Appl. Math. Mech. -Engl. Ed.   2014, Vol. 35 Issue (11): 1411-1420     PDF       
http://dx.doi.org/10.1007/s10483-014-1876-7
Shanghai University
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Article Information

Hong-wei ZHU, Dao-zeng WANG, Peng-da CHENG. 2014.
Dynamic release process of pollutants during suspended sediment transport in aquatic system
Appl. Math. Mech. -Engl. Ed., 35(11): 1411-1420
http://dx.doi.org/10.1007/s10483-014-1876-7

Article History

Received 2013-10-14;
in final form 2014-2-23
Citation
Hong-wei ZHU, Dao-zeng WANG, Peng-da CHENG. 2014. Dynamic release process of pollutants during suspended sediment transport in aquatic system[J]. Appl. Math. Mech. -Engl. Ed., 35(11): 1411-1420.
Dynamic release process of pollutants during suspended sediment transport in aquatic system
Hong-wei ZHU, Dao-zeng WANG , Peng-da CHENG       
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, P. R. China
Received 2013-10-14; in final form 2014-2-23
Fund program：Project supported by the National Natural Science Foundation of China (No. 10972134), the National Key Program of National Natural Science Foundation of China (No. 11032007), and the Shanghai Program for Innovative Research Team in Universities.
Corresponding author: Dao-zeng WANG, Professor, E-mail: dzwang@staff.shu.edu.cn
ABSTRACT：Pollutants release is highly consistent with suspended sediment concentration (SSC) in water column, especially during re-suspension and transport events. The present research focuses on pollutant dynamic release from re-suspended sediment, especially the vertical distribution relationship between them. The sediment erosion experiments on a series of uniform flow are conducted in a circulate flume. Reactive tracer (phosphorus) is used as the contaminant in fine-grained sediments to identify the release characteristic length and time. Experimental results show that the flow condition near-bed depends on the sediment surface roughness. The region with high turbulent intensities corresponds to a high concentration sediment layer. In addition, the SSC decreases with the distance, water depth, and particle grain size. The sediment in a smaller grain size takes much more time to reach equilibrium concentration. Total phosphorus (TP) concentration changes along the water depth as SSC in the initial re-suspension stage, appearing in two obvious concentration regimes: the upper low-concentration layer and the high-concentration near-bottom layer. This layered phenomenon remains for about 3 hours until SSC distribution tends to be uniform. Longitudinal desorption plays an important role in long-way transport to reduce the amount of suspended sediment in water column.
Keywords： sediment pollutant     turbulence     surface roughness     grain size     vertical distribution     longitudinal desorption    
1 Introduction

In recent years,the secondary pollution problem caused by re-suspended contaminated sediments attracts wide attention of researchers in relevant fields[1] . By the hydrodynamic effects of the overlying water,exchange between water andbed sediment often occurs,causing significant re-suspension and sedimentation,in which part of the sediment particles will enter or leave the water. The adsorbed pollutants on the river sediments are released into the water when resuspension occurs [2] . As the main carrier of pollutants,suspended sediment and release process will not disappear in the further particles transport. Suspended particle composition changes with the sediment bed properties. The stronger the re-suspensionand settlement are,the closer the relationship between suspended sediment composition and its concentration is. Most of the suspended load is fine sediment,whereas coarse particle gradually falls as its settling velocity is larger [3] . Sediment concentration in the vertical direction forms a stable distribution when sediment particles take random movement by the role of flow turbulence. Diffusion of various pollutants in water also forms vertical distribution [4] . Different spatial distributions depend on the capacity of the adsorption and desorption of contaminants,the suspended particle size [5] , and flow conditions (see Fig. 1). The sediment vertical concentration distribution and that of pollutants are closely related.

Fig. 1 Schematic of distribution processes of velocity,suspended sediment,and pollutant in water column
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Few studies focused on the relationship betweensuspended sediment particles and pollutants as the vertical distribution of pollutants cannot be stably maintained,and for which the action mechanism has not been fully understood. In this paper,the dynamic effects of different suspended sediment particle size and composition,and the dynamic relationship between the flow turbulent intensity and the dynamic distribution of the pollutants are to be studied in the erosion and re-suspension experiments in a long flume. 2 Materials and methods 2.1 Flume and apparatus

Experiments are conducted in an environment circulating water flume with total length of 26.5 m,width of 0.25 m,height of 0.7 m in Shanghai University,as shown in Fig. 2. Water pumped into the glass flume would get back to the pool,and a rectifier grille is settled at the flume entrance. The flow is controlled through the main valve and tailgate to change flow velocity and water depth. All experimental sediments after treatment are spread evenly over the intermediate sink with length of 2 m and depth of 0.1 m,preventing the unexpected sediment erosion loss.

Fig. 2 Schematic diagram of flume
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2.2 Experimental methods

LGY-II intelligent flow meter is used to measure the velocity distribution in flume. The flow turbulence intensity and Reynolds stress distribution are measured by the laser flow meter. In order to gain the distribution of phosphorus concentration of pollutants under hydrodynamic conditions,seven sampling points are arranged in vertical direction with two cross sections in the middle of the flume as shown in Fig. 2. The height above sediment-water interface of the samplingpointsare1cm,1.5cm,2cm,3cm,5cm,and7cm,respectively. Totalphosphorus (TP) concentration in water is measured by 722 N visible spectrophotometer [6] . Siphon sampling for phosphorus concentration is used with time interval of 5 minutes. The initial concentration ( S0 ) under medium starting intensity is 0.5 g/L−1 g/L,and the relative measurement accuracy (S/ S0 ) of the sediment concentrations is between 0.001 and 0.005. Three kinds of sediments are used in the experiments: manual screening sediment (0.1 mm),natural sediments (0.025 mm),and iodinated starch (0.01 mm),to indicate the sediment suspension process with different diameters of particles and their vertical and longitudinal distribution characteristics. 3 Results and discussion 3.1 Generalization of sediment-water interface and flow condition

Usually,velocity vertical distribution is described by the exponential and logarithmic velocity distribution formula. Due to formula’s shortcomings as well as the side wall effect,the actual vertical velocity distribution in the flume central area agrees with the law of logarithmic,and is deviated in the vicinity of the free surface and the near bed. Logarithmic velocity distribution can be expressed as [7]

in which u* is the friction velocity,z0 is the roughness length,and κis the Karman constant (κ=0.4).

The silt surface is generally regarded as hydraulic smooth. The bed roughness length z0 is only related to the kinematic viscosity ν,

When using coarse sand as the sediment,roughness lengthz0in hydraulic rough or hydraulic transient situation can be described as [7]

where ks is Nigolas’ roughness,for the coarse sediment,ks =2.5d50 ,and d50 is the particle medium diameter.

The vertical average speedU0is obtained as

As U0 is known for excessive water flow (smooth or rough surface),friction velocityu∗can be iterated by the above formulae. Whether the flow condition is hydraulic smooth or rough, it depends on the particle Reynolds number ().

In the two-dimensional uniform steady flow,the relationship between Reynolds stress and friction velocity can be expressed as [8]

in which u' is the longitudinal fluctuating velocity,and v' is the transverse fluctuating velocity.

Turbulence intensities can be represented by the semi-empirical formulae which are general functions of depth (two dimensions)

The flume results under both smooth and rough surfaces are shown in Fig. 3.

As can be seen from Fig. 3(a),the results are fitting well with linear velocity profiles as the open channel flow distribution characteristics,and the velocity gradient variation in the central part is very small. The results in Fig. 3(b) and Fig. 3(c) show that the turbulence characteristics are significantly different with the change in water depth. The turbulence intensities near the bed increase sharply and monotonically while gradually decrease in the upper water region [9] . Complex changes of the turbulence intensity appear in the transition region,within which the maximum value is located. The results show that the turbulence is different in the partition structure in each water section. Not only the average velocity distribution,but also their turbulence characteristics are related to each other. Figure 3(d) shows good agreement between Reynolds stress and theoretical formulae along the water depth with the linear distribution,but the linear relation is not satisfied near the wall due to the bed resistance. From the results of Fig. 3,whether the sediment surface is hydraulic smooth or hydraulic rough,both of them appear to the similar tendency and diminution,and the hydraulic smooth one disperses more evenly.

Fig. 3 Flow conditions in open channel flume
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3.2 Transport of suspended sediments with different grain sizes

Turbulence may play a dominant role in the transport of suspended sediment,as molecular diffusion is very small and can be ignored in environmental engineering. Only the macro observation of suspended sediment transport is mentioned here.

When sediment re-suspension occurs,sediment concentration in the overlying water increases rapidly,and then reaches a relatively stable value. The physical process of sediment vertical distribution depends on the different natures of bed sediments. For coarse sediment,it is a uniform distribution and its concentration results from the balance between the suspension rate and deposition rate [10] . This balance will not be broken in the steady state. For cohesive fine sediment,sediment spatial distribution is not uniform,the exposed surficial sediment becomes more difficult to move with time,and the fine particle concentration is a function of concentration. Compared with the coarse sediment,settling velocity is smaller,and its concentration distribution is more uniform. Results of suspended sediment distribution along the vertical and longitudinal directions are shown in Fig. 4.

Fig. 4 Distributions of suspended sediment concentration
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From the results of Fig. 4,it can be seen that sediment concentration increases gradually with water depth. Firstly muddy water is formed in the bottom,and gradually diffuses to the upper water layer. The vertical sediment concentration distribution tends to be stable over time,a high concentrations of sandywater layer with thickness of 3 cm−5 cm is observed in bed surface,which is accounted for about 10% to 20% of the water depth. Sediment concentration is about 5 to 10 times of the averaged sediment concentration. Sediment starts to suspend and its concentration decays quickly in the vertical and longitudinal directions under the bottom shear stress. Vertical concentration of natural sediment is more uniform,its longitudinal decay rate is between the other two. The particle size of iodinated starch has the smallest concentration with the most uniform vertical distribution.

Figure 4 shows the most obvious feature that the suspended sediment vertical concentration has the hierarchical structure by strong turbulent diffusion resulting in a steep density gradient. Also can be seen from Fig. 4,there are two concentration clines of the suspended sediment near sediment erosion point [11] . After the particle settlement,sediment concentration is gradually homogenized over distance. Generally,it is considered that the lower cline is mainly caused by obstruction due to sediment deposition and the upper one has a relationship with upward turbulent diffusion [12] . The smallest vertical mixing region is formed between the two clines region. Sediment mixing is controlled by buoyancy effects and turbulent rupture in high muddy bottom layer,and is hindered by the buoyancy,which has a feedback effect on the disturbance. These feedback effect generally contributes to the further release of pollutant-containing fine sediment [13,14] .

The time-dependent variation of the suspended sediment concentration (C,g/L) can be obtained from the mass balance equation [15] as follows:

wherehis the water depth,E0 is the initial re-suspension rate,and ws is the deposition rate.

As C0= 0,the solution is

in which is the equilibrium concentration.

Figure 5 shows the variation of suspended sediment concentration with different grain sizes over time. From the result,we can see that with the increasing of grain sizes,it takes longer time to reach equilibrium concentration. This may because the settling velocity of particle depends on the grain size,and the particle with larger grain size has faster settling velocity and deposit within a shorter distance. Sediment with particle medium diameter of 0.01mm needs nearly ten times as much time as the other two require as shown in Fig. 5.

Fig. 5 Variations of suspended sediment concentrations with different grain sizes over time
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3.3 Dynamic release characteristics of pollutants from re-suspended sediment

Figure 6 shows the TP concentration distribution at each water depth with time. It is shown in Fig. 6(a) that in the initial release stage,the TP concentration distribution becomes uniform as the initial one is not even. Concentration near the sediment-water interface is about 0.213 mg/L at first,and the value decreases forward the surface until the least concentration with 0.143 mg/L arrives at 0.07 m above the bottom. Figure 6(b) shows the concentration increased with time and the one near-bed point is larger than the other three.

Fig. 6 Variation of TP concentration distribution
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As mentioned above,sediment concentration gradually increases and diffuses to the upper layer. This phenomenon is also observed in Fig. 6(a),the same to concentration distribution of sediment and pollutants which tends to be stable over time. As we know,there exists a muddy layer with high sediment concentration. The relationship between the sediments and pollutants is clearly direct correlation [16] . As also can be seen from Fig. 6,the TP concentration changes on the initial experimental stage with the water depth are significant. As time goes on,the differences in phosphorus concentration gradually become smaller while the sediment concentration is still basicallythe same. The vertical distribution of pollutant concentration and suspended solids concentration has similar trend near the sediment-water interface [17] . Suspended sediment concentration (SSC) is in line with pollutants one far from the erode point. 3.4 Longitudinal desorption effect ofsuspended sediment in estuarine area

Suspension transport is the main movement form of cohesive fine-grained sediment. When sediment transport capacity reaches saturation,sediments will gradually deposit along the way downward. But sediment particles will experience a reciprocating motion process and be re-suspended due to the estuarine tidal currents [18] . The silt steeling velocity is very small, causing the particle size refinement along the distance. Sediment concentration will exit at a stable sediment value for steady flow conditions. The three-dimensional diffusion equation for suspended sediment movement is represented as

whereSis the suspended sediment concentration,εsxj (j=1,2,3) correspond to the turbulent diffusion coefficients in the flow,andwis the sediment settling velocity.

Generally,the siltation mode can be expressed as

in which S0 and Ssq are the initial concentration and the equilibrium concentration,respectively, and p is the parameter.

The vertical integration mode can be written as

where λ is the synthesis coefficient,which depends on many factors.

To sum up,the following siltation mode can be established:

in whichmreflects the effects of the particle size,the roughness,the sediment concentration,the tidal wave and many other factors,and its value is determined by experiments [19] . During the experiments,the test is carried at four sections siphon sampling with distance of 10 m interval downstream. Each section takes four sampling foraverage thin a tidal cycle. The experimental results are shown in Fig. 7.
Fig. 7 Sedimentation process and vitiation of sediment concentration along distance
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As seen from Fig. 7,the concentration is evenly distributed along the vertical direction. As mentioned above in Fig. 4,smaller sediment particle will result in a more uniformly distribution. the value of mfitted with the data is about 0.01. Due to the limitations of the experimental conditions [20] ,the distance between measuring point and erosion point is very close,stable vertical distribution of sediment concentration has not yet formed,the fitted values ofmoverestimated is modified to 0.007.

Substituting natural sediment particle size gradation =4.41,water depthh= 12,and the ratio of tidal discharge and runoff = 18 into (13),the sediment settlement law is obtained

The results are shown in Fig. 8,when sediment suspends,sediment concentration decays quickly along the way,and at about 800 to 1 000 meters downstream it attenuats to 0.5 percent. It also can be seen that the settling velocity in Huangpu River is quite small,and only about 30% of the sediment would be brought into the Yangtze River.

Fig. 8 Sediment concentration simulation results along distance with different ratios of tidal discharge and runoff in Huangpu River
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4 Conclusions

Turbulence characteristics are significantlydifferent with the depth and surface hydraulic conditions,and it monotonically increases near the bed surface either smooth or rough. The sediment distribution is mainly due to the turbulence diffusion. Sediment concentrations gradually increase with time,which is forming muddy water in the bottom,and then diffuse to the upper layer. Sediment concentration decays quickly under the bottom shear stress. The vertical concentration of suspended sediment has the hierarchical structure of by strongly turbulent diffusion resulting in a steep density gradient. There are two concentration clines of the suspended sediment near the erosion point. Sediment mixing is controlled by buoyancy effects and turbulent rupture in high muddy bottom layer.

Pollutants concentration changes with the water depth on the initial experimental stage. As time goes on,the differences in contaminant concentration gradually become smaller while the sediment concentration is also basically the same. The pollutant concentration and suspended solids concentration on vertical distribution have similar trend near the sediment-water interface. The SSC is in line with pollutants one where far from the erode point. Sediment settlement law are found to estimate the concentration distribution along the distance,which shows that the distribution is under the combined effects of the particle size,the roughness,the sediment concentration,the tidal wave,and many other factors. Acknowledgements The authors would like to thank B. C. ZHONG,Prof. J. Y. FAN,and Prof. J. H. GUO for their valuable discussion.

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