Introduction

Flocculated particles (floccule, or flocs), are composed of small mineral particles (so-called primary particles), often clay (<2 μm) or silt (2–63 μm) sized, aggregated to organic matter1,2,3,4,5,6,7. They often consist of clay minerals, but also non-clay minerals and grains larger than clay can be found back in flocs. Flocs are not only abundant in estuarine systems worldwide8,9,10, but prevail in riverine systems as well11,12,13,14. Compared to the primary particles that make up the flocs, flocs have lower densities and are several orders of magnitude larger (in the order of 1 mm) than clay particles. This causes settling rates of flocs to be up to 100 times larger, and to have a higher critical shear stress for entrainment13. Consequently, unlike primary clay-sized particles, flocs can interact with the sediment-covered bed through settling and entrainment, instead of being transported solely as washload13,15. Understanding the fate of clay, in the form of primary or flocculated particles, is crucial to understand the global carbon cycle16, to create resilience of coastal landscapes against sea level rise17, to interpret river-floodplain morphodynamics18,19, to setup sediment budgets20, and to interpret past climates21.

The impact of flocculation on clay and total sediment transport rates in rivers has been shown in previous studies13,22. Additionally, it has been acknowledged that clay (potentially in the form of flocs) can be buried in the bed23. Observed mud deposits in their flume experiments in which they studied the impact of clay on bedforms. They indicate that flow variability (e.g. a very low flow that allows settling of clay) is not needed to produce clay deposits. Furthermore24, conducted flume experiments in which they let the bed aggregate and form bedforms, while continuously supplying sand and mud to their flume. In the mostly sandy deposits, they also found mud. Despite the observed presence of flocs in the experiments, they could not confirm whether flocs drive the deposition of muddy deposits in riverbeds25. Observed clay aggregates moving as bedload, albeit without interaction with an immobile gravel bed. Similarly26, observed deposition of clay flocs under transport conditions capable of moving sand, despite the low settling velocity of flocs. They also showed how clay can be transported as bed load in the form of floccule ripples27. Indeed, deposited flocs can be found in the Cretaceous (~100 Ma) rock record of mudstone (a clay-rich sedimentary rock)21.

Unlike primary particles, flocs can easily deform and break. Deformation alters floc shape, size, and density28,29, while breaking results in the creation of smaller flocs, having the capacity to re-aggregate. In open water, turbulence is the main driver for the aggregation, break-up, and deformation of flocs30. Flocs grow due to increasing collision frequency and thus with higher shear (i.e. flow velocity): mineral clay and organic matter interact to form clay-organic matter aggregates, which are in turn subjected to floc-floc aggregation. Flocs tend to grow larger and less dense under higher organic material contents, both in high salinity31 as in fresh water environments32. However, long exposure to shear, or a further increase in shear rate, can lead to a decrease in floc size over time29, as flocs break apart or deform into denser aggregates33,34. These cycles of breakage, regrowth, and restructuring, caused by local hydrodynamic conditions, shape the flocs6,28. If, in the process of settling, the floc is sufficiently strong to withstand the near-bed shear stresses, it deposits on the bed and attaches itself to the bed by cohesive bonds (either due to its stickiness or due to electrochemical cohesion)35,36. Weaker flocs may break37 and will be re-entrained. Alternatively, individual flocs might not remain intact during the cycles of settling and entrainment, but rapidly reform13.

In sand-bedded rivers, near-bed turbulence is primarily influenced by ripples and dunes. Locally, the shear stress increases over a bedform crest and decreases in a bedform trough38. Local shear stress could alter floc size39 and density, and therefore the settling velocity22. The migration of river bedforms mainly determines the bed material load sediment flux, via erosion from the stoss and deposition in the lee40,41. As it has been shown that flocs can deposit on the bed and migrate in as bed load transport in the form of floc ripples26,27, the question arises if and how flocculated particles interact with the migration of river bedforms. Vice versa, bedform geometry, primarily determined by the size of the bed material and the strength of the flow42,43,44,45,46, can be altered by biological processes47,48, pollutants in the water column such as plastics49, the size distribution of the bed sediment46, and the suspended sediment concentration44,50, yet the impact of flocculated clay on the river bedforms remains unknown. Altogether, the interaction of flocs with bed sediment in a bedform-dominated environment is unclear.

The aim of this study is to enhance our understanding of how flocs are transported, incorporated, and released in bedform-covered systems and to determine whether flocs can influence bedform dynamics. Additionally, we want to explore how flocculation influences the transport of clay particles in bedform-dominated systems. To achieve this, we conducted systematic laboratory experiments in an annular flume, where continuous shear created bedforms in an initially flattened mixed sand-clay bed (2 mass-percentage (m%) of kaolin clay). To simulate riverine environments, fresh water used and an unidirectional flow was imposed. In riverine environments, flocculation is induced by organic material via extracellular polymeric substances (EPS). EPS are natural polymers of high molecular weight secreted by microorganisms, like microalgaes. EPS is composed mainly of (exo)polysaccharides. In our experiments, flocculation was induced with a synthetic flocculant. A synthetic flocculant was chosen rather than a bioflocculant, as the former has been well-studied and is well-characterised29,33,36,51,52. Similar to other studies, polyacrylamide-based polymers were used as a proxy for the polyssacharides produced by microorganisms (EPS)53,54, since they have similar flocculation properties (Figure 9 in ref. 55, Figure 6 in refs. 29,32, Section “Preparatory experiments to define the parameter space”). During the experiments, two shear stress values and six flocculant dosages were imposed, resulting in diverse bedform sizes and different degrees of clay flocculation. Dune and floc characteristics were measured and visual imaging provided insights into floc-sediment bed interactions.

Results and discussion

Response of flocs to turbulent shear

After three hours of experimental run time, we sampled flocs at 10 cm above the mean bed level (about half the water depth), and subsequently measured their sizes using a settling column with a camera setup (Section “Instrumentation”). The measured floc size seemed to be influenced by shear stress. Under lower shear stress (0.35 N m−2), flocs tended to be larger, with an average size of 75 μm (averaged based on floc count), compared to 59 μm in higher shear conditions (0.5 N m−2) (Fig. 1). The variation in floc size was also greater in low shear conditions, with a standard deviation of 55 μm, compared to 37 μm in high shear. This suggests that turbulence plays a role in breaking up flocs into smaller, more compact particles that are less likely to disintegrate, as supported by previous research28. We found that beyond a certain flocculant concentration (0.46 mg g−1), the increase in floc size levelled off. Combining this with the observed reduction in variability at higher shear supports the idea that floc size is constrained by turbulence, rather than the potential to flocculate56.

Fig. 1: Floc characteristics subject to study.
figure 1

a Cumulative size distribution of sand and clay used in the experiments, and flocs from high and low shear experiments combined. b Floc size during the experiments. The central box represents the interquartile range (Q1–Q3), with the black dot indicating the median. Whiskers extend to the smallest and largest data points within 1.5 times the interquartile range from Q1 to Q3. Outliers are not shown. c–f Example pictures of the flocs as taken by the floc camera. Flocculant concentrations are noted in upper right corner.

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The smallest eddies in turbulent flow, defined by the Kolmogorov length scale η57,58, are often seen as the upper limit for floc size. In our study, η was estimated using flow conditions (see Eq. (2) in the Method section)15. At 10 cm above the mean bed level, η was 332 μm for low shear and 291 μm for high shear, which are much larger than the largest measured flocs (183 μm and 129 μm at the 95th percentile, respectively).

However, local shear stress -and thus η- varies depending on the position relative to bedforms. In our experiments, the bedforms averaged between 0.030 and 0.093 m in height and 0.63 to 1.3 m in length, for low and high shear conditions, respectively. As acknowledged in literature, flow velocities were highest above the dune crests, while the conditions were calmer in the dune troughs38,59. The high shear over dune crests seems to set an upper limit for floc size, and η decreases when approaching the bed. For instance, at a depth of roughly 2 mm (equal to a relative depth, i.e. depth divided by total depth at that point, of 0.01) above the dune crest during high shear, η was 86 μm, while it was 103 μm in low shear conditions. Similarly, in the dune troughs (at around 3 mm above the bed, at a relative depth of 0.01), η was estimated to be 97 μm during high shear and 107 μm in low shear. This shows that larger flocs can exist in low-shear areas and in dune troughs before they break apart or deform. Since η generally decreases with decreasing distance from the bed, flocs that interact with the bed experience smaller turbulent whirls closer to the bed than higher in the water column. Lower shear stress might therefore also lead to a more stratified distribution of the flocs in the water column (due to a smaller gradient of η), which would impact the sampled floc sizes.

Overall, the near-bed shear stress seems to act as a good first indicator of floc size. However, the actual flow above bedforms is complex and not uniform (as are the shear stresses flocs encounter in the natural environment29), which means our estimations are based on simplified conditions. In field conditions, the shear stress above dune crests is higher than the depth-averaged stress38, which could explain why average floc sizes are smaller than the values predicted by η. The dynamic nature of shear stress could mean that flocs do not always reach equilibrium within the flow, although the similarity between floc sizes and η suggests they may still be influenced by it. In cases where the dunes have a steep leeside angle, flow separation occurs on the leeside60,61, creating a recirculation zone that can trap flocs. This could lead to flocs breaking apart over dune crests, while allowing them to settle and aggregate in the more sheltered dune troughs.

Clay transport in the presence of flocs

Shortly after the start of the experiments, bedforms began to develop, resulting in the washing out of the clay (i.e. winnowing62) from the active bed (i.e. all sediment that is in motion, or recently has been in motion) due to bedform migration (Fig. 2a, b). This process, referred to by ref. 63 as ’deep cleaning’, has been observed for primary clay particles in sand-clay mixtures with a clay content of less than 8–12.6% in the past, and leads to suspended transport of the clay particles62,63.

Fig. 2: Transport of clay.
figure 2

a Homogeneously mixed primary particles of clay (a-1) are washed out from the active bed into the water column (a-2). The image is slightly adjusted to remove reflections. b Saltating behaviour of an individual floc (b-1–4), which is almost re-entrained into the water column (b-5), but ultimately becomes trapped in the leeside of the dune (b-6). Images taken with a mobile phone with a frame rate of 30 fps. Flocs can easily be detected by their white colour compared to the brown sand. Flow direction from right to left.

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With the presence of a flocculant, suspended clay particles can aggregate and form flocs, even in experiments with very low flocculant concentration. The ~100-times larger size of the flocs increases their settling velocity to about 1 mm s−1 (measured in the settling column), allowing interaction with the sediment bed. In our experiments, the flocs are transported as mixed-load: they are partially transported in suspension, while also saltating over the bed (Fig. 2b). Saltation refers to the bouncing motion of particles, where they are being lifted up and transported, before depositing. Flocs can saltate over the stoss side of the dune without breaking up (Fig. 2b-1–5). Especially larger flocs, which have a higher settling velocity, interact more with the bed. At the crest of the dune, where the shear is the largest, the flocs can break and resuspend (Supplementary Fig. S3), or saltate down the leeside of the dune (Fig. 2b–6). The flocs can be trapped in the leeside, by the recirculating current caused by flow separation.

Clay incorporation in the bed

Dunes migrate by erosion of sediment particles from the stoss side and deposition at the leeside40,41. We observed flocs being trapped in the leeside of the dunes. There, they may attach to the bed through cohesive bonds36, increasing their resistance to erosion. Flocs that have deposited in the recirculation zone of the leeside are subsequently incorporated or buried in the bed by the migration of dunes.

The incorporation of flocs within the dune (Fig. 3) can occur at the scale of an individual floc, a cluster of flocs, or a floc string. An individual floc may stagnate on the leeside of the dune (Fig. 3a–1, a–2), where the recirculating flow and the current balance each other out. Subsequently, denser grains avalanche down the leeside and bury the stagnant floc (Fig. 3a–3). Depending on timing and quantity of sand avalanching, a different amount of flocs accumulated in the lee. Over time, a cluster of flocs may form on the leeside of the dune, which subsequently gets buried. This happens when a turbulent pulse mobilises a large amount of sand grains, causing them to avalanche over the floc deposit (Fig. 3b). With even more time, a string of flocs can cover almost the entire leeside of the dune (Fig. 2c), with new flocs adhering to formerly deposited flocs, creating a multi-layered deposit, offering shelter from erosion. The classical erosion-deposition pattern within a dune exhibits diagonally-oriented string-like structures at an angle similar to the leeside angle of the dune (Fig. 2c). These laminae (i.e. foresets64) have also been observed in the burial of non-deformable objects such as plastics49 and charcoal65.

Fig. 3: Transport of flocs and burial in the sediment bed.
figure 3

Images are taken every 5 s with a GoPro 6 camera, allowing to track settled flocs. Flow direction from left to right. a Burial of an individual floc into a dune (experiment 10). b Burial of a cluster of flocs (experiment 13). c Burial of a string of flocs in the bed (c-1, c-2) and the subsequent re-entrainment into the water column (c-3, c-4) (experiment 13).

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Generally, a higher concentration of flocs resulting from an increased flocculant amount led to more flocs being temporarily buried in the dunes. At higher shear stresses, smaller flocs were observed than at low shear stresses (Section “Response of flocs to turbulent shear”); however, the higher mobility of the dunes resulted in more visible burial of flocs in the dune. Similarly65, suggested that the amount of charcoal deposition is related to bedform migration rates. It is yet unclear how different floc sizes alter the interaction between flocs and the sediment bed, which may be subject to further study.

Altogether, this means that while primary clay particles are washed out from the bed when entrained, they can be incorporated into the bed through the migration of dunes, which bury the trapped flocs in the form of organised multilayered floc-clusters (group deposits).

The influence of flocs on dune geometry

Under continuous shear, the sediment bed developed into bedforms (Supplementary Figs. S4), often featuring dunes with superimposed ripples. The ripples had a relatively constant near-equilibrium height, length and leeside angle at both imposed shear stresses (Δr = 0.016 m, λr = 0.24 m, LSAr = 9.8°). This behaviour was expected, since ripple geometry is related to particle size of the bed material, and is independent of flow velocity43,66,67,68. As expected, near-equilibrium dune geometry shows a clear relation with shear stress42,43,69,70,71,72. Dunes in the higher shear stress regime are three times as high and twice as long (Δr = 0.093 m, λr = 1.3 m) compared to dunes in the lower shear stress regime (Δd = 0.030 m, λd = 0.63 m), although leeside angle remains constant (LSAd = 9.5°). Dune height of all dunes at the end of each experiment was relatively well-predicted with the dune height predictor of ref. 42 (0.083 m), independent of clay and flocculant concentration.

Near-equilibrium bedform geometry is not directly affected by flocculant amount or floc size (Table 1, Supplementary Fig. S5). This opposes the findings in ref. 47. They mixed flocculant (in their case, Xanthan gum as a proxy for EPS) into the sediment bed, which resulted in a significant decrease in dune height. In their experiments, EPS resulted in clay and sand grains sticking together, while in our experiments, the clay only flocculated with itself. This can explain why the dune height in our experiments is only slightly affected. The difference in flocculation behaviour can potentially be explained by the amount of flocculant added. Although the two flocculants are not directly comparable, our flocculant percentage was lower (maximal 0.7 mg/g of clay, i.e. 0.001 m% of all sediment) than their flocculant amount (maximum 0.1 m% of all sediment). Additionally, the difference in mixing method (i.e. mixing the flocculant into the bed or injecting it in the water) might play a role73, however, we found that under our experimental settings, floc characteristics were independent of the mixing method (Section “Preparatory experiments to define the parameter space” and Supplementary Materials S1).

Table 1 The strength of the relation between dune geometry and floc characteristics, expressed in R2
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Despite the lack of clear trends in dune geometry development, we did observe a slight, non-significant, increase in dune height and length with increasing flocculant amount under low shear conditions (R2 = 0.62 and 0.71, respectively). Contrarily, the incorporation of plastic particles (1–10 mm) in dunes as researched by ref. 49 did lead to altering of dune geometry. Pits or scours formed when plastic particles migrated towards the dune crest from the stoss side. Alternatively, they observed “bursts" of a cluster of plastic and sediment, being eroded rapidly from the stoss side, resulting in shorter dunes with steeper stoss sides. The cohesive character of the flocs in our experiments might have prevented this.

In our experiments, a potential lengthening of the dunes with floc size appeared insignificant (p > 0.05; Table 1). Erosion of flocculated particles from the stoss side (Fig. 3a, c) did not create a pit as observed by ref. 49, nor were there observed bursts of flocs. The former could be explained by flocs being generally smaller than the sediment grains, while the plastic particles were larger than the grains. Hence, erosion of an individual floc from the stoss insignificantly impacted the stoss side. The fact that no mass erosion of flocs occurred, contrary to the bursts of plastics, might relate to the organic nature of the flocs. According to ref. 36, upon settling, flocs form cohesive bonds with the bed and with each other, resulting in a higher erosion threshold than expected based on their density, potentially preventing simultaneous entrainment of entire floc strings. Although flocs stick easily to other flocs, the strength of floc-sand cohesion is unknown. Regardless of this, similar to a small percentage of primary clay particles in the bed63, cohesion seems to be insufficient to limit bedform growth as in refs. 45,47,73. Instead, a slight increase in dune length with flocculant concentration is observed for low shear stresses. At higher flocculant concentrations, more flocs are buried in the bed. The effect on dune length can be related to their lower erosion threshold (e.g. critical shear stress) compared to sand particles of the same size due to their lower densities, likely increasing their transport stage (ratio of shear stress and critical shear stress). A higher transport stage generally results in longer dunes42. This effect could be larger for larger, less dense flocs, and vice-versa for smaller, denser flocs, but confirmation of this hypothesis should come from tailored experiments.

Conclusion and implications

The photo in Fig. 4a visualises the key aspects of floc interaction with the bed. Clay in the water column is transported as suspended load, as primary or as flocculated particles (Fig. 4a–I). These flocculated particles settle rapidly if the flow is halted (Fig. 4a–II), which may represent low river flow conditions or slack tide in nature. During active sediment transport, the larger flocs are transported via saltation (Fig. 2b). This leads to clay being captured in dunes in the form of flocs (Fig. 4a–III), either individually, as clusters of flocs, or as floc strings. Flocs that are trapped in the leeside recirculation zone can be buried by grains avalanching down during a turbulent pulse. Continuous erosion and deposition processes of bedforms of various heights can result in the emplacement of floc drapes just below the currently active bed, as a result of previous migration of larger bedforms (Fig. 4a–IV). Below the active bed, the clay particles remain mixed within the sand bed (Fig. 4a–V).

Fig. 4: The possible fate of clay in rivers.
figure 4

a Capturing of flocs in a bedform, in which five regimes are indicated, I: suspension, II: recent deposition, III: drapes within a dune, IV: drapes below the active surface (remnant), V: homogeneously mixed conditions (initial experiment conditions). The image is taken seconds after the flow has halted. In this time a depositions layer of flocs has formed on the dunes. The image is slightly adjusted to reduce reflections. b Schematic of the suspended and bed load transport of clay particles and flocs, and the subsequent trapping in the sediment bed. Velocity profiles (u indicates the flow velocity, dotted line indicates zero m s−1) are schematised based on the measurements in ref. 38.

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The interaction of clay with the bed is summarised in Fig. 4b. Floc deposition is concentrated in areas with low shear and a higher Kolmogorov length scale (dune trough). Floc transport occurs over the dune stoss, where shear stresses are larger and the Kolmogorov length scale is smaller. The variability in shear stress due to the geometrical complexity of the bed allows for the trapping of flocs. Despite their deformability, flocs behave similar to plastic particles49 and charcoal65. At the top of the dune, where shear stresses are greatest, the fate of flocs is determined as flocs are either resuspended or trapped in the lee.

Although other researchers have shown that fine sediment flocs are incorporated into riverine sandy beds (e.g. refs. 23,27 and 24), to the best of our knowledge, this present study is the first to demonstrate the mechanisms through which this process occurs. This incorporation of flocs into the sediment bed has important impacts across a range of disciplines.

Regarding environmental toxicology, the burial of flocs must be considered in contaminant studies. Flocs are key elements of contaminant transport, such as organic pesticides and heavy metals, due to the adsorption of the contaminant to the floc20,74. Our study shows that the residence time of these clay-bound contaminants might be altered, by being easily incorporated in the bed sediment via flocs. These may then be re-entrained during higher discharge events75,76 that feature larger dunes, with a deeper active bed. Additionally, microplastics could be entangled in flocs or could behave as flocculant77,78,79. With the expected rise in plastic waste in the future80, the incorporation of microplastics in the bed via the process of floc burial might become a severe problem.

Sedimentologically, clay in deposits can serve as a proxy for fine sediment supply24 and ancient flow conditions26. As shown by ref. 23, our experiments confirm that clay occurrence in deposits (e.g. mud drapes) does not only indicate past flow conditions which are variable81, such a during slack water in a tidal cycle82 or calm83,84, but also could indicate steady shear. This suggests that conclusions drawn from sediment deposits containing clay may need to be reconsidered26. This is confirmed by ref. 21, who tracked composite particles (flocs) in sedimentary rocks, and acknowledged that mudstones consist of much coarser-grained components (flocs) than suggested by their petrographic composition (clay). The burial of mud in the bed is substantial24, and we now showed that this can relate to flocculation, even in riverine systems that were, until recently, considered to have minimal floc formation.

Regarding sediment transport, floc capturing in the bed needs to be considered for mud transport modelling in various contexts85,86. The smallest aggregate persisting in a particular flow field may easily contain hundreds of clay particles87,88, and the burial of these flocs can alter clay transport rates. The in situ study carried out by ref. 89 showed that fluid mud, consisting of flocs, were deposited during slack water conditions, and were entrained once the flow regained strength. Our study indicates that floc deposition can also occur during higher flow conditions due to the migration of dunes. The expected mud content in recently deposited clay is relevant for the compaction rate and subsequent subsidence, and the stability of river banks90. The significance of the burial of flocs in the bed for clay transport needs to be studied further, with a potential adjustment of numerical clay transport models as a result.

Ecologically, studies of riverine systems must consider the increased burial of clay flocs into the bed. Flocculation of clay removes clay from the water column, which alters the light climate91,92. Additional burial of flocs within the bed could amplify this effect. Furthermore, an increased concentration of clay lenses in the bed could reduce hyporheic exchange, which may be problematic for biota living in the sediment that rely on gas exchange93.

In essence, this study suggests the need for a more critical look on the transport mechanisms of flocs and clay. It is essential to further investigate how flocs become buried in the sediment bed of rivers, and to quantify the effect of floc capturing, both in the lab and in the field.

Methods

Preparatory experiments to define the parameter space

A series of preliminary settling and rotating wheel experiments were carried out in the joint Deltares-TU Delft laboratory in Delft, the Netherlands. With these tests, the materials for the main experiments (i.e. suitable flocculant type and dosage, clay type and concentration) as well as the mixing method for the flocculant were determined. Additionally, the response of the flocs to shear was assessed. The tests are described in Supplementary Materials Text S1 and their results are summarised below.

Natural ”flocculant”, EPS, as found in nature by excretion of microorganisms, is composed mainly of (exo)polysaccharides. It can include other molecules such as DNA, lipids and humic substances, for example, the EPS used by ref. 32 contains 2.64% of proteins for 97.35% of polysaccharides. Despite the fact that the chemical composition and structure of different EPSs are different, all EPSs display the same flocculation properties. The differences in composition and structure results in changes in flocculation kinetics and maximum size of flocs obtained. However, the growth in particle size of flocs follow the same trends: upon addition of flocculant, the aggregation between sediment and flocculant is initiated and flocs grow fast in a few minutes to their maximum size. After reaching their maximum size, the average size of flocs is decreasing slowly over time as flocs reconform under shear. Polyacrylamide (PAM) flocculants as used in this study, are commonly used in wastewater treatment and therefore widely studied33,51,52,94. They are are hydrophilic polyolefins (polyethylenes with amide substituents on alternating carbons) and commonly used as flocculating agents in water treatment plants. The flocculation mechanism of PAM is very similar to the one of EPSs29,32,55.

PAM flocculants are either cationic (positively charged) or anionic (negatively charged). In this study, a cationic flocculant ZETAG - 812595 was selected, which is a copolymer of acrylamide and quaternised cationic monomer, of low cationic charge and high molecular weight. Using a cationic polyelectrolyte, in contrast to the use of an anionic polyelectrolytes, the polymer-clay flocculation is mainly driven by the electric interaction between the positively charged polymer and the negatively charged clay particles, irrespective of salinity. This prevented cumbersome water quality analysis and matching water properties, as tap water was used.

Flocculant dosage impacts floc size and their resistance (strength) to shear29,51. Its optimal dosage for the experiments was determined based on the preparatory tests. The test parameters were based on a lower limit inferred from the detection limit for the floc camera, being 20 μm, and an upper limit determined by the optimum flocculant concentration. An increasing amount of flocculant leads to the formation of flocs containing a large amount of flocculant, which have slower flocculation kinetics than flocs formed at smaller dosages. Well above the optimum flocculant concentration, unflocculated polyelectrolytes remain in suspension29,51. In our experiments, we remain below the optimum concentration to prevent an increase in water viscosity caused by an overdose of flocculant51,96. Kaolin clay with a D50 of 1.3 μm was used as primary mineral clay particles. The clay concentration was decided to be 2 mass-percentage (m%) (relative to the sand; 0.5-volume% relative to the water). This was sufficient to form substantial flocs, without the clay substantially impacting flow dynamics97 or impeding bedform growth (as seen in refs. 50,63,98).

The appropriate shear stress was determined to fall within the dune regime99, while preserving floc integrity100 (Table 2). This was tested in preliminary experiments, where we observed that flocs interacted with the bed by being buried and re-entrained. As anticipated, flocs were smaller when exposed to shear29,34, yet the determined dosages remained accurate. Finally, the mixing method was tested, from which it was found that the final floc characteristics are insensitive to the mixing method.

Table 2 Experiments (number #) and their corresponding test parameters
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Experimental setup

The experiments took place in an annular flume in the hydraulic lab of the Institute of Hydraulic Engineering and Water Resources Management (IWW) at RWTH Aachen University, Germany. The flume, with a diameter of 350 cm, a width of 25 cm, and a height of 100 cm (Fig. 5), was preferred over other types of flumes for its ability to recirculate water without necessitating pumps, which could break or deform the flocs101,102. Water flow was generated through rotation of a lid, while the counter-rotation of the flume limited secondary currents103,104. The ratio between lid and flume rotation was chosen such that the centrifugal forces balance each other105, converting the annular flume into a representation of an infinite straight river.

Fig. 5: Experimental setup.
figure 5

A picture (a), schematised top-view (b) and schematised side view (c) of the annular flume. d Side-view of the settling column setup. Subfigure (b–d) are not to scale for visualisation purposes.

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The flume was filled with a 10 cm layer of mixed sediment, consisting of medium sand with a median grain size (D50) of 350 μm, and 2 m% kaolin clay with a D50 of 1.3 μm. Before each experiment, the sediment bed was levelled, and the flume was filled with 20 cm tap water. The cationic flocculant was dissolved and mixed overnight before each experiment, to ensure a complete solution and a uniform distribution in the flume. Just before the experiment, the flocculant was added to the water in the flume.

Each experiment ran for 4 h, with a total duration of 5.5 h to accommodate bed level measurements (Section “Instrumentation”). The second bed-level survey was taken 45 min after the first, after which the measurement frequency was increased to every 30 min for the last four surveys. Throughout the experiments, the water temperature was 22.6 °C (standard deviation σ = 0.8), with an electrical conductivity of 310 μS m−1 (σ = 22) and a pH of 7.4 (σ = 0.4). After each experiment, the bed was levelled, and the shear stress and flocculant amount were adjusted to match the next experimental setting.

The parameter set tested was determined through the preparatory experiments (Section “Preparatory experiments to define the parameter space”), and is described in Table 2. Six different flocculant amounts were used in the experiments, ranging from 0 to 22 mg L−1 (corresponding to 0.7 mg g−1 clay and 13 mg kg−1 total sediment). Four base experiments were conducted for the two different shear stresses, including two with no clay and no flocculant, and two with only sand and clay, but no flocculant. This enabled us to observe deviations from conditions without flocs present. Two different shear stresses, 0.35 and 0.5 N m−2, were tested, such that all experiments fall within the dune regime99, while preserving floc integrity100. Imposed shear stress was determined based on the ratio between the lid and flume rotation105. For the two lowest flocculant dosages, only the low shear stress conditions were tested, as flocs were very small during these experiments, and would not have been visible under higher shear conditions.

Instrumentation

An acoustic depth profiler, the StreamPro Acoustic Doppler Current Profiler (hereafter StreamPro), manufactured by Teledyne, was used to measure bed elevation, from which bedform geometry was derived (Section “Data analysis”). This acoustic device is capable of penetrating turbid water. The StreamPro was attached to the moving lid of the flume, positioned 7 cm from the outer edge. By rotating the flume, four profiles corresponding to the four beams of the StreamPro could be measured, with a frequency of 1 Hz. To ensure a millimetre resolution, the rotational speed of the flume bottom was temporarily reduced to 0.11 rotations per minute for the measurements, after which the rotational speed was increased again to the experimental shear stress. Any temporarily deposited flocs were directly re-suspended by the accelerating flow.

A 10 × 10 × 100 cm settling column was used to determine floc characteristics (Fig. 5d), following a setup similar to refs. 106 and 54. After three hours of experimental run time, flocs were collected from 10 cm below the water surface and at the top of the sediment bed. A 25 mL pipette was used to carefully extract flocs from the flume, and by subsequently touching the water surface of the settling column the flocs could flow into the settling column with minor disturbance. The characteristics of the captured flocs were recorded using a UI-3160CP Rev. 2.1 floc camera from IDS with a TC23024 lens from Opto Engineering. A green light (LTCLHP024-G from Opto Engineering) was used to illuminate the flocs in the settling column. The floc camera was controlled using the uEye cockpit software developed by IDS, configured to produce monochrome images for improved contrast to visualise the flocs.

A GoPro 6 was positioned in the middle of the flume, facing outward, to record bed evolution during the experiment at a fixed location, covering ~45 cm in width, and the whole water depth. Pictures were taken every 5 s.

Data analysis

For the analysis of the flocs, the images from the floc camera were processed using the SAFAS software (Sedimentation and Floc Analysis Software)107. Subsequently, the settling speed of the flocs, and the major and minor axis diameters of the flocs were determined. Throughout the experimental runs, there is a balance between breakage and aggregation of flocs, leading to the attainment of equilibrium in floc size28. The floc diameter Df was then computed as106:

$${D}_{f}=\sqrt{{D}_{major}* {D}_{minor}}$$
(1)

The Kolmogorov length scale, η (m), is known to correlate with the size of the flocs and can be approximated with15:

$$\eta ={\left(\frac{\kappa z{\nu }^{3}}{{u}^{* 3}(1-\frac{z}{h})}\right)}^{\frac{1}{4}}$$
(2)

in which κ is the Von Karman constant, ν the kinematic viscosity of water (m2 s−1), u* the shear velocity (m s−1), z the height above the bed (m) and h the water level (m).

The shear velocity u* was calculated by using the bed shear stress τ (N m−2) and the density of the water ρw (kg m−3), via:

$${u}^{* }=\sqrt{\frac{\tau }{{\rho }_{w}}}$$
(3)

For the analysis of the bed level, the StreamPro data was processed using ADCPTOOLS108, and bed elevation profiles from each of the four beams were determined. These profiles served as input for the bedform tracking tool from109, which gives bedform geometry based on specific span values used to differentiate between different bedform scales. Two bedform lengths were identified: 0.2 m ± 0.1 m (hereafter referred to as ripples) and 2.2 m ± 0.8 m (referred to as dunes). In almost all experiments, ripples were superimposed on dunes.

Bedform characteristics were averaged over the four beams. The characteristics include: (1) bedform height Δ (m), the vertical distance between top and downstream trough, (2) bedform length, λ (m), the horizontal distance between two subsequent crests, (3) leeside angle, LSA (°), the slope from a linear fit of the bedform’s leeside, excluding the upper and lower 1/6 of the bedform height and (4) the stoss side angle and SSA (°), calculated similarly to the leeside angle.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.