Flocculation cohesive sediments

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Information on flocculation of cohesive sediments is dispersed over several Coastal Wiki articles. The most relevant sections, imported from the articles Dynamics of mud transport, Sediment deposition and erosion processes and Coastal and marine sediments, are brought together here.


Flocculation and settling of cohesive sediments

Fine-grained sediments such as clay and fine silt behave differently from non-cohesive sediments such as sand because of their cohesive properties. In aquatic environments, these fine particles tend to bind to one another and to organic matter, forming aggregates known as flocs. This process, called flocculation, strongly affects mud transport, settling, and deposition in estuaries, tidal flats, harbors, and other low-energy coastal environments.

Cohesive character of mud

A key feature of mud particles is their cohesion, which distinguishes them from coarser, non-cohesive particles. In soils and sediments, this cohesion is mainly associated with clay minerals. Clay particles are very small, typically with median diameters of about 1–2 μm and a size range of roughly 0.1–10 μm. Because of their very large surface area relative to their mass, electrochemical surface charges play an important role in particle interactions.

Clay particles generally have plate-like shapes and an overall negative surface charge. In water, this charge is balanced by a surrounding cloud of counter-ions, forming an electric double layer. Electrochemical attraction, including Van der Waals forces, allows these particles to aggregate when conditions are favorable[1]. This explains why fine sediments in saline and fresh waters can behave differently, since dissolved ions influence inter-particle forces and floc structure.

A practical threshold between cohesive and non-cohesive behavior is often taken as a particle diameter of about 10 μm [2][3]. Below this size, cohesion becomes increasingly important; above it, sediment behavior is more similar to that of cohesionless grains.

Composition of flocs

Flocs are not single mineral grains but composite particles made up of many much smaller mineral particles, often together with organic matter. They usually contain clay minerals such as kaolinite, illite, and montmorillonite, along with fine silt, detritus, and sometimes quartz. Quartz itself is non-cohesive, but it may still be incorporated into aggregates.

Flocs also commonly contain biological material. Extracellular polymeric substances (EPS), mucus, and other organic binders produced by bacteria, microphytobenthos, and other organisms greatly enhance aggregation. In many coastal waters, biologically derived substances are major controls on floc formation and stability[4]. Organic-rich flocs may become especially abundant during seasonal events such as algal blooms.

Part of the mud flocs may derive from fecal pellets, which are low-density aggregates produced by suspension-feeding and deposit-feeding benthic organisms such as oysters, worms, and barnacles. These pellets consist largely of fine sediment particles (typically in the micrometre range) and ingested flocs that are compacted in the gut and excreted as mucus-bound aggregates. In some environments, biodeposition can contribute a substantial fraction of sedimentation.

Microflocs and macroflocs

Fig. 1. Schematic representation of a macrofloc made up of a multitude of microflocs.

Flocs occur over a wide size range. Small flocs of silt size, typically less than about 100 μm, are often called microflocs or aggregates. Larger, more open structures are called macroflocs. A macrofloc can contain a very large number of mineral particles and microflocs[5]. Instead of microflocs, the term aggregates is also used, while the term flocs designates macroflocs[6].

Microflocs are generally denser and more compact than macroflocs, often because they have undergone repeated cycles of aggregation, break-up, deposition, and resuspension. Macroflocs are looser, less dense, and therefore more fragile. Even though macroflocs are larger, their effective density is low because they contain large volumes of water. Their loose structure makes them especially susceptible to break-up under turbulent stress.

The internal structure of flocs has often been described in terms of fractal geometry[7], but natural flocs are not perfectly self-similar. In general, larger flocs have a more open structure, lower strength, and greater porosity. Recent three-dimensional imaging studies indicate that settling behavior depends not only on floc size, but also on composition, porosity, and pore morphology[8].

Processes controlling flocculation

Fig. 2. Schematic representation of mud floc dynamics. Image from © Maggi (2005)[9].

Flocculation is controlled by the balance between processes that bring particles together and processes that pull them apart. The main factors are:

  • electrochemical attraction between particles,
  • collisions caused by Brownian motion, differential settling, and turbulence,
  • the presence of dissolved salts and organic matter,
  • suspended sediment concentration,
  • pH and salinity,
  • biological binding agents such as EPS,
  • turbulent shear.

Brownian motion is important for the smallest particles, causing random collisions. In saline water, the presence of ions compresses the electric double layer, making aggregation easier than in freshwater. This is one reason why flocculation is often enhanced in estuarine mixing zones.

Frequent particle encounters are essential for floc growth. Flocculation is therefore promoted by elevated suspended sediment concentrations and by low to moderate turbulence, which increases collisions without causing excessive break-up[10]. In many tidal systems, flocculation is strongest around slack water, when concentrations remain high but turbulence decreases.

Disaggregation occurs when turbulent stresses become too strong. Large, loosely bound flocs break up first. Thus, floc size and settling velocity often increase with turbulence at low shear, but decrease again when shear becomes too strong.


Settling Velocity

Figure 3: Fall velocity of quartz spheres (specific density [math]s=\rho/\rho_{water}=2.65[/math]) in still water at temperature [math]\theta=20^{o}C[/math]. The fall velocity at other temperatures [math]\theta[/math] can be deduced by multiplying grainsizes [math]d[mm][/math] by [math]1-0.016*(\theta-20)[/math].
Figure 4: The ratio of floc fall velocity and fall velocity of the constituent particles [2].

If the settling rate for very small particles, such as clay minerals, followed the curve for the settling rate of quartz spheres (see Figure 3), it would be so low that they almost never reach the seabed from suspension. The ubiquitous mud beds in coastal waters point to a different settling mechanism. This mechanism consists of flocculation, which incorporates these very small particles in flocs of much larger size and with aerodynamic shape. Macroflocs can typically reach 1-2 mm in diameter, but their effective densities (i.e. the floc bulk density less the water density) are generally less than 50 kg.m-3 [11]. Observations show that flocs settle much faster than the individual constituent particles - a factor of a thousand or more, see Fig. 4. A substance that serves as a powerful binder is so-called EPS, extracellular polymeric substances[12]. These large organic molecules (polysaccharides, proteins, nucleic acids and lipids) are exuded by living organisms and therefore omnipresent in coastal waters. Flocs grow much faster in natural seawater than in salinized distilled water[13]. In addition to EPS, bacterial colonization also plays a role in flocculation[14]. Flocculation is further influenced by factors such as salinity and pH of the water[15]. When flocs grow, they not only capture smaller flocs that settle more slowly, but also other suspended sediments, such as detritus, silt and fine sand. Frequent encounters between sediment particles are important for floc growth. Flocculation is thus enhanced with a high concentration of suspended material and with a certain (low) degree of turbulence (often expressed as the turbulent shear rate [math]G[/math]), dependent on the suspended sediment concentration[16].

The process of flocculation occurs most often in a tidally dominated system during slack water, when the coincidence of elevated concentration and low-to-moderate turbulence allows flocs to grow. The time scale for floc formation depends on concentration squared[17]. At high concentration, flocs form rapidly and settling begins almost immediately, but at low concentration there is a time lag before settling while particles form flocs. Disaggregation is the process of floc destruction and occurs under energetic conditions; marine flocs break up when turbulent stresses are around or above 0.1-0.5 Pa (the general case in estuaries, at least during part of the tidal cycle)[17][11]. Deposition occurs when stress is low enough for flocs to settle from the water column. It is associated with decreases in concentration and overall particle size. As a suspension settles, however, a temporary increase in concentration near the seabed can occur[6].


Settling velocity formulas

Using a special camera, Van Leussen (1994[10]) observed vertical particle motions in the Ems-Dollard estuary during different tidal phases. From these observations he deduced that the settling velocity of these particles critically depended on two variables: the volume concentration [math]\phi[/math] of the particles and the degree of turbulence, characterized by the turbulent velocity shear rate [math]G[/math]. He proposed for the dependence of the settling velocity on these variables the formula

[math]w_s = w_{sh}(G) \Large \Big( \frac{\phi}{\phi_h}\normalsize \Big)^n , \quad w_{sh}(G) = w_{s0} \Large\frac{1+\lambda_a G}{1+ \lambda_b G^2}\normalsize . \qquad (1)[/math]

The velocity shear rate with dimension [math][s^{-1}][/math] is given by [math]G = \sqrt{\Large\frac{\epsilon}{\nu}}\normalsize = \sqrt{\Large\frac{\tau}{\rho \nu}\frac{dU}{dz}}\normalsize . \qquad (2)[/math]

Symbols designate: [math]\epsilon=[/math] energy dissipation rate per unit mass, [math]\tau=[/math] shear stress, [math]\nu=[/math] kinematic viscosity, [math]\rho=[/math] water density, [math]U(z)=[/math] the current velocity as a function of depth [math]z[/math]. The volume fraction at the onset of hindered settling is [math]\phi_h[/math] and [math]w_{sh}(G)[/math] is the maximum settling velocity for this volume fraction. The constants [math]w_{s0}, \; \phi_h,\; n,\; \lambda_a, \; \lambda_b[/math] are supposed to be independent of [math]G[/math] but depend, inter alia, on local sediment characteristics and must be determined experimentally. For Ems-Dollard mud, Van Leussen found [math]\lambda_a \approx 0.3, \, \lambda_b \approx 0.09[/math]. Values of the exponent [math]n[/math] widely varied between 0.6 and 3.

Positive values of the parameters [math]n,\, \lambda_a, \, \lambda_b[/math] imply that the settling velocity increases with increasing volume concentration of the suspended particles and increases as the turbulence increases, as long as the shear rate is small. Above a critical value the settling velocity decreases, because turbulent shear destroys the flocs, the large ones first and the smaller ones as the turbulent shear increases further.

For fixed values of [math]G[/math] (from [math]1[/math] to [math]50[/math] s-1), the settling velocity [math]w_s[/math] characteristically increases with [math]\phi[/math] as collisions between flocs/particles increase with particle concentration. Experimental data of floc settling velocity from the Tamar estuary (UK) are shown in Figs. 5 and 6. These data suggest a value [math]n \approx 1/3[/math]. The value [math]n \approx 0.344[/math] was obtained from data on the settling of flocs of sediment from the San Francisco Bay in laboratory flumes, even though the hydraulic conditions were not entirely comparable with those in the bay[18]. The value [math]1/3[/math] is also supported by data from other estuaries (Winterwerp and van Kesteren[19]. However, a compilation of empirical settling velocity data from the literature reported values of [math]n[/math] between 0.4 and 2.5, with [math]n=0.55[/math] as best fit for the Gironde estuary[20].

Figure 5. Variation of floc settling velocity with volume fraction and shear rate. Lines are from Eq. (1) with [math]n=1/3[/math]. Data are from Manning[21].
Figure 6. Variation of floc settling velocity with shear rate and volume fraction. Curves are calculated from Eq. (1) with [math]\lambda_a=10, \, \lambda_b=0.01[/math]. Data are from Manning[21].
Fig. 7. Settling velocity as function of the velocity shear rate measured in Barataria basin (USA Gulf coast). Redrawn after McDonell et al. (2024[22]).


According to field data from the Tamar estuary (Fig. 6) and Barataria lagoon (USA, Fig. 7), turbulent fluid motions promote floc formation and particle settling up to a value of [math]G \approx 10 \; [s^{-1}][/math]. The settling velocity in the absence of turbulence is very small ([math]w_s \lt 0.1 \; mm/s[/math]), which implies a value of [math] \lambda_b[/math] on the order of 0.01 [s2] and [math]\lambda_a^2 \gt \gt \lambda_b[/math]. The flocculation process is promoted by salt ions, leading to higher settling velocities in seawater compared to fresh water, as shown in Fig. 7.

From field observations in the Tamar and Gironde estuaries, Soulsby et al. (2013[23]) determined empirical formulas for the settling velocity of mud flocs distinguishing between microflocs and macroflocs. Macroflocs are mainly agglomerates of microflocs, but are less stable than the smaller microflocs. Macroflocs have a higher fall velocity than microflocs because of their much greater size. The various factors that determine the fall velocity are captured in the following formulas, for macroflocs [math] w_{M}[/math] and microflocs [math] w_{\mu}[/math], respectively:

[math] w_{M}=\Large\frac{g B_M}{G}\normalsize \left(\Large \frac{c}{ \rho}\normalsize \right)^k \left(\Large \frac{G d_\mu^2}{\nu}\normalsize \right)^{0.33} \exp \left[-\left( \Large \frac{u_{*M}}{\sqrt{\tau / \rho}}\normalsize \right)^{0.463} \right] , \qquad w_{ \mu}= \Large \frac{g B_\mu}{G}\normalsize \left(\Large \frac{Gd^2}{\nu}\normalsize \right)^{0.78} \exp \left[-\left(\Large \frac{u_{\mu}}{\sqrt{\tau / \rho}}\normalsize \right)^{0.66} \right] , \qquad (5)[/math]

where the index [math]M[/math] designates the macroflocs and the index [math]\mu[/math] the microflocs. The turbulent shear rate [math]G[/math] is given by Eq. (2). Other symbols stand for: [math]d[/math] the grainsize of the constituent primary particles and/or flocculi, [math]d_{\mu}[/math] the grainsize of the constituent microflocs, [math]\tau[/math] is the near-bed shear stress and [math]c [/math] the suspension concentration in [math] kg/l [/math]. For the Tamar and Gironde estuaries the following parameter values were established: [math] B_M = 0.13, \; B_{\mu} = 0.6, \; k = 0.22, \; u_{*M} = 0.067 m/s, \; u_{*\mu} = 0.025 m/s, \; d_\mu = 10^{-4} m, \; d = 10^{-5} m [/math]. The settling velocities observed in the Tamar and Gironde are 0.5-1 mm/s for microflocs and about 5 times larger for macroflocs. The formulas (5) are not simply applicable to every estuary; large differences may occur, for example due to differences in sediment type and composition and biotic processes (extracellular polymeric substances – EPS, and transparent exopolymeric particles – TEP) that promote flocculation[24][25]. In situ observations are necessary for parameter tuning.

The ratio of micro- to macro-flocs is not constant in tidal areas. However, the fluctuations are moderated by the antagonistic effects of coagulation and sedimentation. During periods of strong coagulation (slack tide), the largest flocs are removed from the suspension by settling to the bottom, while the opposite occurs during periods of floc breakup by strong currents[26].

Floc deposition

Figure 8. Deposition flux of flocculated sediment from the San Francisco Bay tested in a flume. Modified from Mehta et al. [18]).

When sinking flocs reach the bottom, it is often assumed that settling on the sediment bed will only occur if the bed shear stress [math]\tau_b \approx \rho u_*^2[/math] is smaller than a critical shear stress for deposition [math]\tau_d[/math]. With this assumption, the volume deposition flux can be written, according to Eq. (1),

[math]F_s = w_s \phi \Big( 1 - \Large\frac{\tau_b }{\tau_d}\normalsize \Big) = w_{sh}(G) \phi_h^{-n} \Big( 1 - \Large\frac{\tau_b }{\tau_d}\normalsize \Big) \phi^{n+1} . \qquad (6)[/math]

In shallow estuaries, flocs are conveyed by current over the entire water depth [math]h[/math]. If we therefore assume for simplicity that the floc volume concentration [math]\phi[/math] and the settling velocity [math]w_s[/math] are uniform over the vertical, then the deposition of flocs in terms of time-rate of decrease of [math]\phi[/math] is given by

[math]h \Large \frac{d\phi }{dt} \normalsize = - F_s = - F_h \phi^{n+1} , \quad F_h = w_{sh}(G) \phi_h^{-n} \big( 1-\Large \frac{\tau_{b}} {\tau_{d}} \normalsize \big) , \qquad (7)[/math]

Solving for [math]\phi[/math] yields

[math]\phi (t)=\phi_0 \Big( 1+\Large \frac{n F_h}{h} \normalsize t \Big)^{-\Large\frac{1}{n}} \normalsize , \qquad (8)[/math]

where [math]\phi_0[/math] is the value of [math]\phi[/math] at the start of deposition (e.g. at the beginning of a time-step in a numerical model), which causes [math]\phi(t)[/math] to decrease[18].

In the hypothetical case that [math]w_s[/math] does hardly depend on the floc volume concentration, the value of [math]n[/math] is small. The expression (8) can then be approximated by

[math]\phi (t) \approx \phi _0 \; \exp\Big[-\Large \frac{w_s}{h} \normalsize \left( 1-\Large \frac{\tau_b}{\tau_d} \normalsize \right) \; t \Big], \qquad (9)[/math]

which is known as the Krone equation.

In Fig. 8, the expression (8) and (9) are fitted to experimental data from a deposition test run in a flume ([math]h = 0.3 \;[/math] m, [math]\; \tau_b = 0.032 \;[/math] Pa, [math]\; \tau_d = 0.081 \;[/math] Pa) using sediment from Mare Island Strait in San Francisco Bay. The difference between the two curves is due to the inclusion of aggregation in Eq. (1). It is evident that, in general, floc aggregation cannot be ignored when modeling floc deposition.


Hindered settling

Hindered settling, which begins when [math]\phi[/math] exceeds [math]\phi_h[/math], is manifested as a decrease in the settling velocity with increasing [math]\phi[/math]. The particles are so close together that the rate at which they settle depends on the rate at which interstitial water can escape upward; this rate decreases as [math]\phi[/math] increases (and flow permeability decreases). A lutocline occurs at the depth of water at which hindered settling starts. According to Eq. (1) the maximum velocity achieved at the onset of hindered settling is dependent on the shear rate.

Figure 9. Settling velocity as a function of volume fraction; data from Lake Apopka and curves from Eqs. (1) and (6).

The simplest model for hindered settling is the Richardson and Zaki[27] equation

[math]w_s = w_{sh}(G) \Big[1-k\left( \Large \frac{\phi }{\phi_{h}} \normalsize -1 \right) \Big]^{5} \quad ; \Large \frac{\phi }{\phi_{h}} \normalsize \ge 1, \qquad (10)[/math]

in which [math]k[/math] depends on the sediment. The exponent 5 (rounded from the experimental 4.65) was shown by the investigators to be consistent with the correction to Stokes law derived by considering the forces on a free-falling particle due to neighboring particles in the viscous regime. As [math]w_{sh}(G)[/math] is not always known, it may be taken from Eq. (1) with [math]G=1[/math], the lowest value arising from shear-induced aggregation, i.e.

[math]w_{s1} = w_{sh}(1) \Large\frac{1+\lambda_a}{1+ \lambda_b}\normalsize . \qquad (11)[/math]

In Lake Apopka in central Florida settling velocities of organic-rich mud ([math]\rho_s = 1,873 \;[/math] kg m-3) were measured with LabSFLOC/INSSEV and also in a laboratory settling column. As shear rates in the lake were low, assuming [math]G = 1 \;[/math] s-1, Eqs. (1) and (10) are plotted in Fig. 9 along with the data.


Related articles

Dynamics of mud transport
Sediment deposition and erosion processes
Coastal and marine sediments
Fluid mud
Estuarine turbidity maximum
Coastal and marine sediments


References

  1. ↑ van Olphen, H. 1963. An introduction to clay colloid chemistry. Interscience Publishers (John Wiley & Sons) pp 301
  2. ↑ 2.0 2.1 Migniot, C. 1968. A study of the physical properties of different very fine sediments and their behavior under hydrodynamic action, La Houille Blanche 7: 591-620 (in French, with abstract in English)
  3. ↑ McCave, I.N., Manighetti, B. and Robinson, S.G. 1995. Sortable silt and fine sediment size/composition size slicing: parameters for palaeocurrent speed and palaeoceanography. Paleoceanography 10: 593-610
  4. ↑ Gerbersdorf, S.U., Bittner, R., Lubarsky, H., Manz, W. and Paterson, D.M. 2009. Microbial assemblages as ecosystem engineers of sediment stability, Journal of Soils and Sediments 9: 640-652
  5. ↑ Eisma, D. 1986. Flocculation and de-flocculation of suspended matter in estuaries, Netherlands Journal of Sea Research 20(2/3): 183-199
  6. ↑ 6.0 6.1 Law, B.A., Milligan, T.G., Hill, P.S. and Bugden, G.L. 2021. The effect of concentration on particle settling in the Minas Basin, Nova Scotia. Continental Shelf Research 223, 104448
  7. ↑ Kranenburg, C. 1994. On the fractal structure of cohesive sediment aggregates. Estuarine, Coastal and Shelf Science 39: 451-460
  8. ↑ Lawrence, T.J., Carr, S.J., Manning, A.J., Wheatland, J.A.T., Bushby, A.J. and Spencer, K.L. 2023. Functional behaviour of flocs explained by observed 3D structure and porosity. Front. Earth Sci. 11, 1264953
  9. ↑ Maggi, F. 2005. Flocculation dynamics of cohesive sediment. PhD dissertation, TU Delft
  10. ↑ 10.0 10.1 Van Leussen, W. 1994. Estuarine macroflocs and their role in fine‐grained sediment transport. PhD thesis Utrecht University
  11. ↑ 11.0 11.1 Manning, A. J., Friend, P. L., Prowse, N, and Amos, C. L. 2007. Estuarine mud flocculation properties determined using an annular mini-flume and the LabSFLOC system. Cont. Shelf Res. 27: 1080–1095
  12. ↑ Grabowski, R.C., Droppo, I.G. and Wharton, G. 2011. Erodibility of cohesive sediment: the importance of sediment properties. Earth Science Reviews 105 (3-4): 101-12
  13. ↑ Skinnebach, K.H., Fruergaard, M. and Andersen, T.J. 2019. Biological effects on flocculation of fine-grained suspended sediment in natural seawater. Estuarine, Coastal and Shelf Science 228, 106395
  14. ↑ Linley, E.A.S. and Field, J.G. 1982. The nature and significance of bacterial aggregation in a nearshore upwelling ecosystem. Estuarine, Coastal and Shelf Science 14: 1-11
  15. ↑ Abolfazli, E. and Strom, K. 2023. Salinity impacts on floc size and growth rate with and without natural organic matter. Journal of Geophysical Research: Oceans 128, e2022JC019255
  16. ↑ Mietta, F., Chassagne, C., Manning, A.J. and Winterwerp, J.C. 2009. Influence of shear rate, organic matter content, pH and salinity on mud flocculation. Ocean Dynamics 59: 751–763
  17. ↑ 17.0 17.1 Hill, P.S., Voulgaris, G. and Trowbridge, J.H. 2001. Controls on floc size in a continental shelf bottom boundary layer. J. Geophys. Res. 106: 9543–9549
  18. ↑ 18.0 18.1 18.2 Mehta, A.J., Manning, A.J. and Khare, Y.P. 2014. A note of the Krone deposition equation and significance of floc aggregation, Marine Geology 354: 34-39
  19. ↑ Winterwerp, J.C., van Kesteren, W.G.M. 2004. Introduction to the Physics of Cohesive Sediment in the Marine Environment. Elsevier.
  20. ↑ Defontaine, S., Jalón‐Rojas, I., Sottolichio, A., Gratiot, N., Legout, C. and Lienart, C. 2024. Factors controlling mud floc settling velocity in a highly turbid macrotidal fluvial‐estuarine system. Journal of Geophysical Research: Oceans 129, e2024JC021558
  21. ↑ 21.0 21.1 Manning, A.J. 2001. A study of the effects of turbulence on the properties of flocculated mud. Ph.D. Thesis, University of Plymouth, Plymouth, UK.
  22. ↑ McDonell, M., Strom, K., Nittrouer, J. and Mariotti, G. 2024. Quantifying mud settling velocity as a function of turbulence and salinity in a deltaic estuary. Continental Shelf Research 273, 105180
  23. ↑ Soulsby, R.L., Manning, A.J., Spearman J. and Whitehouse, R.J.S. 2013. Settling velocity and mass settling flux of flocculated estuarine sediments. Marine Geology 339: 1–12
  24. ↑ Maggi, F. 2009. Biological flocculation of suspended particles in nutrient rich aqueous ecosystems. J. Hydrol. 376: 116–125
  25. ↑ Fettweis, M. and Baeye, M. 2015. Seasonal variation in concentration, size, and settling velocity of muddy marine flocs in the benthic boundary layer: Seasonality of SPM Concentration. Journal of Geophysical Research: Oceans 120: 5648–5667
  26. ↑ Li, E. and Wirtz, K. 2025. Aggregation of suspended particles limited by preferential settling. Journal of Geophysical Research: Oceans 130, e2025JC022471
  27. ↑ Richardson, J.F. and Zaki, W.N. 1954. The sedimentation of a suspension of uniform spheres under conditions of viscous flow, Chemical Engineering Science 3: 65-73.


The main author of this article is Job Dronkers
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