Cohesive Sediment Transport in River Systems: Comparison
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Mathematical modelling of cohesive sediment transport is a challenge because of the large number of governing parameters controlling the transport processes. These parameters have to be determined using a rotating circular flume for site specific sediments. The parameters that that need to be determined using a rotating circular flume during the application of the RIVFLOC model to different river systems include the critical shear stress for erosion of the cohesive sediment, critical shear stress for deposition according to the definition of Partheniades, critical shear stress for deposition according to the definition of Krone, the cohesion parameter governing the flocculation of cohesive sediment and a set of empirical parameters that define the density of the floc in terms of the size of the flocs. An examination of the variability of these parameters shows the need for testing site-specific sediments using a rotating circular flume to achieve a reliable prediction of the RIVFLOC model. Application of the model to various river systems has highlighted the need for including the entrapment process in a cohesive sediment transport model.

  • cohesive sediment transport
  • flocculation
  • critical shear stress
  • erosion
  • entrapment

1. Introduction

Cohesive sediments play an important role in the transportation of contaminants and nutrients in a river system. Cohesive sediments are characterized as a mixture of predominantly clay- and silt-sized fractions of clay-type minerals but may also contain a range of organic compounds [1]. Contaminants and nutrients interact with these cohesive sediment mixtures and become part of the assemblage of the mineral and organic particles due to physical, chemical and biological controls [2]. Therefore, the contaminants and nutrients are transported in the river systems predominantly in association with cohesive sediments. A better understanding of the transport processes of cohesive sediment is of paramount importance for understanding the water quality and the quality of the river ecosystem.
Transport processes of cohesive sediment were studied extensively in the literature for over sixty years. The pioneering work in this area was carried out by Partheniades [3][4][5], Partheniades and Kennedy [6] and Partheniades et al. [7]. Partheniades used a rotating circular flume to study the physical behavior of cohesive sediments in the laboratory and concluded that the cohesive sediment behavior is very different from that of the cohesionless coarse-grained sediments, which had been studied extensively in this area of research (see, e.g., [8][9][10]). Among the differences in the transport behaviors between cohesive and cohesionless sediments, the one that sets them apart is the flocculation process. Because of the fineness of the cohesive sediments, the surface forces of attraction and repulsion become the same order of magnitude as the body (gravity) forces. As a consequence, the cohesive sediments undergo the process of flocculation in which the cohesive sediment particles interact and become agglomeration of particles called flocs [3][7][11][12][13][14][15]. Cohesionless sediments, on the other hand, behave as individual particles in a flow field.
Analysis of cohesive sediment transport in a flow field is much more difficult in comparison to the analysis of cohesionless sediment. Since the cohesionless sediment behaves as individual particles and the density of the particles is also constant (~2.65), the settling velocity of the cohesionless sediment is well defined for a sediment of a certain size (Stokes Law). The same cannot be said for the cohesive sediment. In the case of cohesive sediment, because of the flocculation process, the size of the transporting unit in a flow field is a variable and depends, among other things, on the intensity of the flow field, which can break up the flocs into smaller units. Moreover, the density of the transported unit is also variable as a result of the incorporation of suspending fluid into the floc structure. Therefore, the specification of settling velocity for cohesive sediment is much more difficult than for the cohesionless sediment.
In addition, the erosion and deposition characteristics of cohesive and cohesionless sediments are also different. From his laboratory studies, Partheniades [3] concluded that for cohesive sediments, the critical shear stress for erosion is different from the critical shear stress for deposition, and at a particular bed shear stress, cohesive sediments undergo either erosion or deposition but not both simultaneously. Cohesionless sediments, on the other hand, have only one critical condition that is valid for both erosion and deposition and undergo simultaneous erosion and deposition processes under all bed shear stress conditions.
Earlier research had treated the cohesive sediment as part of the “wash load”, which was defined as the sediment load consisting of grain sizes that are considerably finer than those present in the stream bed [8]. It was further assumed that the wash load is “supply limited” and its transport rate is independent of flow characteristics. However, recent research has shown that the cohesive sediments do interact with stream beds and the transport characteristics of cohesive sediments, including the flocculation mechanism, do depend on flow characteristics [3][4][7][11][12][13][14][15][16][17].
When modelling the transport of cohesive sediments in rivers, the aforementioned differences between the cohesive and cohesionless sediments have to be taken into account rather than simply extending the cohesionless sediment transport models to cohesive sediment as has often been done in the literature. In cohesionless transport models, a mass balance equation is usually solved with the critical shear stress for erosion, as given by the Shield’s diagram and employing any one of the numerous sediment transport formulae that have been derived experimentally for these types of sediments. For cohesive sediments on the other hand, the critical shear stress conditions for erosion and deposition that are universally accepted are not available and the sediment transport rate functions are also not readily available. The flocculation process also needs to be taken into account. Under these circumstances, the modelling of cohesive sediment transport in river systems requires a fresh approach that will address the unique nature of cohesive sediment transport processes such as flocculation and the distinctive erosion and deposition processes that the sediment experiences over a certain range of bed shear stresses prevailing in a river system. An examination of the flocculation process and the erosion deposition processes is undertaken here to highlight the complexities of a cohesive sediment transport model.

2. Flocculation Process

Early studies on the flocculation of cohesive sediments were carried out in estuarial systems where the mixing of freshwater from the river with the salt water in the ocean caused the river sediments to flocculate [3][18]. In these studies, the flocculation process was treated as a two-step process; in step one, called the “collision process”, the particles are made to collide against each other by processes such as Brownian motion, turbulence, velocity gradients, inertia and differential settling, and in step two, called the “cohesion process” the collided particles are bonded together to form an agglomeration of particles called flocs. In estuarine systems, the bonding or the cohesion was provided by the relative strengths of attractive versus repulsive forces between the particles. The attractive forces are due to van der Waal’s forces, which vary inversely as the seventh power of the distance between the particles. The repulsive forces are due to the like charges of the ion clouds surrounding the clay particles [18].
In recent studies on flocculation, cohesive sediments were observed to form flocs even in freshwater systems [19][20][21]. The cohesion mechanism involved in the freshwater flocculation is different from the one found in estuarine systems. In freshwater flocculation, bacteria and other microorganisms were found to play a role in the floc formation [2][21][22]. The microorganisms secrete polymers [23], which provide the bonding among particles. The mechanism of flocculation by polymers can be explained on the basis of the classical interparticle bridging model described in Ruehrwein and Ward [24] and La Mer and Healy [25]. Busch and Stumm [26] reported that the amount of polymers required for optimal flocculation is extremely small, of the order of a mg/L.

3. Distinct Nature of Erosion and Deposition Processes of Cohesive Sediment

A better understanding of the erosion and deposition processes governing the transport of sediment in a river system is important for modelling the sediment fluxes at the sediment–water interface. The settling and the dispersive fluxes at the sediment–water interface is balanced by the net amount of sediment entering the flow domain from the bed. For cohesionless sediments at a given bed shear stress greater than the critical shear stress for erosion, the deposition and erosion of the sediment occur simultaneously, and for a steady state condition, the deposition flux is equal to the erosion flux. For the cohesive sediment, on the other hand, since the deposition and the erosion processes are mutually exclusive, there is only one flux at a time, either a deposition flux or an erosion flux. The existence of two different critical conditions for the cohesive sediment can be explained as follows: when a cohesive sediment floc deposits onto a bed consisting of cohesive sediment flocs, the deposited floc sticks to the flocs that are part of the bed due to cohesion and requires a slightly higher bed shear stress to dislodge the deposited floc from the bed. Therefore, for cohesive sediments, two distinctive critical shear stresses can be identified, one for deposition and the other for erosion: the critical shear stress for erosion is always higher than the critical shear stress for deposition.
The erosion characteristics of cohesive sediment have been studied extensively in the literature [3][6][7][11][12][13][14][27][28][29][30][31]. These studies have shown that the erosion characteristics of cohesive sediment deposits depend on a number of parameters, including the manner in which the sediment deposit is created, the time of consolidation, the rate of application of the bed shear stress and the stabilizing effects of the microorganisms. A comprehensive list of all the governing parameters that control the erosion process of cohesive sediment deposits can be found in Hayter [32].
Because of the numerous controlling parameters involved in both the flocculation process and the erosion and deposition processes of cohesive sediment, it is practically impossible to derive analytical expressions representing the flocculation and the erosion and deposition processes of cohesive sediment transport. Therefore, the approach of a semi-empirical formulation of a mathematical model to represent the transport of cohesive sediment becomes attractive for finding practical solutions to problems pertaining to the transport of cohesive sediment and the associated contaminants. Krishnappan [33][34] developed a cohesive sediment transport model for rivers (RIVFLOC) and employed a semi-empirical approach to determine the parameters of the model by carrying out experiments in a rotating circular flume for site-specific sediment and the river water. Using these parameters, the model can then be applied to the actual rivers to predict the transport of cohesive sediment and the associated contaminants. This modelling approach had been used successfully to a number of river systems [34][35][36][37][38][39]. In this review paper, the RIVFLOC model of Krishnappan [33][34] is described highlighting the model parameters and their determination using a rotating circular flume. The variability of the model parameters of different river systems is also examined. The objective of this review is to provide guidance for modelling cohesive sediment transport and the associated contaminants in a river system.

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