical parameter for upward erosion flux f ρ Δ Immersed density of floc [kg/m 3 ] s ρ Δ Immersed density of primary particle [kg/m 3 ] ε Turbulent dissipation rate (dissipation rate of energy) [m 2 /s 3 ] 0 λ Kolmogorov micro scale [m] μ Dynamic viscosity [N·s/m 2 ] ν Kinematic viscosity [m 2 /s] t ν Eddy viscosity [m 2 /s] f ρ Density of floc [kg/m 3 ] s ρ Density of primary particle [kg/m 3 ] w ρ Density of water [kg/m 3 ] c σ , k σ , ε σ , Numerical parameter b τ Bottom stress [N/m 2 ]

16 c τ Critical shear stress [N/m 2 ] s τ Surface shear stress [N/m 2 ] y τ Yield stress of floc [N/m 2 ] 0y τ Scaling parameter for y τ [N/m 2 ] w x z τ

x -direction fluid stress [N/m 2 ] y z w τ

y -direction fluid stress [N/m 2 ] f φ Volumetric concentration of floc s φ Solid volume concentration of primary particle sf φ Solid volume concentration of primary particle within a floc / p x∂ ∂ Pressure gradient in x -direction [N/m 3 ] / p y∂ ∂ Pressure gradient in y-direction [N/m 3 ]

17 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

FLOCCULATION AND TRANSPORT OF COHESIVE SEDIMENT By Minwoo Son

December 2009

Chair: Tian-Jian Hsu Major: Civil Engineering

An earlier model for floc dynamics utilizes a constant fractal dimension and a constant yield strength as a part of the model assumptions. However, several prior studies suggest that the fractal dimension of floc changes as floc size increases or decreases. Furthermore, the yield strength of floc is observed to be proportional to floc size and fractal dimension during breakup process. In this research, a variable fractal dimension is adopted to improve the previous flocculation model. Moreover, an equation for yield strength of floc is theoretically and mathematically derived. The newly derived equation is combined with flocculation models. By comparing with laboratory experiments on temporal evolution of floc size (mixing tank and Couette flow), this research demonstrates the importance of incorporating a variable fractal dimension and a variable floc yield strength into the model for floc dynamics. However, it still remains unclear as what are effects of variable fractal dimension and variable yield strength on the prediction of cohesive sediment transport dynamics. The second goal of the present study is to further investigate roles of floc dynamics in determining the predicted sediment dynamics in a tide-dominated environment. A 1DV numerical model for fine sediment transport is revised to incorporate four different modules for flocculation, i.e., no floc dynamics, floc dynamics with assumptions of constant fractal dimension and yield strength, floc dynamics for variable fractal

18 dimensional only, and floc dynamics for considering both fractal dimension and yield strength variables. Model results are compared with measured sediment concentration and velocity time series at the Ems/Dollard estuary. Numerical model predicts very small (or nearly zero) sediment concentration during slack tide when floc dynamics is neglected or incorporated incompletely. This feature is inconsistent with the observation. When considering variable fractal dimension and variable yield strength in the flocculation model, numerical model predicts much smaller floc settling velocity during slack tide and hence is able to predict measured concentration reasonably well. Model results further suggest that, when sediment concentration is greater than about 0.1 g/l, there exists a power law relationship between mass concentration and settling velocity except very near the bed where turbulent shear is strong. This observation is consistent with earlier laboratory and field experiment on floc settling velocity. It is concluded that a complete floc dynamics formulation is important to modeling cohesive sediment transport.

19 CHAPTER 1 INTRODUCTION 1.1 Significance of Study on Cohesive Sediment Transport Sediment transport is an important physical process that further controls many environmental, geo-morphological, and biological processes and their relationship with the natural environment. Furthermore, studying sediment transport is of economical interest such as the maintenance of navigatable harbors and channels through dredging. Sediment transport process is determined by hydrodynamics of carrier flow and sediment characteristics. However, these are very dynamic factors that are determined in accordance with complicated fluid- sediment interactions (Winterwerp and van Kesteren, 2004). Thus, to study sediment transport, it is important to understand two representative characteristics, the hydrodynamics of carrier flow and the dynamics of sediment. Hydrodynamic conditions in fluvial, estuarine, and coastal environment are generally highly dynamic temporally and spatially and flow is often turbulent. Turbulence is the main mechanism to suspend sediment. Here, turbulence is one of the essential elements in the study of sediment transport. Sediment is classified into two groups, non-cohesive sediment and cohesive sediment in a broad sense. Sand and gravel are typical non-cohesive sediments. Their electro-chemical or biochemical attraction is small enough to be ignored and, as a result, sediment particles are transported individually. On the other hand, Cohesive sediments, the mixture of water and fine- grained sediments such as clay, silt, fine sand, and organic material, have cohesive characteristics due to significant electrochemical or biological-chemical attraction. The physics of cohesive sediment transport is more complicated than non-cohesive sediment due to flocculation processes (e.g. Dyer, 1989; Winterwerp and van Kesteren, 2004). Cohesive sediments form floc aggregates through binding together of primary particles and smaller flocs

20 (aggregation), and flocs can disaggregate into smaller flocs/particles due to flow shear or collision (breakup or disaggregation) (Dyer, 1989). The properties of floc aggregates continuously change with the fluid flow condition. The averaged size of cohesive sediment aggregate is determined by flow turbulence, concentration of sediment, biological-chemical properties of water, properties of primary particle and so on (Lick et al., 1992). Thus, accurate prediction of cohesive sediment transport may require detailed water column models that resolve time-dependent flow velocity, turbulence and sediment concentration (Winterwerp, 2002; Hsu et al., 2007). Moreover, the density of floc aggregates, which is of great importance to further estimate of settling velocity, has a tendency to decrease or increase as the floc size changes (Dyer, 1989; Mehta, 1987; Kranenburg, 1994). Hence, flocculation process should be appropriately investigated when studying cohesive sediment transport. The earth’s surface is almost entirely covered with large or small amounts of cohesive sediment (Winterwerp, 2004). In estuaries, large amount of cohesive sediment can be found near the river mouth. Studying the fate of these terrestrial sediments in the estuary is critical because it significantly affects properties of river and sea bed, carbon sequestration and the health of riverine and coastal habitat/ecology (Goldsmith et al., 2008; Fabricius and Wolanski, 2000). Hence, understanding detailed dynamics of cohesive sediment transport is as important as non- cohesive sediment transport process.

1.2 Objectives of This Study The major objective of this research is to understand the dynamics of cohesive sediment transport in tide-dominated environment. The primary tasks performed to achieve this objective are to: (1) develop a flocculation model representing natural properties of cohesive sediments,

21 (2) develop a comprehensive sediment transport model which can describe transport of cohesive sediment under the condition of tide flow and river flow (3) incorporate a flocculation model into a numerical model for cohesive sediment transport, (4) apply the model to estuaries where river input from upstream and tidal flow coexist, (5) investigate the effect of modeling floc dynamic on cohesive sediment transport, and (6) assess the needs for future research. 1.3 Terminology In this section, terminology adopted in this study is defined: Aggregate : see “floc” Aggregation : the process to increase floc size through binding together of primary particles and smaller flocs Breakup : the process to break floc into smaller flocs/particles due to flow shear or collision Brownian motion : the random movement of particles in fluid due to thermal molecular motion Cohesive force : a physical property of a substance, caused by the electrochemical or bio- chem ical attraction Cohesive sediment : the mixture of fine-grained sediment, such as clay particles, silt, fine sand, organic material and so on, having cohesive properties Critical shear stress : the minimum stress to cause erosion of bed Disaggregation : see “breakup” Dissipation parameter (shear rate) : the parameter that characterizes the effects of turbulence on the evolution of floc size (Winterwerp and van Kesteren, 2004) Equilibrium floc size : the size of floc when aggregation and breakup are in equilibrium state Erosion : the removal of sediment from a bed Erosion flux : the rate of erosion from a bed (m/s) Floc : an aggregated particles through binding together of primary particles

22 Flocculation : a series of aggregation and breakup due to cohesive properties of sediment and flow turbulence Fractal dimension : a statistical quantity that gives an indication of how completely a fractal appears to fill space Hindered settling effect : the effect of particles or concentratio n on settling velocity of a substance Kolmogorov micro scale : the smallest scales of turbulent eddy Lagrangian flocculation model : flocculation m odel of which interest is in closed system and averaged values Lutocline : a pycnocline due to sediment concentration stratification Mass concentration : the mass of sediment pre unit volume of fluid-sediment mixture Non-cohesive sediment : general coarser sediment, such as sand and gravel, of which attraction is not sufficient to aggregate particles Number concentration : the number of suspended particles such as floc and particles per unit volume of fluid-sediment mixture Primary particle : an individual particle not to be broken into smaller particles by general stress in nature such as turbulent shear and collisional stress between particles Sediment transport : the movement of solid particles (sediment) and the processes that govern their motion Self similarity : the property of aggregate that the whole has the same shape as one or more of the parts Self-weight consolidation : Compaction of bed due to self-weight of sediment Settling velocity : the gravity-induced terminal velocity at which particles fall through the water column Shear rate : See “dissipation parameter” Size-classes flocculation model : flocculation model of which interest is in individual particles having various sizes and which considers input and output of particles Solid volume concentration : the volume of suspended primary particles per unit volume of fluid-sediment mixture and the mass concentration is obtained by multiplying it with density of primary particle Total eroded mass : the mass of suspended sediment in the water column above unit area of bottom

23 Turbulent eddy time scale : characteristic timescale of an eddy turn-over Turbulent kinetic energy : the mean kinetic energy per unit mass associated with eddies in turbulent velocity fluctuations Turbulent dissipation rate : the rate of the dissipation of turbulent kinetic energy Volum etric concentration of floc : the volume occupied by flocs per unit volume of fluid- sediment mixture Yield strength of floc : the minimum force to break a floc Yield stress of floc : the yield strength divided by the ruptured area of floc 1.4 Outline of Presentation This dissertation is organized with seven chapters and one appendix. Chapter 1 (Introduction) presents the importance of study on cohesive sediment, the objectives of the present research, and definitions of terminology used in this dissertation. In Chapter 2 (Literature Review), previous studies on flocculation, floc yield strength, and sediment transport modeling are reviewed. Chapter 3 (Study on Properties of Cohesive Sediment) presents general properties of cohesive sediment, fractal theory, fractal dimension, and flocculation process, one of the most important properties of cohesive sediment. Chapter 4 (Modeling Flocculation of Cohesive Sediment) first discusses the characteristics of two types of flocculation models, size-classes flocculation model and Lagrangian flocculation model. Secondly, the Lagrangian flocculation models are derived based on the different assumptions: a constant fractal dimension and a constant yield strength of floc, a variable fractal dimension and a constant yield strength of floc, and a variable fractal dimension and a variable yield strength of floc. Thirdly, these different flocculation models are used to model several laboratory experiments on the equilibrium floc sizes and temporal evolutions of floc size. In Chapter 5 (Modeling Transport of Cohesive Sediment), governing equations for flow momentum, concentration, turbulent closures, boundary conditions for tidal flow forcing adopted in the

24 numerical model of sediment transport are presented. These proposed equations and boundary conditions are tested with idealized conditions as preliminary study. Chapter 6 (Model Application to Ems/Dollard Estuary) discusses results of sediment transport models combined with three different flocculation models. The numerical models are applied to the in-situ measurement conducted at the Ems/Dollard estuary (van der Ham et al., 2001). The effects of flocculation and bed erodibility on cohesive sediment transport in tide-dominated environment are studied in details. In Chapter 7 (Summary, Conclusions and Remarks), major findings of this study are summarized. Concluding remarks for future study is also suggested in this chapter. The appendix demonstrates the detailed derivation of the equation for the number of particles in the plane crossing the center of a floc with schematic figures to show application of the method of mensuration by parts to this derivation.

25 CHAPTER 2 LITERATURE REVIEW 2.1 Studies on Flocculation and Yield Strength of Floc The flocculation process has been studied by many researchers. The theoretical aspects of the flocculation process have been developed by pioneering studies such as Smoluchowski (1917), Camp and Stein (1943), and Ives (1978). These studies have been based on the rate of change of particle numbers due to particle aggregation after collision (Tsai and Hwang, 1995). Lick and Lick (1988) present a more general model for floc dynamics that includes the effects of disaggregation due to collision and shear. Tsai et al. (1987) investigate the effect of fluid shear with natural bottom sediments and suggest the important factors of collision mechanism according to particle sizes. Lick et al. (1993) further study the effect of differential settling on flocculation of fine-grained sediments using natural sediments. McAnally and Mehta (2000) develop a dynamical formulation for estuarine fine sediment aggregation. The spectrum of fine particle has been represented by a discrete number of classes and the frequency of particle collisions due to Brownian motion, turbulent shearing and differential settling are described by statistical relationships. They conclude that it is very important to characterize particle density and strength when flocculation approaches equilibrium state. Flocculation of fine-grained particles depends on collisions resulted from Brownian motion, differential settling, and turbulent flow shear (Dyer, 1989; Dyer and Manning, 1999; Lick et al., 1993). According to the studies of O’Melia (1980), McCave (1984), van Leussen (1994), and Stolzenbach and Elimelich (1994), it can be concluded that for cohesive sediment transport in rivers, estuaries and continental shelves (or other aquatic system with more energetic flow) the effects of Brownian motion and differential settling on the flocculation process may be less important. Hence, many studies have focused on understanding the effects of turbulence on

26 the flocculation process. Parker et al. (1972) describe the change of number of particles in a turbulent flow as a function of G , the dissipation parameter (or shear rate) defined as / ε ν . Herein, ε is the turbulent dissipation rate and ν is the kinematic viscosity of the fluid. It is important to note that G is a measure of the small scale turbulent shear. To control G , many studies use a mixing tank. Ayesa et al. (1991) develop an algorithm to calibrate the parameters proposed by Argamam and Kaufman (1970) using data obtained from mixing tank experiments. Tambo and Hozumi (1979) conclude that the maximum floc size is in proportional to the Kolmogorov turbulent length scale. However, none of these studies explicitly describes the variation of floc size with time, which may be necessary for proper understanding and modeling of cohesive sediment transport processes in dynamical environment, especially wave-dominated condition (Hill and Newell, 1995; Hsu et al., 2007; Traykovski et al., 2000; Winterwerp, 2002). Biggs and Lant (2000) conduct experiments in order to obtain the temporal change of floc size with respect to a prescribed constant dissipation rate. In this experiment, samples of activated sludge are stirred in a batch mixing vessel. They conclude that the change in floc size with flow shear follows a power law relationship due to the breakage mechanisms. Bouyer et al. (2004) analyze the relationship between characteristic floc size and turbulent flow characteristics in a mixing tank. This experiment demonstrates that the average floc sizes are similar after flocculation or reflocculation steps, but the floc size distributions can be different with different impellers. Manning and Dyer (1999) investigate the relationship between floc size and dissipation parameter under different sediment concentrations using an annular flume. They conclude that at low shear rate, increasing turbidity encourages floc growth. However, at high shear rate, increasing turbidity in suspension may enhance breakup of floc.