Floc morphology and size distributions of cohesive sediment in steady-state flow

Water Research 37 (2003) 2739–2747

Floc morphology and size distributions of cohesive sediment in steady-state flow M. Stonea,*, B.G. Krishnappanb b

a School of Planning, Department of Geography, University of Waterloo, Waterloo, Ont., Canada N2L 3C5 Aquatic Ecosystem Impacts Research Branch, National Water Research Institute, Burlington, Ont., Canada L7R 4A6

Received 14 August 2002; received in revised form 27 January 2003; accepted 29 January 2003

Abstract Fractal dimensions of particle populations of cohesive sediment were examined during deposition experiments in an annular flume at four conditions of steady-state flow (0.058, 0.123, 0.212 and 0.323 Pa). Light microscopy and an image analysis system were used to determine area, longest axis and perimeter of suspended solids. Four fractal dimensions (D; D1 ; D2 ; Dk ) were calculated from the slopes of regression lines of the relevant variables on double log plots. The fractal dimension D; which relates the projected area (A) to the perimeter (P) of the particle (PpAD=2 ), increased from 1.2570.005 at a shear stress of 0.058 Pa to a maximum of 1.3670.003 at 0.121 Pa then decreased to 1.3470.001 at 0.323 Pa. The change in D indicated that particle boundaries became more convoluted and the shape of larger particles was more irregular at higher levels of shear stress. At the highest shear stress, the observed decrease in D resulted from floc breakage due to increased particle collisions. The fractal dimension D1 ; which relates the longest axis (l) to the perimeter of the particle (Ppl D1 ), increased from 1.0070.006 at a shear stress of 0.058 Pa to a maximum of 1.2570.003 at 0.325 Pa. The fractal dimension D2 ; which relates the longest axis with the projected area of the particle (Apl D2 ), increased from 1.3570.014 at a shear stress of 0.058 Pa to a maximum of 1.8170.005 at 0.323 Pa. The observed increases in D1 and D2 indicate that particles became more elongated with increasing shear stress. Values of the fractal dimension Dk ; resulting from the Korcak’s empirical law for particle population, decreased from 3.6870.002 at a shear stress of 0.058 Pa to 1.3370.001 at 0.323 Pa and indicate that the particle size distribution changed from a population of similar sized particles at low shear to larger flocculated particles at higher levels of shear. The results show that small particle clusters (micro-flocs) are the formational units of larger flocs in the water column and the stability of larger flocs is a function of the shear stress at steady state. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Flocculation; Particle size distribution; Fractal dimension; Steady-state flow

1. Introduction Flocculation is an important mechanism for the removal of particles from the water column in streams, lakes and oceans. The process of flocculation alters the hydrodynamic characteristics of solids by changing the density, porosity, settling velocity and surface area of *Corresponding author. Tel.: +1-519-888-4567 ext. 3067; fax: +1-519-725-2827. E-mail address: [email protected] (M. Stone).

flocs [1]. Flocs have relatively low densities, large pore spaces and reactive surfaces that remove contaminants from the water column [2]. Because flocculation influences the transport behavior of suspended particles in aquatic systems [3,4], knowledge of how cohesive sediments settle and deposit is necessary to model the pathways and fate of sediment-associated contaminants [5]. During flocculation, several phases of floc growth occur. A multi-stage growth model of floc formation was proposed where micro-flocs are the building units of

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larger flocs [6]. In this model, micro-flocs form at the initial stage of flocculation and combine to form larger flocs through random collisions due to fluid shear. Flocs formed under these conditions have large, porous and open structures that are more susceptible to breakup by fluid shear [7]. A study of the effect of shear on coagulation of polystyrene particles in a baffled stir tank showed that aggregates reach an equilibrium or steadystate structure and floc size distribution [8]. They argued that floc breakage was the main process responsible for maintaining a stable particle size distribution thus preventing further aggregate growth. Consequently, floc morphology at steady state is a function of process conditions, which influence solids removal efficiency during settling by controlling floc size, porosity and density [6,9]. Fractal dimensions have been used to quantify the morphology of particle populations formed in different fluid mechanical [9,10], stream [11,12] and marine environments [13–15]. Fractal dimensions reflect the morphology of particles and their mechanism of formation [16], and particle properties such as settling velocity and density are a function of their fractal dimensions [10]. While several studies have been conducted in fluid mechanical devices (i.e. horizontal Couette-type flocculators and baffled stir tanks) to quantify floc morphology using fractal dimensions, flow conditions in these devices are not typically found in rivers [9,10]. The objective of our study is to examine floc morphology and the size distribution of particle populations of cohesive river sediment as a function of shear stress in a rotating circular flume where flow conditions in the vicinity of the bed more closely approximate that in natural rivers. Image analysis is used to evaluate the morphology and size distribution of flocs formed during the deposition process at four conditions of steady-state flow.

2. Methods 2.1. Theoretical background The application of fractals and fractal dimensions [17] to the analysis of the geometrical properties of aggregates has been described in detail [9,10]. Relevant aspects of the fractal approach to this paper are reviewed in the following. Fractal dimensions relate aggregate size to some property in n-dimensions, where n ¼ 1; 2; 3; and Dn is the fractal dimension in the nth dimension. Collections of similar, natural objects have been found to have area–perimeter relationships described by a power function PpAD=2 ;

ð1Þ

where P is the perimeter, A is the projected area and D is the fractal dimension of the objects. For Euclidean objects, D ¼ 1 but values of D > 1 have been found for individual flocs (1:20oDo1:36) and floc populations (1:21oDo1:37) in streams [12]. Consequently, as the object area becomes larger, the perimeter increases more rapidly than for Euclidean objects indicating that the boundary of the objects is becoming more convoluted. A one-dimensional fractal dimension can be calculated for all objects in a particle distribution as Ppl D1 ;

ð2Þ

where P is the perimeter and l is the maximum particle length. Values of D1 > 1 indicates that with increasing object size, the perimeter increases faster than the object length scale so that the object becomes more complex for larger objects. The fractal dimension of aggregates in two dimensions is Apl D2 :

ð3Þ

Values of D2 o2 indicate that as the object size increases, the projected area increases slower than the square of the length scale. In this case, the projected area of larger objects is less than Euclidean objects of the same scale due to elongation of the larger objects or because the larger objects surround or partially surround regions, which are not part of the object. Distributions of particle populations can also be described using Korcak’s empirical law Nrða > AÞpADk =2 ;

ð4Þ

where Nr (a > A) is the rank or the number of objects with an area greater than a certain A and Dk is the fractal dimension that describes the total object area over small and large objects [17]. The fractal dimension Dk was calculated as minus two times the slope of the regression line between projected area and particle rank (Eq. (4)). Small values of Dk indicate that most of the total object area is concentrated into a smaller number of large objects, whereas large values indicate a more equal size distribution over the entire size range of the particles. 2.2. Description of rotating flume Deposition experiments were conducted in a rotating circular flume 5.0 m in diameter located at the National Water Research Institute (NWRI) in Burlington, Ont., Canada. Complete details of the flume and its flow characteristics are found in [18]. The flume is equipped with a laser doppler anemometer (LDA) that measures the flow field, which has been used to verify a threedimensional numerical model of turbulent flows in rotating flume assemblies [19]. The relationship between the bed shear stress and the rotational speeds of the flume was obtained as part of the flume calibration [20].

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suggests that these fine-grained aggregates are of fluvial origin (Fig. 2).

A Malvern particle size analyzer mounted on the flume measured the in situ size distributions of suspended solids. Sediment–water mixtures were drawn from a sampling port on the side of the flume and suspended sediment concentrations were determined by the filtration method [21].

2.4. Experimental procedure The sediment/water mixture was passed through a 70 mm mesh screen and added to the flume. Full mixing of the sediment was achieved by rotating the flume and the lid at high speeds, which corresponds to a bed shear stress of 0.6 Pa. After 20 min, the flume speed was lowered to a constant bed shear stress and maintained for a period of about 5 h. Deposition tests were carried out for four bed shear stress conditions (0.058, 0.121, 0.212, 0.352 Pa). Sediment concentration was measured every 5 min and the in situ size distribution determined every 2 min with the Malvern particle size analyzer.

2.3. Study site and sediment collection Cohesive sediment for the flume experiments was collected from the Hay River, Northwest Territories, Canada approximately 100 m above the Water Survey of Canada hydrometric gauge (WSC 09OB001; Hay River at Hay River; Lat 60 440 4200 N; Long 115 510 2600 W). The Hay River drains an area of 48,100 km2 in the northwest portion of the Great Central Plains of Canada and flows into Great Slave Lake near the town of Hay River in the Northwest Territories. A large volume (800 l) of water/sediment was collected for the flume experiments using a newly designed and constructed fine-sediment sampler. The sampler consisted of an inverted cone fitted with a propeller to dislodge deposited fine sediment from the riverbed. The sediment/water mixture was delivered to sample containers with a submerged pump fitted to the sampler. The sediment/water mixture was kept in cold storage and transported to NWRI in 1 week for use in the flume experiments. The primary (dispersed) grain size distribution of the Hay River sediment shown in Fig. 1 indicates this sediment is predominantly fine-grained (o140 mm). The presence of diatoms incorporated in the sediment

2.5. Image analysis The water–sediment mixture was collected from the sampling port of the flume at steady state (300 min). A triplicate 5 ml aliquot was transferred by pipette into 50 ml plastic tubes containing pre-filtered Hay River water and passed through 0.45 mm Millipore HA filters at low vacuum. Digital images of particles deposited on the filters were collected by a previously used method [22]. In this procedure, filters are rendered (semi) transparent by applying droplets of Stephens Scientific  C low-viscosity immersion oil (n23 ¼ 1:5150) to distinD guish particles from the background (i.e. the filter).

3

2.5

1.5

1

0.5

Fig. 1. Primary size distribution of Hay River sediment.

9

4 1.

18

9

6.

15

4

5.

13

3

7.

11

.6

.8

.6

1.

10

87

75

.7

Geometric Mean of Size Classes (microns)

65

56

.4

.0 49

.7

.7

42

36

31

.7

.5

.7

.3

.2

.4 27

23

20

17

15

13

9

.5 11

5

6

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1

4.

8.

6

4.

4

1

3.

4

7

3.

7.

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2.

6.

0

2.

0 2.

Percent by Volume

2

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resuspend particles nor affect particle morphology. During image analysis, background subtraction was applied to minimize the impact of non-uniform light levels. All fractal dimensions were calculated from the slopes of regression lines of the relevant variables on log–log plots for a minimum of 4500 particles per sample.

Particles are sized by image analysis to a lower resolution of 2 mm (20  objective) using a Zeiss Axiovert 100 microscope fitted with a Sony XC75 CCD camera connected to a Pentium computer running the Northern Exposuret image analysis software. Observation of particle morphology during and after oil immersion indicated that immersion oil did not

3. Results and discussion 3.1. Sediment concentrations and size distributions Sediment concentrations in the flume decreased gradually and tended to reach a steady-state value as a function of shear stress (Fig. 3). The deposition experiments provide a quantitative estimate of the amount of sediment that will deposit for a given shear stress. The critical shear stress for deposition is defined as the bed shear stress at which all of the initially suspended sediment will be deposited. A critical shear stress of 0.0570.005 Pa was determined for the Hay River sediment by extrapolating the measured values. Changes in the median particle size (D50 ) as a function of shear stress indicate that flocculation was occurring in the flume (Fig. 4). At the lowest steady-state shear stress (0.058 Pa), the D50 decreased as larger particles settled from the water column and only the finer particles remained in suspension. Representative images of cohesive sediment at steady state (t ¼ 300 min) show

Fig. 2. Scanning electron micrograph of Hay River sediment.

360 0.058 Pa 320 0.121 Pa 0.212 Pa

240

0.323 Pa

200

160

120

80

40

Fig. 3. Sediment concentration as a function of time and shear stress.

0

0

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0

Time (minutes)

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Sediment Concentration (mg/L)

280

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200 180 160

D50 (microns)

140 120 100

0.058 Pa

80

0.123 Pa 60

0.212 Pa 0.323 Pa

40 20 0 0

40

80

120

160

200

240

280

320

Time (minutes)

Fig. 4. D50 as a function of time and shear stress.

0.058 Pa

0.121 Pa

Microflocs

0.212 Pa

0.323 Pa

Fig. 5. Photomicrographs of flocs at steady state (t ¼ 300 min).

that individual particles and small particle clusters (micro-flocs) are present in the water column for the lowest shear stress (Fig. 5). As the shear stress increased,

the D50 of particles in suspension increased due to the formation of larger flocs. Flocs formed under these conditions have large porous structures that are

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susceptible to breakup by fluid shear. The largest flocs were produced at a shear stress of 0.212 Pa but a lower D50 observed at the highest shear stress (0.323 Pa) indicates that floc breakage was occurring (Fig. 4). The data show that turbulence has a dual role in the flocculation process, where flocs are formed at lower shear stresses but tend to break up at higher levels of turbulence and suggests there is an optimum shear stress for the formation and stability of flocs. The presence of larger flocs in suspension is due to the fact that effective floc densities decrease as a function of floc size but after a certain size, floc-settling velocity decreases with the floc size due to the inverse relationship between floc size and effective density [23]. A multi-stage growth model of floc formation was proposed where micro-flocs are formed at the initial stage of flocculation through random collisions in turbulent flow and that micro-flocs combine to form larger flocs [6]. In a study on the effect of shear on coagulation [8], it was reported that particles reach an equilibrium or steady-state structure and floc size distribution. They argued that the balance of the opposing phenomena of flocculation and breakup determines the floc size and mass distribution that maintains a stable particle size distribution thus preventing further floc growth. Images of floc morphology at steady state (Fig. 5) support the floc formation model [6] and clearly show that small particle clusters (micro-flocs) combine due to collisions in the flume to form larger flocs at higher shear stress.

3.2. Floc morphology at steady state The morphology of the particle populations changed as a function of shear stress in the flume. At steady state (t ¼ 300 min), the fractal dimension D increased from 1.2570.005 at a shear stress of 0.058 Pa to a maximum of 1.3670.002 at 0.121 Pa then decreased slightly to 1.3470.01 at 0.323 Pa (Fig. 6). D increased as the shear stress increased from 0.058 to 0.121 Pa. Consequently, the area of particle populations increased but the perimeter increased more rapidly than for Euclidean objects indicating that particle boundaries became more irregular with increasing shear. However, there was a decrease in D at the highest shear stress resulting from floc breakage due to the increased number of particle collisions. The change in D represents a change in the particle shape as a function of shear stress and is interpreted as an increase in shape irregularity of larger particles compared to smaller particles. Similar D values have been reported for suspended solids in Saskatchewan (1:25oDo1:42) [11] and Ontario streams (1:24oDo1:35) [22]. In the Saskatchewan streams, changes in D were attributed to the effect of algal blooms on suspended solids [11], whereas variable sediment sources explained differences in the fractal dimensions of suspended solids in Ontario streams [22]. Values of D1 and D2 were calculated as the slopes of the regression line for length and perimeter (Eq. (2)) and for length and area (Eq. (3)) that changed as a function of shear stress (Figs. 7 and 8). D1 increased from

1.38

1.36

1.34

D

1.32

1.3

1.28

1.26

1.24

1.22 0

0.05

0.1

0.15

0.2

0.25

Shear Stress (Pa)

Fig. 6. D at steady state (n ¼ 3; 7one standard deviation).

0.3

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1.26

1.2

D1

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1.02

0.96

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Shear Stress (Pa)

Fig. 7. D1 at steady state (n ¼ 3; 7one standard deviation).

2

1.9

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D2

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1.2 0

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Shear Stress (Pa)

Fig. 8. D2 at steady state (n ¼ 3; 7one standard deviation).

1.0070.006 at a shear stress of 0.058 Pa to a maximum of 1.2570.003 at 0.325 Pa. D2 increased from 1.3570.004 at a shear stress of 0.058 Pa to a maximum of 1.8170.005 at 0.325 Pa. Values of D1 > 1 show that with increasing particle size, the perimeter increases

faster than the particle length and indicates that the particle outline is more complex for larger particles. Values of D2 o2 indicate that as particle size increases, the particle area increases slower than the square of the length scale. The observed changes in D1 and D2 for

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different steady-state conditions show a change in particle morphology towards more elongated particles with increasing shear stress. Similar ranges of D2 values have been reported in the literature [11,24,25]. Under different fluid mechanical conditions, carboxylate micro-spheres had fractal dimensions of D1 ¼ 1:1970:01 and D2 ¼ 1:8970:02 in a paddle mixer and D1 ¼ 1:1470:01 and D2 ¼ 1:6870:02 in a rolling cylinder [10]. Densely packed aggregates have higher fractal dimensions, while branched and loosely bound structures have lower fractal dimensions. Flocs become elongated as they grow causing the collision frequency to increase and floc strength to decrease [26]. Consequently, the trajectories of larger flocs become increasingly rectilinear and the dominant aggregation mechanism is differential sedimentation [27]. The lower limit of D2 for aggregates dominated by this mechanism is 1.60 [9]. In the present study, measurements of D2 suggest that differential sedimentation is a mechanism for settling of larger particles in the annular flume under conditions of low turbulence but with increasing turbulence shear coagulation becomes more important in the development of floc structure and size distribution. The results of the present study are comparable to the range of modeled cluster–cluster aggregation structures that have fractal dimensions of 1:42oD2 o1:61 [28]. Values of Dk decreased from 3.6870.002 at a shear stress of 0.058 Pa to 1.3370.001 at 0.325 Pa (Fig. 9). Small values of Dk indicate that most of the total particle area is concentrated into a small number of

larger particles, whereas larger values of Dk indicate a more equal size distribution over the entire size range of the particles. With increasing shear stress, the particle size distribution changes from a population of similar sized particles at low shear to larger flocculated particles as shown in particle images (Fig. 5). These images show that small particle clusters (micro-flocs) are the building blocks of larger flocs suspended in the water column and the stability of larger flocs is a function of the shear stress at steady state.

4. Conclusions Image analysis is a useful technique to characterize the morphology of particle populations of cohesive sediment during deposition experiments in an annular flume. Measurement of parameters such as area, longest axis, and perimeter permitted the calculation of four fractal dimensions that were used to study floc behavior in turbulent flow. Changes in particle morphology as a function of shear stress were related to flocculation due to shear coagulation in the flume. Image analysis showed that small particle clusters (micro-flocs) are the building blocks of larger flocs that form in the flume with increasing shear stress. The stability of larger flocs is a function of shear stress that influences both floc formation and breakup. The results of the present study are comparable to the range of modeled cluster–cluster aggregation structures reported in the literature.

4

3.5

Dk

3

2.5

2

1.5

1 0

0.05

0.1

0.15

0.2

0.25

Shear Stress (Pa)

Fig. 9. Dk at steady state (n ¼ 3; 7one standard deviation).

0.3

0.35

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Acknowledgements The authors thank Robert Stephens of the Aquatic Ecosystem Impacts Research Branch of the National Water Research Institute for sample collection and conducting the flume experiments. The technical assistance of Ryan Stainton and Joel Greenwood is greatly appreciated.

[12]

[13]

[14]

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