transport of biofilm-coated sediment particles · hydro-science and engineering, tsinghua...

Journal of Hydraulic Research Vol. 54, No. 6 (2016), pp. 631–645http://dx.doi.org/10.1080/00221686.2016.1212938© 2016 International Association for Hydro-Environment Engineering and Research

Research paper

Transport of biofilm-coated sediment particlesHONGWEI FANG (IAHR Member), Professor, Department of Hydraulic Engineering, State Key Laboratory of Hydro-science andEngineering, Tsinghua University, Beijing 100084, People’s Republic of ChinaEmail: [email protected] (author for correspondence)

MEHDI FAZELI, Doctoral Research Fellow, Lecturer, Department of Hydraulic Engineering, State Key Laboratory ofHydro-science and Engineering, Tsinghua University, Beijing 100084, People’s Republic of China; Department of Civil Engineering,Yasouj University, Yasouj, Islamic Republic of IranEmail: [email protected]

WEI CHENG, Doctoral Research Fellow, Department of Hydraulic Engineering, State Key Laboratory of Hydro-science andEngineering, Tsinghua University, Beijing 100084, People’s Republic of ChinaEmail: [email protected]

SUBHASISH DEY (IAHR Member), Professor, Distinguished Visiting Professor, Department of Civil Engineering, Indian Instituteof Technology, Kharagpur 721302, West Bengal, India; Department of Hydraulic Engineering, State Key Laboratory ofHydro-science and Engineering, Tsinghua University, Beijing 100084, People’s Republic of ChinaEmail: [email protected]

ABSTRACTIn this study, an analytical model for the transport of biofilm-coated sediment (bio-sediment) particles is developed. Experiments were conducted cul-tivating biofilm-coat around fine sediment particles (silt type) in an experimental flume for a specific period of time. The particle tracking velocimetrymethod was used to detect the saltation trajectory, the size of bio-flocs, and the flow velocity. A concentration meter was used to measure the concen-trations of near-bed and suspended sediment transport. It was observed that the ratio of saltation length to saltation height for bio-flocs is greater thanthat for uncontaminated (without a biofilm-coat) sediment particles. The experimental data were used to calibrate the analytical model. A relationshipfor the bed-load transport rate of bio-sediments as a function of transport stage and particle parameters is proposed. Also, a formula for the referenceconcentration is given. Then, a computational scheme of bio-sediment transport (both bed-load and suspended-load transport) is furnished.

Keywords: Biofilm; bio-sediment; biostabilization; hydraulics; saltation; sediment transport

1 Introduction

Mechanics of sediment transport is important to describe flu-vial processes and sedimentation. Significant advancement hasso far been made to understand the underlying mechanism ofsediment transport through experimental and theoretical stud-ies, especially for the transport of noncohesive sediments (e.g.Dey, 2014). Sediment particles are transported due to the hydro-dynamic forces induced by the flow in addition to the effectsof turbulent events. There are two modes of noncohesive sedi-ment transport: bed-load and suspended-load transport. In recentyears research has increased into the transport of biogenic

sediments, i.e. the biofilm-coated sediments (henceforth bio-sediments) formed by microbes such as bacteria, microalgaeand fungi (Andersen, 2001; Andersen, Lund-Hansen, Pejrup,Jensen, & Mouritsen, 2005; Decho, 1990; Fang, Shang, Chen, &He, 2014; Gerbersdorf, Jancke, Westrich, & Paterson, 2008;Huang, Fang, & Chen, 2012; Righetti & Lucarelli, 2007, 2010;Stal, 2003).

Natural cohesive sediments are capable of absorbing organicsubstances (or pollutants) due to the formation of a matrixof extracellular polymeric substance (Chen, Fang, & Huang,2013; Fang, Chen, Chen, Zhao, & He, 2013). Existence of anincreased amount of nutrients in Chinese rivers and reservoirs

Received 31 January 2015; accepted 11 July 2016/Open for discussion until 30 June 2017.

ISSN 0022-1686 print/ISSN 1814-2079 onlinehttp://www.tandfonline.com

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632 H. Fang et al. Journal of Hydraulic Research Vol. 54, No. 6 (2016)

(for example, Three Gorges Reservoir in China) was reported(Cong et al., 2014; Sahu, Bhangare, Tiwari, Ajmal, & Pandi,2014). The presence of nutrients provides a favourable conditionfor biofilms to grow. Biofilms have a skeleton of extracellularpolymeric substances (EPS), which can fill the pores betweensediment particles (Flemming & Wingender, 2010). Transportof biofilm sediments starts just after demolition of the sur-face biofilm. The depth of a biofilm depends on a numberof parameters including the amount of nutrients, hydrodynam-ics, light intensity, temperature, sediment type and size (Hult-berg, Asp, Marttila, Bergstrand, & Gustafsson, 2014; Stone,Emelko, Droppo, & Silins, 2011; Thom, Schmidt, Gerbersdorf,& Wieprecht, 2015; Villanueva, Font, Schwartz, & Romani,2011). Biofilm potentially has a bonding effect on sedimentparticles, the effects of which can be described as an additiveadhesive working as a stabilizing force (Lick, Jin, & Gailani,2004; Righetti & Lucarelli, 2007). Focusing on flocs, Righettiand Lucarelli (2007) framed the contribution of adhesion tothe incipient motion of particles through a modification of theShields theory as a function of both biofilm adhesive propertiesand floc density. The theory was then validated by experimen-tal data of different kinds of bio-sediments (Fang et al., 2014;Righetti & Lucarelli, 2007, 2010). Another important observa-tion is that the bio-sediments transport as flocs, which have alarger size, but a lower mass density and terminal fall veloc-ity as compared to the pure (without biofilm) sediment particles(Amos, Droppo, Gomez, & Murphy, 2003; Banasiak, Verho-even, de Sutter, & Tait, 2005; Droppo et al., 2015; Righetti &Lucarelli, 2007, 2010; Shang, Fang, Zhao, He, & Cui, 2014).Some studies reported the characteristics and biostabilization ofcohesive sediments (Droppo, 2009; Fang et al., 2014; Gerbers-dorf, Jancke, & Westrich, 2005; Khan & Wu, 2013; Righetti &Lucarelli, 2007; Shang et al., 2014; Stone et al., 2011). How-ever, to the authors’ knowledge the transport of bio-sedimentshas not yet received adequate attention. For noncohesive sedi-ment particles, van Rijn (1984a) gave a simple expression forthe bed-load concentration as a function of flow and sedimentcharacteristics. Later, van Rijn (2007) obtained a new relation-ship to describe sediment transport for a wide range of sedimentsizes (from fine silt to coarse sand). Although he considered aspecific factor in his later study to account for the effects of thebiological and organic substances, he did not verify the effectsof them due to the lack of experimental data. Therefore, little isknown about the transport process of bio-sediments due to thecomplexity of bio-sediment characteristics.

The aim of the present study is therefore to determine thetransport rate for bio-sediment flocculated particles (henceforthbio-flocs) through a theoretical analysis aided by experimen-tal results. The experimental results are used to calibrate thetheoretical model, enabling us to determine the bed-load andsuspended-load transport for bio-sediments. In the experimen-tal programme, a series of flume experiments were conductedcultivating biofilm around fine sediment particles (silt type) for aspecific period of time. In the theoretical approach, the equations

of motion for a saltating bio-floc are solved, following vanRijn’s (1984a) method modified for bio-sediments. Then, a bed-load transport rate equation is proposed. It is used to formulatea relationship for the reference concentration of the suspendedsediment concentration of bio-sediments. The suspended sedi-ment concentration is obtained from the Rouse equation (e.g.Dey, 2014).

2 Experimentation

Experiments were conducted in a glass-walled recirculatingflume of 14 m length, 0.5 m width and 0.6 m depth, locatedat the State Key Laboratory of Hydro-science and Engineer-ing, Tsinghua University, China. The longitudinal slope of theflume bed could be adjusted by a lifting and lowering device.The water entered the flume through a damper installed at theentrance (within 1 m from the entry) of the flume to trap theincoming suspended sediment particles in the flow. Two verti-cal glass sheets were installed within the flume along its lengthto reduce the flume width to 0.16 m for the first 6 m of length.The narrow portion of the flume was then enlarged to mergewith the original flume width (0.5 m) for the remaining length(6 m) of the flume through a gradual transition of 2 m (Fig. 1a).It may be noted that the narrow portion of the flume facilitatedtransport of the bed sediments by increasing the flow velocitydue to a reduction of flow area. The flow depth h was main-tained by an adjustable tailgate located at the downstream endof the flume. Three uniform sediments having median sizesD50 = 0.041, 0.049 and 0.064 mm (silt type) sampled from theThree Gorges Reservoir were used in the experiments. In orderto grow the biofilm around the sediment particles, a portion (2 mlong and 0.012 m deep) of the flume (within the narrow por-tion) was closed at its two ends. Sediment mixed with waterwas poured into this closed portion of the flume. A mixture ofwater (from the Lotus Lake situated in the Tsinghua Universitycampus) and nutrients was added to the sediment after a day ofthe initial placement of sediment in the flume. Thereafter, halfof the volume of the mixture was exchanged every day witha new mixture. The biofilm growth took place in the labora-tory under electrical light (neon light) condition with an averageambient temperature of 19.6°C. The proportions of nutrientsused for the culturing process and the biostabilization prop-erties of the resulting bio-sediments were reported elsewhere(Fang, Fazeli, Cheng, Huang, & Hu, 2015). After biofilm cul-tivation for a period up to 10 or 14 days, the flow was run witha step by step increase in flow discharge until there was sedi-ment movement. For bio-sediments, the sediment transport tookplace as the movement of flocs. Flow depths along the flumewere measured by a number of vertical scales installed on theoutside glass wall of the flume. Sediment concentration wasmeasured in the narrow part of the flume for each flow dis-charge. Thereafter, with a further increase in flow discharge,the bio-sediments, as flocs, were transported as suspended-load.

Journal of Hydraulic Research Vol. 54, No. 6 (2016) Transport of biofilm-coated sediment particles 633

(a)

(b) (c)

Figure 1 (a) Schematic of experimental flume showing narrow, transition, and wide portions; (b) view of narrow portion of flume showing thesediment bed, a laser light source (also shown in the photograph), a camera, and a data processing PC; (c) sediment concentration sampling performedby a right-angled copper tube at a specified depth (here 0.1 h)

After each increment of the flow discharge, a quasi-equilibriumcondition of the biofilm bed was reached within a short periodof time. Figure 1b shows the experimental arrangement used todetect the ambient particles and the floc motion by capturing asequence of images. A laser light source (DPSSL driver, classIV laser product) positioned at the top of the flume emitted ade-quately intense light enabling a camera to capture the images ata frequency of 24 Hz. The digital images were transferred to aPC for further analysis. The images were first examined care-fully to detect the motion of the target near-bed flocs. Then, aparticle tracking velocimetry method was used to analyse thechanges of size gradation and the floc velocity.

Figure 1c shows a device consisting of a right-angled cop-per tube with 1 cm diameter opening directed towards the flow.It was capable of isokinetic sediment sampling by positioningit at a desirable depth (elevation). By regulating the controltap, a volume of 1.6 × 10–3 m3 of water–sediment mixture wassampled in a container through a connecting tube. Sedimentconcentration samples were taken at three elevations 0.1, 0.5and 0.9 h (Fig. 1c), in which the near-bed sample was regardedas a bed-load sample. A CYS-III concentration meter was usedto measure the sediment concentration of the sampled water-sediment mixtures. The CYS-III was a photoelectric sediment

concentration meter made by the Nanjing Hydraulic ResearchInstitute, China. This device could detect the sediment concen-tration from the variation of the light intensity inside the probegap. The probe was calibrated by previous experimental resultsof different sediment sizes (Huang et al., 2015). To determine theconcentration of a sample, the probe of CYS-III concentrationmeter was plunged into the container of water-sediment mixture(sample) after mixing it for a period of 10 s.

2.1 Particle tracking velocimetry (PTV) method

The particle tracking velocimetry method was performed aidedby the 2D-PTV algorithm for extracting the velocities fromthe sequential digital images (e.g. Nikora, Nokes, Veale,Davidson, & Jirka, 2007). Its application was limited to the lowconcentration particle-laden flows (Nezu & Sanjou, 2011). Inthis study, the prevailing condition for the investigation of incip-ient motion corresponded to the low discharge and bed shearstress. Figure 2a shows a raw image and Fig. 2b depicts the sameimage after processing for the floc size. Figure 3a and b displaythe rolling motion of a floc on the bed and the saltating motionof another floc, respectively. The number of pixels for a single1 mm floc was nearly 30 × 30. The uncertainty in determining

Figure 2 View of a detected floc (indicated by an upward arrow) moving close to the bed: (a) raw image; (b) processed image


Figure 3 Successive views of two flocs showing (a) the rolling motion; (b) the saltating motion. Arrows indicate positions of flocs. Time differencebetween two successive positions of floc was 1/24 s

the floc centroid was less than 3.5%. It is revealed that whenthe bed shear stress exceeded the critical value, the movementof flocs was mainly as rolling and/or sliding modes, as shownin Figs 2 and 3a. For a higher bed shear stress, the movementof the flocs was as saltating mode, as evident from Fig. 3b. Forthe flow condition in Fig. 3a and b, the corresponding bed shearstress was 0.27 Pa, which was calculated from ρgRS, where ρ

is the mass density of water, g is the gravitational acceleration,R is the hydraulic radius, and S is the bed slope.

2.2 Velocity tracking

The LGY-II digital velocity meter was used to measure thevelocity. The LGY-II was a propeller type flow meter, havinga propeller radius of 6 mm and a distance from the centreline ofthe propeller to the bottom probe of 10 mm. It could be used fora wide range of flow rates and sediment concentrations. LGY-IIwas used to measure the flow velocities (time-averaged values)at three elevations, 0.1, 0.5 and 0.9 h. The 2D-PTV algorithmwas also used to obtain the instantaneous flow velocity by track-ing the trajectory of the bio-flocs. However, it could not work ifthe sediment concentration was higher than 0.001 (by volume).

Thus, the 2D-PTV algorithm was used at the initial stages forthe incipient motion of bio-sediments with lower discharges( < 0.005 m3 s–1) and flow depths of about 0.06 m. Then, at ahigher flow rate, the LGY-II was used to measure the veloc-ity at different elevations. Figure 4a and b show the positionsof a few particles in two successive images for a known timeinterval, as obtained from the particle tracking. Figure 4c showsthe plots of the measured vertical distribution of time-averagedstreamwise velocity u and the fitted line that follows a log-arithmic law (henceforth log-law). Series 1 to 4 in Fig. 4care the experimental data obtained from successive images ofthe same experiment. These data were used to calculate thetime-averaged velocity. The measured data plots satisfactorilycorrespond to the fitted log-law. If an average particle displace-ment was 8 mm (240 pixels) between two successive images,then the uncertainty in estimation of velocity was less than0.5%. In particular, Fig. 4 shows the data plots for the lower dis-charges ( < 0.005 m3 s–1) and the flow depths of about 0.06 m forthe initial stages of incipient motion. Also, Fig. 5 shows someresults of the measured velocity distributions for three initialsizes of bio-sediment particles corresponding to the dischargesof 0.008–0.019 m3 s–1 and the flow depths of 0.08–0.14 m. It

Figure 4 Velocity tracking to show successive positions of detected particles (a) at 0 s; (b) after 1/24 s; (c) streamwise velocity distribution


Figure 5 Vertical distributions of measured velocities for three initial sizes of sediments (D50 = 0.041, 0.049 and 0.064 mm) measured by theLGY-II, The related hydraulic boundary conditions are furnished in Table 1

Table 1 Hydraulic boundary conditions for Figs 4a, b and 5

Parameter Fig. 4a and b Fig. 5a Fig. 5b Fig. 5c

Discharge (l s–1) 2.0 8.7 19.0 12.4Water depth (cm) 6.4 8.7 14.9 11.1Bed shear stressa (Pa) 0.87 1.00 1.24 1.08

aBed shear stress was computed as ρgRS. The mean values of bedshear stress along a 3 m length were obtained. As the flow withinthe test section was almost uniform, it was feasible to calculate thebed shear stress as ρgRS considering the bed slope S equalling thefriction slope Sf .lUnit of volume, i.e. 103 mL.

may be noted that the velocity distributions in Fig. 5 are relatedto the flows with high sediment concentrations, where the 2D-PTV algorithm could not be applicable due to its limitations, asalready stated. The difference of the velocity ranges, as evidentfrom Figs 4c and 5, corresponds to the different flow conditionsas furnished in Table 1.

2.3 Properties of bio-flocs

The mass density ρ f of bio-sediments (bio-flocs) depends on themass density of pure sediment particles ρs, the wet mass densityof biofilm ρbw, and the ratio of biofilm to floc volumes. For thegiven values of ρs ( = 2650 kg m−3) and the ratio of biofilm tofloc volumes, one requires ρbw to determine the ρ f . Generally,the dry mass density of biofilm ρbd refers to the average drymass density of biofilm, which means the attached dry biomassper unit wet biofilm volume. The ρbw is reported to vary linearlywith ρbd (Ro & Neethling, 1991). The ratio of biofilm to flocvolumes depends on the biofilm thickness and the ratio of floc tomean particle diameters. The mass density of bio-flocs decreaseswith an increase in biofilm thickness and eventually the drymass density becomes stable within a certain range (Shang et al.,2014). The recommended range of biofilm dry mass density isfrom 27 to 115 kg m−3 (Ro & Neethling, 1991). The values ofthe biofilm wet mass density vary in different studies. However,the water content in the biofilm-coating has a higher proportion,being nearly 93% by weight (Grady, Daigger, & Lim, 1999). Fora relatively thin biofilm, the wet mass density of biofilm wasconsidered close to that of water, that is 1000 kg m−3 (Grady

et al., 1999; Horn & Hempel, 1997; Tsezos & Benedek, 1980;Wäsche, Horn, & Hempel, 2000). Zhang and Bishop (1994) cal-culated the wet mass density of biofilm by a numerical modelfrom 1001 kg m−3 at the biofilm surface to 1020 kg m−3 at thelower portion. Hermanowicz and Ganczarczyk (1983) measuredthe terminal fall velocity and the floc size to calculate the massdensity of bio-flocs as 1140 kg m−3. Ro and Neethling (1991)obtained a linear relationship for dry mass density with wet massdensity based on measured data in a laboratory scale fluidizedbed reactor and an analytical model.

Based on experimental observation, it is revealed that thebiofilm formed in natural water has larger mass density thanpure water (Fazeli, 2014). Grady et al. (1999) suggested that themass density of bio-flocs ρ f could be considered as 1100 kg m−3

based on Myška and Švec’s (1994) analysis. In an attempt todirectly measure the mass density of biogranules by a den-sity column, Saravanan and Sreekrishnan (2005) observed ρ f

to rarely vary with biofilm thickness. Its value was about1040 kg m−3. Andalib, Zhu, and Nakhla (2010) followed thesame method, but with a different instrument, and found the ρ f

to be in the range 1070–1100 kg m−3. Shang (2011) assumedthe ρ f as 1070 kg m−3 for bio-sediments after eight weeks ofbiofilm growth. Considering a period of 15 days for the biofilmgrowth, the ρ f of bio-sediments is considered as 1100 kg m−3 inthis study. It corresponds to the typical value reported by Gradyet al. (1999).

3 Theoretical formulation for sediment transport

Sediment transport takes place in the bed-layer as a bed-loadand in the main flow layer as a suspended-load (Dey, 2014;van Rijn, 1984a, 1984b). In bio-sediment transport, the impor-tant parameters are the floc size, bed-layer thickness, terminalfall velocity, and sediment concentration. Figure 6 shows thedefinition sketch of flow over a bed configured with an overlainbed-layer of bio-sediments. The suspended bio-sediment con-centration c(z) decreases with an increase in z. At the referencelevel a, the reference concentration is ca. The δb is the thicknessof bed-layer, where the bed-load transport is prevalent. The Δ isthe apparent roughness height or the bedform height. The datum


Figure 6 Definition sketch of flow over a bio-sediment bed

(virtual bed level) is set at 0.5Δ below the mean crest level ofthe bed surface fluctuations.

3.1 Bed-load transport

The bed-load transport rate qb can be defined as the productof the volumetric concentration cb of transported flocs, the flocvelocity ub in the streamwise direction and the thickness δb ofbed-layer (assumed as mean saltation height) (Dey, 2014). Thus,bed-load transport rate is given by:

qb = cbubδb (1)

According to van Rijn (1984a), the ub and δb can be computedby solving the equations of motion in streamwise and verti-cal directions, respectively; and the cb can be determined byanalysing the bed-load transport rate.

The schematic of the trajectory and the forces acting on asaltating bio-floc in a streamflow is shown in Fig. 7. The forcesacting on a saltating floc are the submerged weight of floc FG

acting downward and the hydrodynamic drag FD and lift FL

(Fig. 7). The direction of FD is opposite to that of the floc veloc-ity vr relative to the fluid flow while the FL is in the normaldirection. Assuming a spherical saltating floc and the forces dueto fluid acceleration to be of a second order, the equations ofmotion, given by White and Schultz (1977), are used here toanalyse the saltation of a bio-floc. This analysis is analogous tothat of van Rijn (1984a), who studied the saltation of a pure sed-iment particle. In streamwise and vertical directions (i.e. in x-and z-directions), the equations of motion of a saltating floc are:

mx − FL

(zvr

)− FD

(u − x

vr

)= 0 (2a)

mz − FL

(u − x

vr

)+ FD

(zvr

)+ FG = 0 (2b)

where m is the bio-floc mass including added fluid mass, i.e.(ρf + αmρ)πD3

f /6, ρ is the mass density of water, αm is theadded mass coefficient assumed to be 0.5 (van Rijn, 1984a), Df

is the median size of bio-floc, vr is the velocity of a bio-flocrelative to the flow, i.e. [(u − x)2 + z2]0.5, u is the local time-averaged flow velocity in x-direction, x and z are the streamwiseand vertical velocities of a bio-floc, respectively, and x andz are the streamwise and vertical accelerations of a bio-floc,respectively.

The submerged weight FG of the bio-floc is:

FG = (s − 1)ρgπ

6D3

f (3)

where s is the relative density of bio-floc ( =ρ f /ρ), and g isthe gravitational acceleration. The hydrodynamic drag FD isexpressed as:

FD = CDfρ

2v2

rπ

4D2

f (4)

where CDf is the drag coefficient for bio-floc. For bio-flocs,Shang et al. (2014) proposed:

CDf = 63.36 R−0.754 (5)

where R is the floc Reynolds number ( = wf Df /υ), wf is theterminal fall velocity of a bio-floc, and υ is the coefficient ofkinematic viscosity. Shang et al. (2014) gave an expression forthe bio-flocs of size Df (in m) with biofilm growth for a periodof less than 20 days and initial pure sediment sizes in the range0–0.10 mm as:

Df = D50

[1 + 0.6

(1000D50)1.21

](6)

where D50 is the median size of pure sediment (in m). For bio-flocs, Shang et al. (2014) argued that the CDf approximatelyequals the drag coefficient due to terminal fall velocity. For ter-minal fall velocity of a bio-floc, the equilibrium of force balance

Figure 7 Schematic of the trajectory and the forces acting on a saltating bio-floc in a streamflow, which is assumed to be analogous to those of asaltating uncontaminated sediment particle according to van Rijn (1984a)


due to the submerged weight and the hydrodynamic drag (Shanget al., 2014) is:

(s − 1)ρgπ

6D3

f − CDfρ

2w2

fπ

4D2

f = 0 (7)

Substituting R = wf Df /υ in the above equation, the wf isobtained as (Fazeli, 2014):

wf =[

(s − 1)gD1.754f

47.52υ0.754

]0.803

(8)

For a floc moving in a viscous fluid, Saffman’s (1965, 1968) liftFL due to shear is given by:

FL = αLρυ0.5D2f vr

(∂u∂z

)0.5

(9)

where αL is the lift coefficient. The velocity distribution in thewall shear layer is assumed to follow the log-law:

u(z) = u∗κ

ln(

zz0

)(10)

where κ is the von Kármán constant ( = 0.4), u∗ is theshear velocity, z0 is the zero-velocity level, considered asz0 = 0.11(υ/u∗) + 0.03ks, and ks is the Nikuradse’s equiva-lent roughness height. It may be noted that this expression forz0 is used for the transitional flow regime 3 < R∗ ≤ 70 (Dey2014; van Rijn 1984a), where R∗ is the shear Reynolds num-ber ( = u∗ks/υ). However, it can be marginally extendable to asmooth flow (R∗ ≤ 3) or a rough flow (R∗ > 70).

Using Eqs (6)–(10), Eqs (2a) and (2b) can be solved simul-taneously for a given boundary condition to determine thetrajectory of a saltating floc.

3.2 Suspended-load transport

Based on the diffusion theory, the distribution of sedimentconcentration c(z) in a steady-uniform flow for a small concen-tration (c < ca < 0.001, where ca is the reference concentrationat a reference level z = a), given by the Rouse equation, can beapplicable to bio-sediment transport as follows (Dey, 2014):

c(z)ca

=(

az

· h − zh − a

)ζ1

(11)

where h is the flow depth, ζ 1 is the modified Rouse num-ber ( = ζ + ϕ), ζ is the Rouse number, i.e. wf /(βκu∗),u∗ = (ghSf )0.5, Sf is the friction slope (assumed to beequalling bed slope S for a uniform flow), β is the factorfor diffusion of suspended sediment, i.e. β = 1 + 2(wf /u∗)2,ϕ = 2.5(wf /u∗)0.8(ca/c0)0.4, and c0 is the maximum concentra-tion of bio-flocs in the bed-layer. According to van Rijn (1984a),the maximum concentration c0 is 0.65 for pure sediments.

Considering Fig. 6, if the effective velocity at referencelevel a of bed-load transport of flocs is ua ( = α2ub, whereα2 is a velocity coefficient, given by ua/ub), the qb isobtained as:

qb = qa ⇒ cbubδb = cauaa ⇒ qb = caα2uba (12)

where qa is the bed-load transport rate at reference level a. In theabove, qb and ub are determined from the bed-load theory, andthe reference level a is defined as a = 0.5Δ. For bio-sediments,the ca is determined from the distribution of suspended sedi-ment concentration obtained from the experiments. In an earlierstudy on bio-sediments, Fazeli (2014) obtained the bedformheight Δ = 6.7 mm. Therefore, for the calculation, the value ofa ( = 0.5Δ ) is considered as 3.35 mm, in absence of any otherliterature results available on bio-sediment transport to the bestof the authors’ knowledge.

4 Results and discussion

4.1 Saltation of a floc during incipient motion

In this study, the saltating motion of bio-floc was closelyobserved. The saltation was found to occur in two modes. First,a floc moving obliquely towards the bed can strike the bed. Thefloc may either merge to become the part of the bed or bounceback to the near-bed flow. In the latter case, it could add moremass from the cohesive substance. Second, a part of the bedmight have an incipient motion in the form of dislodging flocs,once the flow induced bed shear stress overcomes the biofilmadhesion and/or cohesion with the bed.

The flocs may either come to the flow as suspended flocs orreturn back to the bed following a saltating trajectory. From anexamination of some sequential images, the saltating of motionof the flocs was clearly identified. For instance in Fig. 3b, a flocwhile detaching from the bed moves forward and then returnsback to the bed.

4.2 Size of bio-flocs

To evaluate the size of bio-flocs, one may consider two maindimensions. They are the floc length in the direction of motionand the floc width perpendicular to it. During the time of cap-turing (closing time of shutter) of the images, as a floc movedcontinuously, the floc length thus appeared as the white streaksin Fig. 4a and b. On the other hand, the floc width is not affectedby its motion. Hence, in this study, the floc width is assumed tobe the representative size of a floc. Table 2 furnishes the mea-sured and the computed floc size Df , relative saltation heightδb/Df , and relative saltation length lb/Df for a series of imagesof flocs. Here, lb is the saltation length. It is noticeable that thesizes of flocs display an increase of approximately 25 times theinitial sizes.


Table 2 Particle size, floc size, relative saltation height and length

Cultureperiod(day)

Initial sizeD50 (mm)

Comp. flocsizeaDf

(mm)

Meas. flocsize Df(mm)

Terminal fallvelocitybwf

(m s–1)Meas.

Df /D50

Meas.δb/Df

Meas.lb/Df

Flow rate(l s–1)

Flowdepth (cm)

Bed shearstressc

(Pa)

10 0.064 1.133 0.56 0.0125 13.66 1.73 21.40 3.36 5.8 0.8210 0.064 1.133 0.72 0.0125 17.56 1.25 18.50 3.36 5.8 0.8210 0.064 1.133 1.13 0.0125 27.56 1.32 14.46 3.36 5.8 0.8210 0.064 1.133 1.19 0.0125 29.02 2.31 39.09 3.36 5.8 0.8210 0.049 1.179 0.44 0.0132 8.98 1.88 38.37 3.80 6.2 0.8310 0.049 1.179 2.58 0.0132 52.65 1.92 20.00 3.80 6.2 0.8314 0.041 1.214 1.15 0.0138 17.97 1.47 38.75 2.75 7.1 0.92Min. 0.041 1.133 0.44 0.0125 8.98 1.25 14.46 2.75 5.8 0.82Max. 0.064 1.214 2.58 0.0138 52.65 2.31 39.09 3.80 7.1 0.92Average 0.06 1.16 1.11 0.0129 23.92 1.70 27.23 3.40 6.1 0.84

aComputed from Eq. (6).bComputed from Eq. (8).cComputed from the bed slope method (see footnote of Table 1).

4.3 Input parameters and boundary conditions

The parameters used in the computation of incipient motionmodel to obtain the floc trajectories are the bio-floc sizeDf = 1.11 mm, i.e. the average value of Df in Table 2. This

Df value was used to validate the model by the experimen-tal results of the same average diameter (Fig. 8), ks/Df = 0.1,αL = 10, the mass density of bio-flocs ρ f = 1100 kg m−3, theaverage shear velocity u∗ = 0.015 m s–1 (obtained from a fit-ting of the log-law with experimental data of different series,

(a)

(b)

(c)

Figure 8 (a) Measured trajectories of flocs for three initial sediment sizes without biofilm; (b) computed trajectories of flocs for different ks/Df andαL = 12; (c) computed trajectories of flocs for different αL and ks/Df = 0.1


as shown in Fig. 4c), and the coefficient of kinematic viscosityof water υ = 10–6 m2 s–1. The initial velocity components of thesaltating bio-floc were assumed as x(t = 0) = z(t = 0) = 2u∗,as was done by van Rijn (1984a). Regarding the initial positionof a spherical particle, van Rijn (1984a) assumed it as 0.6D50

with respect to the virtual bed level for a stable position of a par-ticle resting on closely packed identical particles. In this study,however, the initial position of a floc was assumed as 0.5Df

above the virtual bed level owing to bio-flocs forming the bedon which the solitary bio-floc rests with slightly more embeddedposition. The virtual bed level was considered at 0.5Δ below themean crest level of the bed.

Concerning the experimental condition, the dynamic equilib-rium condition of the bed can strictly be obtained by feeding thesediment in the upstream at the same rate of the transported sed-iment. However, in the case of experiments with bio-sediments,the feeding of bio-sediments was not feasible. Although thedynamic equilibrium in the present study was not strictly pre-served, the degradation of the bio-sediment bed with respectto the measuring time was so slow that in the experiments, aquasi-equilibrium condition of the biofilm bed was maintained.

4.4 Simulation results

Equations of motion, Eqs (2a) and (2b), were transformedto a system of ordinary, first order, simultaneous differential

Table 3 Comparison of transport characteristics of a bio-sedimentobtained from the present study with those of a pure sedimentobtained from van Rijn (1984a)

Source R∗ αL ks/Df δb/Df lb/Df lb/δb

Present study(bio-sediment)a

16 12 1 1.3 21 16.1

van Rijn (1984a) (puresediment)b

70 20 1 3.3 23 6.97

aBio-sediment data are based on the measured data, where R∗ = 16refers to a transitional flow.bPure sediment data are based on the computed data for D50 = Df ,where R∗ = 70 refers to a transitional flow.

equations. This system was solved using the Runge–Kuttafourth-order method. To calibrate the analytical model, thelift coefficient αL and the Nikuradse’s equivalent roughnessheight ks were used as free parameters. Based on the compu-tational results, the trajectories of saltating flocs are plotted inFig. 8a–c. The axes, x and z, are represented in nondimensionalform dividing the respective lengths by Df . For the comparison,the experimentally measured trajectories are also overlapped.Figure 8a shows the trajectories of saltating flocs for three ini-tial sizes. The lack of data used in Fig. 8a and Table 2 is relatedto the lower number of detected flocs. Note that in Fig. 8a,Df equals D50. The larger initial size of sediment shows agreater saltation height. It is evident that for a given αL, thesaltation height and length increase with a decrease in ks/Df

(Fig. 8b), and for a given ks/Df ; they increase with an increasein αL (Fig. 8c). These suggest a possible route to calibrating themodel by seeking the values of free parameters (αL and ks). Forinstance, Fig. 8b shows that the computed trajectories belong tothe zone of measured trajectories for αL = 12 and ks/Df = 0.1–1. On the other hand, Fig. 8c shows that the computed trajecto-ries are within the zone of measured trajectories for ks/Df = 0.1and αL = 3–10. The values of ks/Df = 0.1–1 for bio-sediments,shown in Fig. 8b and c, differ from those for pure sedimentswhich were reported as ks/D90 = 2.5 by Kamphuis (1974),ks/D84 = 5.1 by Mahmood (1971), ks/D80 = 2.3 by Gladki(1975), and ks/D90 = 2–3 by van Rijn (1984a). The differenceis attributed to the bio-sediment size Df of 1.11 mm againstthe initial sediment size D50 of 0.05 mm (see Table 2). Con-sequently, the values ks/Df = 0.1, 0.5 and 1 correspond toks/D50 = 2.2, 11 and 22, respectively. For lift coefficient αL, itsvalues (3, 6 and 10) for bio-sediments obtained from Fig. 8c areless than the values recommended for pure sediments.

The saltation related parameters obtained from this study fora bio-sediment and those obtained from van Rijn (1984a) for apure sediment are given in Table 3. It is revealed that the nondi-mensional saltation height δb/Df for a bio-floc is shorter thanthat for pure sediment particles. For pure sediments, the saltationheight and length are sensitive to FL/FD. For instance, a largerFL/FD results in a longer saltation height and a shorter salta-tion length. Figure 9 displays the computed FL/FD for a pure

Figure 9 Computed lift to drag ratios as a function of x/Df for a bio-sediment and a pure sediment (Df = D50)


sediment obtained from experiments of Fernandez Luque andvan Beek (1974) as analysed by van Rijn (1984a) and that for abio-sediment obtained from this study. It may be noted that bothhave a transitional flow regime (5 < R∗ ≤ 70) and relativelylarge sediment sizes (1.8 and 1.11 mm). The lift coefficientswere considered as αL = 20 for a pure sediment and αL = 10for a bio-sediment, by which the best agreement between thecomputed and the experimental results (for the measured zonein Fig. 8b and c) on the floc trajectory was obtained. The plotsof FL/FD for a bio-sediment show lower values than those for apure sediment, by which a smaller ratio of saltation height to flocsize (δb/Df ) for a bio-sediment can be substantiated. Althoughthe nondimensional saltation length of bio-floc in Table 3 isslightly lower than that of pure sediment, the ratio of saltationlength to saltation height for a bio-floc is more than twice thatof a pure sediment particle. Additionally, the peak for a bio-sediment bed corresponds to the peak of the trajectory of floc,where both vr and FD attain their minimum values. Thus, FL /FD

increases to a maximum at that point. In contrast, a weak peakis evident for a pure sediment particle in between x/Df = 10and 15. It corresponds to the peak of the trajectory of a puresediment particle. The weak peak for a pure sediment particlemay be due to a higher saltation height for a pure sediment par-ticle (the last column in Table 3), which results in lower valuesof ∂u/∂z and FL.

4.5 Bed-load transport

The essential prerequisite to formulate the bed-load transportis to know two important parameters. They are the particleparameter D∗ and the transport stage parameter T for bio-flocs,defined as:

D∗ = Df

[(s − 1)g

υ2

]1/3

(13a)

T = u′2∗ − u2

∗cr

u2∗cr(13b)

where u′∗ is the shear velocity due to floc roughness defined

as u′∗ = U(g0.5/C′), C′ is the Chézy coefficient due to floc

roughness, U is the average flow velocity, and u∗cr is the thresh-old shear velocity according to Shields (1936). The u∗cr wasobtained from the expressions given by Fang et al. (2014), fol-lowing the modification by Righetti and Lucarelli (2007) forbio-sediments. The C′ for bio-sediments is defined as:

C′ = 18 log(

12R3Df

)(14)

In the above, the Df can be obtained from Eq. (6).The findings of Righetti and Lucarelli (2007) from a series

of experiments of natural benthic sediments and those of Fanget al. (2014) on different “cultivated” sediments (cultivation timefrom one to eight weeks) showed that two additional forcesare effective at the threshold of bio-sediment motion. They arethe cohesive force between flocs F∗, which is proportional tofloc diameter Df (Righetti & Lucarelli, 2007) and can also beexpressed as F∗ = ρg(h – ha)Ak (Fang et al., 2014), and theadhesive force, which can be given by FA = AD2

f (Fang et al.,2014; Righetti & Lucarelli, 2007). Here, ha is the equivalenthead of water at the atmospheric pressure, Ak is the interfa-cial area between two adjacent flocs, and A is the adhesioncoefficient. Figure 10a shows the variations of threshold veloc-ities Uc with bio-floc size Df . The Uc(Df )-curve for bio-flocsafter 10 days of biofilm colonization obtained from the formulagiven by Fang et al. (2014) lies above that for pure sedimentparticles obtained from the formula given by Tang (1963) forD50 < 30 mm. It suggests that both the cohesive and adhesiveforces affect the magnitude of threshold flow velocity Uc forD50 < 30 mm. The experimental data of Shang (2011) were

Figure 10 (a) Threshold flow velocity as a function of bio-floc size after a biofilm cultivation time of 10 days obtained from Fang et al.’s (2014)formula and a comparison with the threshold flow velocity curve for pure sediments obtained from Tang’s (1963) formula; (b) threshold Shieldsparameter versus particle parameter for bio-sediments after a biofilm cultivation time of four weeks based on Fang et al.’s (2014) formula


used to obtain the curve of threshold Shields parameter θ cr ver-sus particle parameter D∗ for a biofilm cultivation time of fourweeks, as shown in Fig. 10b. According to Fang et al. (2014), thetheoretical values of biofilm adhesion for two and four weeksare very close. Hence, the values of threshold Shields parame-ters after four weeks are used in this study. The threshold Shieldsparameter is defined as:

θcr = u2∗cr

(s − 1)gDf(15)

The analytical solutions for nondimensional saltation heightδb/Df for bio-sediments as a function of transport stage param-eter T for different particle parameters D∗ are shown in Fig. 11a.

(a)

(b)

Figure 11 (a) Nondimensional saltation height as a function of trans-port stage parameter for different particle parameters; (b) nondimen-sional saltation length as a function of transport stage parameter forαL = 10 and ks/Df = 0.1

The computed results were used for a multiple-linear regressionanalysis to obtain an equation of δb with an error of 15% as:

δb

Df= 0.05D1.2

∗ T0.5 (16)

Using the computed results of saltation length of bio-sediments,a regression equation of nondimensional saltation height lb/Df

as a function of transport stage parameter T can be presented asfollows (Fig. 11b):

lb

Df= 3.5T1.15 (17)

Similarly, the equations of the floc velocity ub and the bed-loadconcentration cb were obtained using the regression analysis andexpressed in nondimensional form (Fig. 12a and b) as:

ub

[(s − 1)gDf ]0.5 = 0.5(D∗T)0.6 (18a)

cb

c0= 0.18

TD∗

(18b)

Among Eqs (16)–(18a), Eq. (18b) is identical to that for puresediments (van Rijn, 1984a). Uncertainties in ρ f influence mand FG, which in turn influence wf . Considering 1050 and1150 kg m−3 as the lower and upper limits of ρ f , the uncertain-ties in wf according to Eq. (8) are calculated as 43 and 39% forthe lower and upper limits of ρ f , respectively. Further, to assessthe effects of the values of ρ f and wf on the estimations of δb,ub and cb, one may redraw Figs 11a, 12a and b for some othervalues of ρ f (for instance, 1050 instead of 1100 kg m−3), but anegligible changes (about 10%) of the estimated values of δb, ub

and cb would be obtained.The relationship for bed-load transport rate qb of bio-

sediments are obtained substituting Eqs (16), (18a) and (18b)into Eq. (1) as:

qb

[(s − 1)g]0.5D1.5f

= 0.0029D0.8∗ T2.1 (19)

It is pertinent to mention that van Rijn (1984b) did not considerthe bed-load concentration as a reference concentration for thecomputation of suspended sediment concentration c. Instead heused an effective reference concentration ca, as given in Eq. (12).Substituting Eq. (19) into Eq. (12), the ca is obtained as:

ca = 0.0058D0.2∗ T1.5 Df

α2a(20)

The coefficient α2 can be determined from the experimentaldata. Equation (20), which defines the reference concentrationca, and the Rouse equation, Eq. (11), for suspended sedimentconcentration are used to fit the curves with the experimentaldata. The experimental data describing the near-bed and the sus-pended sediment concentrations of bio-sediments are used for


(a)

(b)

Figure 12 (a) Nondimensional floc velocity as a function of transportstage parameter for different floc sizes; (b) nondimensional bed-loadconcentration as a function of the ratio of transport stage parameter toparticle parameter

this purpose. These data correspond to the biofilm cultivation fora period of 10 days for the initial sediment sizes D50 = 0.041,0.049 and 0.064 mm. Figure 13 shows the computed results aswell as the experimental data for these three sediment sizes for

Table 4 Hydraulic conditions for Fig. 13

Parameter Fig. 13a Fig. 13b Fig. 13c

Discharge (l s–1) 17.3 19.0 12.4Water depth (cm) 14.0 14.9 11.1Bed shear stressa (Pa) 1.20 1.24 1.08

aBed shear stress was computed from ρgRS.

the flow conditions as described in Table 4. Rouse equation,Eq. (11), is found to correspond well with the experimentaldata. The following relationship for ca with α2 = 1.6 pro-vides the best agreement between the computed results and theexperimental data:

ca = 0.00363D0.2∗ T1.5 Df

a(21)

It may be noted that the value α2 = 1.6 corresponds to thelimited experimental data for concentration of suspended bio-sediments.

5 Computational scheme

For a given average flow velocity U, flow depth h, hydraulicradius R, initial median particle size D50 (before biofilmgrowth), mass density of water ρ, mass density of flocs ρ f ,coefficient of kinematic viscosity of water υ, and gravitationalacceleration g, the bed-load and the suspended-load transportrates can be computed as follows:

(1) Computation of bed-load transport rate:(i) Compute the size of bio-flocs Df and the particle

parameter D∗ using Eqs (6) and (13a), respectively.(ii) Determine the Chézy coefficient C′ from Eq. (14).

(iii) Obtain the critical shear velocity u∗cr for bio-sedimentflocs from Fig. 10b.

(iv) Compute the transport stage parameter T usingEq. (13b).

(v) Compute the bed-load transport rate qb using Eq. (19).(2) Computation of suspended-load transport rate:

(i) Compute the reference level a as a = 0.5Δ or ks.(ii) Compute the reference concentration ca using Eq. (21).

(a) (b) (c)

Figure 13 Distributions of concentration of bio-sediments for three initial sediment sizes (a) D50 = 0.041; (b) D50 = 0.049; (c) D50 = 0.064 mm


(iii) Compute the terminal fall velocity of a bio-floc wf

using Eq. (8).(iv) Compute the modified Rouse number ζ 1 ( = ζ + ϕ).

Note ζ = wf /(βκu∗), u∗ = (gRSf )0.5, β = 1 + 2(wf

/u∗)2, and ϕ = 2.5(wf /u∗)0.8(ca/c0)0.4.(v) Compute the vertical distribution of suspended sedi-

ment concentration c using Eq. (11).(vi) Compute the suspended-load transport rate qs using

following equation:

qs =∫ h

aucdz (22)

In the above, the flow velocity u(z) and the suspended sedimentconcentration c(z) are obtained from Eqs (10) and (11), respec-tively. Finally, the integration in Eq. (22) can be performednumerically by Simpson’s rule to estimate qs.

6 Conclusions

This study proposes a method of computation of transport ofbiofilm-coated sediments. Both the bed-load and the suspended-load transport rates are analytically modelled. Biofilms werecultivated within the flume to form a coat around fine sedimentparticles (silt type). Experiments were conducted to determinethe flow velocity, saltation trajectory and sediment transportrate in terms of concentration, which were used to calibrate themodel determining the unknown parameters.

The important conclusions of this study are as follows.

(1) The initial size of a pure sediment particle becomesapproximately 25 times larger after formation of biofilmaround it.

(2) Longer saltation length and shorter saltation height forbio-flocs, as compared to those for pure sediments, wereobserved. The reason is attributed to the less values ofFL/FD for bio-flocs than those for pure sediment particles.

(3) Bed-load transport model is based on the computation of thetrajectory of a saltating bio-floc. Finally, a simple empiricalequation of bed-load transport rate is proposed.

(4) The suspended-load model is based on the sediment con-centration equation, called the Rouse equation.

(5) A formula for the reference concentration of bio-sedimenttransport is proposed.

(6) Finally, schemes for the computation of bed-load andsuspended-load transport rates for bio-sediments are pro-posed.

It is important to mention that this is the first attempt to modelbiofilm-coated sediment transport. More experimental results,as a future scope of research, can provide an improved calibra-tion of the free parameters for a more precise prediction by usingthe proposed model.

Funding

This work was supported by the National Natural ScienceFoundation of China [grant numbers 51139003, 11372161].

Notation

Ak = interfacial area between two adjacent flocs (m)a = reference level (m)C′ = Chézy coefficient due to floc roughness (m0.5 s−1)CDf = drag coefficient for a bio-floc ( − )c = sediment concentration ( − )c0 = maximum concentration of bed-layer ( − )ca = reference concentration ( − )cb = concentration of flocs transported in bed-layer ( − )D∗ = particle parameter ( − )D50 = median size of pure sediment particles (m)Df = median size of bio-flocs (m)F∗ = cohesive force between flocs (N)FA = adhesive force between floc and bed (N)FD = hydrodynamic drag (N)FG = submerged weight of floc (N)FL = hydrodynamic lift (N)g = gravity acceleration (m s−2)h = flow depth (m)ha = equivalent head of water at atmospheric pressure (m)ks = Nikuradse’s equivalent roughness height (m)m = floc mass including added fluid mass (kg)qa = bed-load transport rate at reference level a (m2 s−1)qb = bed-load transport rate (m2 s−1)qs = suspended-load transport rate (m2 s−1)R = hydraulic radius (m)R∗ = shear Reynolds number [ = u∗ks/υ] ( − )R = floc Reynolds number [ = wf Df /υ] ( − )S = bed slope ( − )Sf = friction slope ( − )s = relative density of bio-flocs [ =ρ f /ρ] ( − )T = transport stage parameter ( − )t = time (s)U = average flow velocity (m s−1)Uc = threshold flow velocity (m s−1)u = streamwise flow velocity (m s−1)u∗ = shear velocity [ = (ghSf )0.5] (m s−1)u′

∗ = shear velocity due to floc roughness (m s−1)u∗cr = threshold shear velocity (m s−1)ua = effective velocity of bed-load flocs (m s−1)ub = floc velocity (m s−1)vr = floc velocity relative to flow (m s−1)wf = terminal fall velocity of a bio-floc (m s−1)x, z = Cartesian coordinates (m)x = streamwise velocity of a bio-floc (m s−1)x = streamwise acceleration of a bio-floc (m s−2)z = vertical velocity of a bio-floc (m s−1)


z = vertical acceleration of a bio-floc (m s−2)z0 = zero-velocity level (m)αL = lift coefficient ( − )αm = added mass coefficient ( = 0.5) ( − )β = factor for diffusion of suspended sediments ( − )Δ = apparent roughness height (m)δb = bed-layer thickness (m)κ = von Kármán constant ( = 0.4) ( − )θ cr = threshold Shields parameter ( − )ρ = mass density of water (kg m–3)ρbd = dry mass density of biofilm (kg m–3)ρbw = wet mass density of biofilm (kg m–3)ρ f = mass density of bio-flocs (kg m–3)ρs = mass density of pure sediment particles (kg m–3)υ = coefficient of kinematic viscosity (m2 s−1)ζ = Rouse number [ = wf /(βκu∗)] ( − )ζ 1 = modified Rouse number ( − )

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