FAN Jing-yu (樊靖郁), WANG Dao-zeng (王道增)

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China, E-mail: jyfan@shu.edu.cn

Experimental investigation on diffusive contaminant release from permeable sediment layer under unidirectional unsteady flow*

FAN Jing-yu (樊靖郁), WANG Dao-zeng (王道增)

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China, E-mail: jyfan@shu.edu.cn

(Received July 27, 2014, Revised September 27, 2014)

The interfacial diffusive contaminant (phosphorus) release from permeable sediment layer into overlying water column under a unidirectional unsteady (periodic) flow condition was experimentally measured and analyzed. The experimental results indicate that the gross diffusive contaminant release rate is substantially enhanced as compared to that under a steady flow condition, and this enhancement trend is much more pronounced in an immediate release stage. The interfacial diffusive contaminant release rate tends to increase with the increasing flow velocity, decreasing period and augmenting amplitude for the case of the unsteady flow. The additional interfacial diffusive contaminant release under the unsteady flow condition may be related to the hydrodynamic response of the diffusive boundary layer to the flow unsteadiness of the overlying water, depending upon not only the periodic thickness variation of the diffusive boundary layer immediately above the sediment-water interface modulated by the temporal flow velocity of the overlying water column but also the intensified turbulent mixing between the overlying water and the pore-water within the superficial sediment layer induced by an alternate acceleration/deceleration fluctuation during each period.

unsteady flow, contaminant, sediment, diffusive release, sediment-water interface

Introduction

The mass transfer processes of particulate or dissolved substances like nutrients, heavy metals and other potentially harmful materials between the contaminated sediments and the overlying water column in rivers, lakes, reservoirs, and estuaries are of considerable importance in water environment field[1-3]. It has been known that the hydrodynamic effect of the overlying water flows on the mass transfer rate across the sediment-water interface for the case of the static release, i.e., the case of no sediment resuspension, is largely due to the formation and development of a thin (typically with the thickness on the order of 0.001 m-0.002 m) diffusive boundary layer within which the contaminant concentration gradient occurs and molecular diffusion commonly dominates over turbulence diffusion[4,5]. As a consequence, the mass transfer across the sediment-water interface is relatively limited for the case of the static release. The quantification of this diffusive release flux is still important in respect of the assessment of the potential environmental risks and effective remediation strategies associated with the contaminated sediments[6]. In this regard, steady or quasi-steady flow conditions of the overlying water column have been usually considered in most of previous research. The effect of the flow velocity in the overlying water column on the mass transfer across the sediment-water interface is significant since the thickness of the diffusive boundary layer is governed or at least greatly influenced by the mean flow velocity or friction (shear) velocity[7-10]. However, unsteady flow conditions of the overlying water column are widely present in natural aquatic environments, such as an internal standing wave in lakes[11,12]and tidal flow in rivers or estuaries[13]. In these circumstances, the flow velocity, water depth and flow direction of the overlying water column are subjected totime-dependent (periodic) changes with the periods ranging from minutes to hours, and it can be expected that the mass transfer across the sediment-water interface may show the corresponding variations with time. Nevertheless, the hydrodynamic response of the diffusive boundary layer to the unsteady bottom boundary flow as well as the associated interfacial diffusive contaminant release properties have not been extensively studied so far[14,15], especially the linkage between the flow unsteadiness and its impact on the interfacial transport mechanism.

The superficial sediment layer is an active exchange zone between water column and sediment bed[3]. The interfacial diffusive contaminant release from the permeable sediment layer is much more susceptible to the flow conditions. In this study, a series of water flume experiments are conducted to assess the effect of the diffusive contaminant release from the superficial contaminated sediment layer on the short-term water quality under a unidirectional unsteady (periodic) flow condition for the case of no sediment resuspension. The influence of mean flow velocity, period and velocity amplitude on the time-dependent diffusive contaminant release process is quantified. Moreover, the associated hydrodynamic response of the diffusive boundary layer to the unsteady flow conditions and its effect on the interfacial mass transfer are analyzed and discussed.

1. Experimental facilities and measurement techniques

The interfacial diffusive contaminant release from the permeable sediment layer under different unidirectional unsteady flow conditions were experimentally studied in an open channel recirculating flume with a rectangular test section of 6 m in length, 0.25 m in width and 0.45 m in height[16]. The time varying flow velocity (u) and water depth (h) of the channel flume could be obtained by suitably adjusting both the rotating speed of a frequency-controlled centrifugal water pump and the opening variations of two electrically operated valves located at the inlet and outlet pipes of the channel flume. In particular, the recirculatory pipes of the channel flume were designed to be dual-recirculating configuration by which the inlet and outlet of the channel flume could be mutually converted to produce a bidirectional flow in the test section of the channel flume. The operation procedures in adjusting the time-dependent flow velocity, water depth and flow direction of the channel flume were automatically implemented through a programmable logic control (PLC) system. For the convenience of quantitatively comparison of the diffusive contaminant release properties between the unidirectional unsteady and steady flow conditions, the period-averaged flow velocity (uave) and water depth (have≈ 0.1 m/s) of the unsteady flow were chosen to be the same values as the mean flow velocity (U) and water depth (H=0.1m/s)of the steady flow. The flow unsteadiness was quantified by its flow period (T) and velocity amplitude, i.e., the difference between the maximum velocity (umax) anduavein each period. The mean or period-averaged flow velocity of the overlying water (U=uave=0.1m/s) was selected in such a way that no sediment resuspension occurred during the experiments. For the unidirectional unsteady flow, theumaxranged fromuave=(0.1m/s)to 2uave=(0.2 m/s)to avoid the flow direction reversal and the sediment disturbance, and hence two values (0.15 m/s and 0.2 m/s) were adopted forumaxduring the experiments. The experimental instrument used in the flow field monitoring and measurement was a two-dimensional acoustic Doppler velocimetry (ADV) with the maximum data sampling rate up to 200 Hz.

The artificial sediment samples were prepared with the median grain size of nearly 350 μm. The adsorbed contaminants in the sediment samples were removed by a pre-treatment procedure before the first experimental run. The obtained clean sediment samples were dried and used in each experimental run. For all experimental runs, the dried sediment samples with the same volume (Vs=2.3× 0.25 × 0.05 m3) were put into a adsorption chamber, and the same high concentration phosphorus (P) solution was then metering into the adsorption chamber to soak through the sediment samples for 24 h until an approximate adsorption equilibrium was achieved. After taking out the solute overlying the sediment samples by the siphoning method, the saturated sediment samples were uniformly placed in a cavity with the length of 2.3 m and the thickness of 0.05 m in the middle of the test section of the channel flume, and the planar surface area (As) of the sediment layer was 2.3×0.25 m2. The P concentration of the pore-water in the sediment layer was maintained at the same initial value (Cs0=163mg/L)for all experimental runs. The surface of the underlying sediment layer was manually smoothed by scraping to eliminate the bed topography before each experimental run, and the sediment bed was hydraulically smooth. During the course of each temporal release experiment, the initially P-free overlying water (Cw0= 0 mg/L) with the same volume (V≈ 0.8× 103L) con

wtinuously circulated through the channel flume in a closed loop, and the time-dependent diffusive contaminant release rate from the undisturbed sediment layer could be examined from the measured phosphate concentration variationCw(aqueous concentration) in the overlying water column by using a spectrophoto-meter with a standard procedure (the molybdenum blue/ascorbic acid method)[16]. During the course of the experiments, the aqueous concentrationsCwwas determined based on the mean concentration value of the aqueous samples of different sampling points at the heights of 0.005 m to 0.1 m above the sedimentwater interface.

2. Results and analyses

2.1The gross diffusive release trend under unsteady flow conditions

In general, the mass transfer across the sedimentwater interface depends on several interacting transport processes, among which the molecular diffusion is an important transport process due to the presence of the diffusive boundary layer immediately above the sediment-water interface. The schematic concentration profile of the overlying water near the sediment-water interface for the case of the steady flow is shown in Fig.1. The sharp concentration gradient occurs within the thin diffusive boundary layer, of which the thickness (δc) can be estimated based on the scaling arguments asδc～δvSc-1/3whereδvis the viscous sublayer thickness andScis the Schmidt number (the ratio of momentum to mass diffusivity, i.e.,Sc=v/Din whichvis the kinematic viscosity andDis the molecular diffusion coefficient)[5,8]. For the typical dissolved substances such as dissolved oxygen (DO) or soluble reactive phosphorus (SRP), their Schmidt numbers are commonly relatively large (≫1), e.g.,Sc≈ 500 for DO in water at 20oC.δcis expected to be much smaller thanδv(on the order of one-tenth of the thickness of the viscous sublayer for DO).

Fig.2 The measured concentration variation of overlying water with time

It can be seen from Fig.2 that at the same mean flow velocity (U=uave), the measured P concentration in the overlying water column under the unsteady flow condition is considerably higher than that under the steady flow condition, and the interfacial diffusive release rate for the former exceeds that for the latter by a factor of about 0.76. This indicates that the interfacial diffusive release rate under the unsteady flow condition tends to be substantially enhanced as compared to that under the steady flow at the same mean flow velocity. It can be reasonably extrapolated that the interfacial diffusive release rate under the steady flow may be a lower limit of that under the unsteady flow at the same mean flow velocity (U=uave), which can be approached asymptotically whenT→∞ andumax→Ufor the unsteady flow. It is evident that the intrinsic deviation of the interfacial diffusive release rate under the unsteady flow from that under the steady flow is mainly dependent on the flow period and velocity amplitude, and the additional interfacial diffusive release rate under the unsteady flow relative to the steady flow case may be introduced by the flow unsteadiness of the overlying water column. As a result, the quasi-steady treatment with respect to the mass transfer coefficient or interfacial diffusive flux for the case of the unsteady flow will unavoidably underestimate these values to some extent.

At the same amplitude ofumaxandU(umax=U=0.15 m/s)of the overlying water, the measured P concentration variations with time under the steady and unsteady flows are shown in Fig.3.

Fig.3 The measured concentration variation of overlying water with time

It can be seen from Fig.3 that the diffusive release rate under the unsteady flow atumax=0.15 m/s is appreciably lower in magnitude than that under the steady flow atU=0.15 m/s . This implies that the diffusive release rate under the unsteady flow can be parameterized using the mass transfer model in terms ofkorkeff(effective mass transfer coefficient) since the diffusive release rate under the unsteady flow has not a qualitative change as compared to that under the steady flow. In this regard, the interfacial diffusive release rate under the steady flow with itsUequal toumaxmay be a upper limit of that under the unsteady flow atumax, which can be approached asymptotically whenT→0 andumax→Ufor the unsteady flow. Therefore, the gross interfacial diffusive release rate for the unsteady flow at specificuaveandumaxwill range from that under the steady flow atU=uaveto that under the steady flow atU=umax, depending upon both the period and velocity amplitude of the unsteady flow.

2.2The effect of flow unsteadiness on interfacial diffusive release under unsteady flow conditions

The unidirectional unsteady flow of the overlying water column considered in the experiment is a kind of relatively simplified flow regime with the water depth varying little and without the flow direction reversal. In this case, the mean flow velocity profile along the vertical direction (y) is expected to be somewhat similar to that under the steady flow. The temporal flow velocity at any point can be divided into two components: a period-averaged flow velocityuaveand an approximate sinusoidal velocity fluctuation (umax-uave)sin(2π /T). By comparison, the effect of the flow unsteadiness, including the period (T) and velocity amplitude (represented byumaxfor simplicity), on the interfacial diffusive contaminant release rate is taken into consideration.

Figure 4 shows the measured P concentration variation with time in the overlying water column under the unsteady flow conditions at the same velocity amplitude (umax=0.15 m/s)and various periods (T= 10 min and 30 min).

Fig.4 The measured concentration variation of overlying water with time

It can be seen from Fig.4 that the effect of the period of the unsteady flow on the interfacial diffusive release rate exhibits the comparatively consistenttrend. With the decreasing period, the interfacial diffusive release rate under the unsteady flow tends to increase. It can be inferred that for the slowly varying unsteady flow, i.e., with relatively long period, the diffusive boundary layer is likely to closely follow the transient bottom boundary layer flow variation and tends to be fully developed during the long period. While for the rapidly varying unsteady flow, i.e., with relatively short period, the diffusive boundary layer is merely able to loosely follow the transient bottom boundary layer flow variation and tends to be less developed during the short period. As a result, for the long period the average diffusive boundary layer thickness is in large part imposed by the mean flow velocity and weakly dependent on the flow unsteadiness, and for the short period the diffusive boundary layer thickness is unable to completely response to the temporal flow velocity variation and more strongly dependent on the flow unsteadiness.

At the same period (T=10 min), the effect of the various velocity amplitudes (umax=0.15 m/s and 0.2 m/s) of the overlying water flow on the interfacial diffusive release rate under the unsteady flow is shown in Fig.5.

Fig.5 The measured concentration variation of overlying water with time

It can be seen from Fig.5 that the velocity amplitude of the overlying water flow can also influence the interfacial diffusion release rate to some extent, and with the augmenting amplitude, the interfacial diffusive release rate tends to increase. It should be noted that the effect of the velocity amplitude of the overlying water flow on the interfacial diffusive release rate is closely related to the period variation, and such effect becomes less significant as the period increases. Considering the case in which half the velocity amplitude is equal to the mean flow velocity, i.e.,umax= 2uave, the contribution of the velocity amplitude to the interfacial diffusive release rate is always less efficient as comparing to that of the mean flow velocity for a specific period, and only in the case ofT→0, their contributions to the mass transfer rate across the sediment-water interface is nearly equivalent. While in the case ofT→∞, the velocity amplitude has the weakest effect on the mass transfer rate as compared to the mean flow velocity, and the induced additional interfacial diffusive release rate will be substantially reduced, depending on the periodic curve of the temporal flow velocity variation.

2.3The diffusive contaminant release mechanism analysis under unsteady flow conditions

For the case of the considered unidirectional unsteady flow, the temporal flow velocity or friction velocity of the overlying water column produce a periodic change during each period. It can be expected that the diffusive boundary layer just above the sedimentwater interface is in response to this period-scale flow variability of the overlying water column. On the one hand, the thickness of the diffusive boundary layer is modulated by the periodically changed flow velocity, and the maximum and minimum thicknesses of the diffusive boundary layer alternatively occur during each period, which are imposed by the minimum and maximum flow velocities or friction velocities, respectively. Consequently, the period-averaged thickness of the diffusive boundary layer is dependent largely on the mean flow velocity instead of the velocity amplitude, and such effect on the interfacial diffusive release rate is exclusive of the flow unsteadiness of the overlying water. On the other hand, the influence of the dynamic fluctuation of the diffusive boundary layer on the interfacial diffusive release rate under the unsteady flow should be taken into account. In despite of an absence of the flow reversal in the case of the unidirectional unsteady flow, an alternate acceleration/deceleration change of the overlying water flow during each period will occur. In the acceleration phase, the diffusive boundary layer may be compressed and thinned down. While in the deceleration phase, the diffusive boundary layer may be dilated and thickened. This dynamic fluctuation of the diffusive boundary layer during each period is likely to cause an additional interfacial diffusive release mechanism through the intensified turbulent mixing between the overlying water and the pore-water within the superficial sediment layer. This additional interfacial diffusive release mechanism by which the enhanced mass transfer across the sedimentwater interface under the unsteady flow occurs is more pronounced for the permeable sediment bed with relatively high porosity. In such cases, the mass transfer across the sediment-water interface under the unsteady flow is likely to transit from the water-side controlled transport process to the sediment-side controlled one owing to the additional interfacial mass transfer mechanism responsible for the intensified turbulent mixing induced by the flow unsteadiness. Therefore, the comprehensive interaction between the overlying water and the underlying pore-water shouldbe taken into consideration with regard to quantifying the mass transfer across the sediment-water interface under the unsteady flow.

3. Conclusion

The interfacial diffusive contaminant (phosphorus) release from the permeable sediment layer into the overlying water column under unidirectional unsteady (periodic) flow conditions was experimentally measured and analyzed. The experimental results indicate that the gross diffusive contaminant release rate from the permeable sediment layer into the overlying water column under unsteady flow conditions is shown to be substantially enhanced as compared to that under steady flow condition. This enhancement trend is much more pronounced in an immediate release stage. The interfacial diffusive contaminant release rate tends to increase with the increasing flow velocity, decreasing period and augmenting amplitude for the case of the unsteady flow. The additional interfacial diffusive contaminant release under the unsteady flow condition may be related to the hydrodynamic response of the diffusive boundary layer to the flow unsteadiness in the overlying water column, depending upon not only the periodic thickness variation of the diffusive boundary layer modulated by the temporal flow velocity in the overlying water column but also the intensified turbulent mixing between the overlying water and the pore-water within the superficial sediment layer induced by an alternate acceleration/ deceleration fluctuation during each period.

[1] HUETTEL M., RØY H. and PRECHT E. et al. Hydrodynamical impact on biogeochemical processes in aquatic sediments[J]. Hydrobiologia, 2003, 494(1-3): 231-236.

[2] AREGA F., LEE J. H. W. Diffusional mass transfer at sediment-water interface of cylindrical sediment oxygen demand chamber[J]. Journal of Environmental Engineering, 2005, 131(5): 755-766.

[3] FAN Jing-yu, HE Xiao-yan and WANG Dao-zeng. Experimental study on the effects of the sediment size and porosity on the contaminant adsorption/desorption and interfacial diffusion characteristics[J]. Journal of Hydrodynamics, 2013, 25(1): 20-26.

[4] GAO Zeng-wen, ZHENG Xi-lai and ZHAO Quansheng. Diffusive boundary layer and its resistance on salt release from deposited sediments in a polder reservoir[J]. Advances in Water Science, 2010, 21(2): 255-260(in Chinese).

[5] STEINBERGER N., HONDZO M. Diffusional mass transfer at sediment-water interface[J]. Journal of Environmental Engineering, 1999, 125(2): 192-200.

[6] EEK E., CORNELISSEN G. and BREEDVELD G. D. Field measurement of diffusional mass transfer of HOCs at the sediment-water interface[J]. Environmental Science and Technology, 2010, 44(17): 6752-6759.

[7] QIAN Jin, ZHENG Sha-sha and WANG Pei-fang et al. Experimental study on sediment resuspension in Taihu Lake under different hydrodynamic disturbances[J]. Journal of Hydrodynamics, 2011, 23(6): 826-833.

[8] DADE W. B. Near-bed turbulence and hydrodynamic control of diffusional mass transfer at the sea floor[J]. Limnology and Oceanography, 1993, 38(1): 52-69.

[9] INOUE T., NAKAMURA Y. Effects of hydrodynamic conditions on DO transfer at a rough sediment surface[J]. Journal of Environmental Engineering, 2011, 137(1): 28-37.

[10] FRIES J. S. Predicting interfacial diffusion coefficients for fluxes across the sediment-water interface[J]. Journal of Hydraulic Engineering, 2007, 133(3): 267-272.

[11] CHATELAIN M., GUIZIEN K. Modelling coupled turbulence-dissolved oxygen dynamics near the sedimentwater interface under wind waves and sea swell[J]. Water Research, 2010, 44(5): 1361-1372.

[12] LORKE A., MÜLLER B. and MAERKI M. et al. Breathing sediment: The control of diffusive transport across the sediment-water interface by periodic boundary-layer turbulence[J]. Limnology and Oceanography, 2003, 48(6): 2077-2085.

[13] WANG Jia-ning, ZHAO Liang and WEI Hao. Variable diffusion boundary layer and diffusion flux at sedimentwater interface in response to dynamic forcing over an intertidal mudflat[J]. Chinese Science Bulletin, 2012, 57(13): 1568-1577.

[14] HIGASHINO M., STEFAN H. G. and GANTZER C. J. Periodic diffusional mass transfer near sediment/water interface: Theory[J]. Journal of Environmental Engineering, 2003, 129(5): 447-455.

[15] HIGASHINO M., GANTZER C. J. and STEFAN H. G. Unsteady diffusional mass transfer at the sediment/ water interface: Theory and significance for SOD measurement[J]. Water Research, 2004, 38(1): 1-12.

[16] ZHANG Kun, CHENG Peng-da and ZHONG Baochang et al. Total phosphorus release from bottom sediments in flowing water[J]. Journal of Hydrodynamics, 2012, 24(4): 589-594.

[17] GRANT S. B., STEWARDSON M. J. and MARUSIC I. Effective diffusivity and mass flux across the sedimentwater interface in streams[J]. Water Resources Research, 2012, 48(5): W05548.

10.1016/S1001-6058(14)60106-2

* Project supported by the National Natural Science Foundation of China (Grant Nos. 11032007, 11472168), the Shanghai key Laboratory of mechanics in energy Engineering and Shanghai Program for Innovative Research Team in Universities.

Biography: FAN Jing-yu (1968-), Male, Ph. D.,

Associate Professor

WANG Dao-zeng,

E-mail: dzwang@staff.shu.edu.cn