Changes in the critical erosion velocity for sediment colonized by biofilm

Authors


Abstract

In flowing water the incipient motion of sediment can be affected by the presence of microbial biofilm growth. This article documents a series of flume experiments using non-uniform sediments, in which sediment entrainment was investigated for cases where the sediment was immersed in deionized water, so that no biofilm developed, and for cases where a bio-sediment was cultivated by placing the sediment in a mixture of natural water and nutrient solution. Differences in entrainment and the velocity at incipient motion were measured over an eight week period, as biofilm grew. It was found that the incipient motion phenomena were quite distinct between the two kinds of sediment. Sediment with biofilm was more stable and, over time, incipient velocity increased to a threshold level, before declining. Biofilm development is clearly an important control on the stability of sediments, especially in eutrophic water bodies. Two incipient velocity formulas were derived for sliding and rolling conditions. Film water theory was utilized to describe the cohesive force between sediment particles and the adhesive force generated by biofilm was introduced into the formula derivation; the time variation characteristics of biofilm strength and the features of the substrate were also taken into consideration. Such analyses can help to predict sediment transport changes due to biofilm presence in nutrient-rich water bodies.

Introduction

Sediment incipient motion conditions are important in fluvial processes and sedimentation. A considerable number of experimental and theoretical studies have been conducted on the incipient motion conditions of sediments, especially non-cohesive particles. Sediment particles start to move only when the bed shear stress or current velocity exceeds a certain value. It is generally accepted that the forces which tend to resist particle movement are particle weight and the forces generated by interaction with neighbouring particles. However, in recent years, the importance of biogenic sediment stabilization, which is mainly due to the biofilm produced by microbes (such as bacteria, microalgae and fungi) has been increasingly noted (Andersen, 2001; Stal, 2003; Andersen et al., 2005; Gerbersdorf et al., 2008; Huang et al., 2012). The discrepancy in critical erosion velocity and settling velocity between biogenic and normal sediment eventually leads to different sedimentation processes and geomorphology (Fang & Wang, 2000).

In aquatic ecosystems, nutrient enrichment encourages microbes to grow on solid surfaces. The production of extracellular polymeric substances (EPS) often forms a relatively stable sediment surface and generates a binding force between particles. These phenomena change the structure and morphology of exposed sediments leading to a higher incipient motion threshold. Many studies of biofilm effects have been undertaken in marine areas. For example, Grant & Gust (1987) tested the coastal sediment affected by purple sulphur bacteria and found that the erosion threshold was as much as five times higher compared with sterile sediments. Yallop et al. (1994) measured the incipient shear stress of marine non-cohesive and cohesive sediments in situ and found that they were ca 9·6 times and 2·9 times higher, respectively, than for sediment without biofilm. Tolhurst et al. (2008) investigated the development of biofilm and the erosion threshold of sediments cultivated in sea water over 45 days and showed that the erosion threshold tended to increase with time. While field data have shown that microbial coatings can enhance the stability of sediment, some researchers (e.g. Stal, 2003) have questioned the relation between biofilm and the stability of intertidal sediments. The effect of biofilm on the roughness coefficient and critical shear stress needed to move particles in sewer pipes has also been considered (Chen et al., 2003; Guzman et al., 2007).

The effect of biofilm on incipient motion in fresh water systems also requires attention and explicit predictive formulas are required. Compared with marine research, few studies have been completed in fresh water systems. It is notable that the physico-chemical and biological environments in fresh water are different from that of marine environments because the grains and surface sedimentary characteristics of the sea bed are significantly affected by the salinity of the water (Fang et al., 2009). Biofilm affects bed properties in fresh water systems without the influence of high salinity. Battin et al. (2003) and Besemer et al. (2007) investigated the effect of flow on biofilm cultivated in stream water and presented evidence that biofilm growth was thicker and less strong under slow flow regimes. Other research focused on bio-stabilization. Gerbersdorf et al. (2008) studied the stability of sediment sampled from near-bank regions along vertical profiles, and found that, with depth, micro-organisms can increase resistance to sediment. Vignaga et al. (2009) examined the bio-stabilization of substrate (comprised of 1·09 mm glass spheres, instead of natural sediment particles) using biofilm grown for one to ten weeks in fresh water. These authors found that biofilm increased the critical shear velocity of particles by 23 to 77% and that the threshold reached its maximum within a four-week colonization period. Righetti & Lucarelli (2007) proposed an extension of the Shields criterion to cohesive and adhesive benthic sediment and validated it using measurements of the the incipient motion of field samples from seven lakes. Their theoretical contributions are highlighted below. Further work by Righetti & Lucarelli (2009) applied their formulation in laboratory resuspension experiments designed to establish the link between biological adhesion in lacustrine sediments and trophic state. These experiments showed that biological adhesion is linked to the life and growth of phytoplankton and bacteria.

In summary, there are few methods available to determine the incipient velocity of sediment after biofilm colonization in fresh water systems. In order to establish a predictive formula for incipient velocity, the relation between biofilm properties and the basic sediment particles on which biofilm grows must be considered (i.e. sediments of different sizes need to be grouped) and established theory should be utilized to calculate the cohesive forces between particles. Laboratory flume experiments provide a useful method of capturing data on non-uniform sediment entrainment after biofilm colonization by avoiding factors that might interfere with relevant measurements in the field. In addition, there is only a limited amount of information on how biofilm colonization over an extended period of time affects incipient motion. This is important because it takes into account the fact that biofilm development is a dynamic process in rivers and lakes, such that biofilm ultimately becomes mature and stable.

In view of the foregoing considerations, the biofilm effect on two different non-uniform bed particle size groups was investigated for fresh water environments using flume experiments. The sediment samples were cultivated in standing water and incipient motion conditions were evaluated over a period of eight weeks. Formulae for predicting the incipient motion velocity of biofilm-affected fresh water sediments were subsequently derived using dimensional analysis and force analysis for sliding and rolling conditions, respectively.

Experimental Setup and Procedure

Sample preparation

Sediment was collected from the stabilization pond of Guanting Reservoir, Beijing, China and sorted into two groups: finer than 0·05 mm and 0·05 to ca 0·1 mm. The median diameters of the two grain-size categories are 0·035 mm and 0·077 mm, respectively, as measured by a laser diffraction size analyzer. According to the classification standard (see Chien et al., 1999), the finer group belongs to silt, because the silt content (0·005 mm < d < 0·05 mm) in the samples is over 95% and the clay content (d < 0·005 mm) is less than 3%. The coarser group belongs to sand: the clay content is less than 3%; the silt content is less than 16%; and the sand content (0·05 mm < d < 2 mm) is over 81%.

Sediment samples were immersed in two types of water: one was oligotrophic deionized water to provide sediment without biofilm colonization; the other was a mixture of natural lake water (Lotus Pond, located in the west of Tsinghua University) supplemented by a nutrient solution, which allowed biofilms to be cultured on the sediments. Lotus Pond covers an area of 2·3 hectares and some domestic waste water from the university discharges into the pond. The water quality has been tested, and the organic fractions are as follows: the total natural microflora is 22 600 per ml in summer and 15 800 per ml in winter; CODMn index (chemical oxygen demand by permanganate) is 2·81 mg l−1.

The sediment samples were mixed with water and loaded into boxes made of plexiglass and allowed to stand for one day. The boxes were then placed into two separate tanks. One tank was filled with deionized water and the other with the nutrient-rich mixture. The latter supplies sufficient nutrition to maintain natural microbe concentrations in fresh water and supports natural growth processes on sediment substrate. The nutritional solution compositions were proposed by Wu et al. (2005) and optimized by Zhao (2009) as: glucose 0·5 g l−1; potassium dihydrogen phosphate (KH2PQ4) 0·05 g l−1; sodium bicarbonate (NaHCO3) 1·0 g l−1; anhydrous magnesium sulphate (MgSO4) 0·05 g l−1; ammonium chloride (NH4Cl) 0·1 g l−1; and calcium chloride (CaCl2) 0·015 g l−1. In each tank, eight samples of each grain-size group were immersed, and then were soaked for one, two, three, four, five, six, seven and eight weeks, respectively, to prepare the samples for the flume experiments. Water temperature in the tanks was 15 ± 1°C and, because temperature is an important environmental factor that affects biofilm growth, the laboratory was kept at a relatively uniform temperature suitable for microbial activities.

Flume experiment

The incipient motion velocity experiments were conducted in a glass-sided, 16 m long by 0·5 m wide and 0·6 m deep, water recirculating flume with a fixed bed slope of 0·85‰. The floor of the flume was tiled with 0·04 m thick terrazzo. Two recesses were set symmetrically along the centreline in order to compare the different incipient motion processes with and without biofilms, as shown in Fig. 1.

Figure 1.

Top view of observation section (unit: mm).

The biofilm growth and its strength are dynamic processes varying with time. The incipient motion velocity was measured once per week. In weeks one, two, three, four, five, six, seven and eight, the sediment samples of the same size group immersed in the two kinds of water were taken out of the holding tanks, and then put into the two grooves of the flume.

Measuring instrument and methods

Two methods have been used to establish a threshold for incipient motion of sediment (Dey, 1999). These are based on sediment flux (Shields, 1936) and bed particle motion (Kramer, 1935). Here, the critical threshold of incipient motion was defined as occurring when ‘weak transport’ commenced; that is when 20 or more particles were simultaneously in motion across the surface of a box. Particle-image velocimetry (PIV) and an automated software routine were used to determine that particles were in motion. The criteria were the same for samples with and without biofilms.

Given the flume width of 0·5 m, water depths were chosen to be ca 0·1 m in order to achieve a width/depth ratio of approximately 5 and so guarantee a two-dimensional steady flow. Discharge was controlled by an electric pump and was measured by an electro-magnetic flow-meter. Water-level point gauges were used to measure the water depth. Reynolds number, Re, remained above 10 000 and Froude number, Fr, was consistently less than 1. During each experiment, the flow was slowly increased until the incipient motion velocity was reached. An Acoustic Doppler Velocimeter was used to measure the mean velocity in section, with the probe fixed at a relative water depth of 0·6. Because the flow was fully turbulent, the mean section velocity is a reliable parameter to reflect the incipient motion condition.

Experimental results and analysis

Experimental phenomena

For the sediments cultured in nutrient solution, biofilm gradually covered the surface. The surface colour changed from yellowish-brown to brown and finally dark brown after six weeks of cultivation. Similar surface change characteristics were observed by Graba et al. (2010). Protozoa and metazoa are visible in the nutrient mixture about two weeks later, mostly copepods and flagellates, which are the main consumers of microbes and organic matter. These organisms form an integrated ecosystem together with the bacteria and algae. In contrast, the surface of samples soaked in deionized water was unchanged, except that the colour gradually deepened into grey after four weeks. The colour change may be due to the non-aseptic environment leading to redox reactions, which is consistent with the natural aquatic environments.

Variation of incipient velocity with cultivation period

The development of a biofilm mat stabilizes sediment against entrainment. As velocity above such a stabilized bed is increased, the flow strips the biofilm mat from the surface exposing biofilm filaments rooted in the sediments. Particles are bound together and sediments are difficult to erode. The network of filamentous biofilm is obvious and intensive for the first five weeks and then gradually decreases. Evidently, as the biofilm grows thicker, the lower layer of biofilm dies as microbes near the sediment surface are unable to obtain adequate nutrients and convert into a non-active substance.

Table 1 contains the experimental results, and it is apparent that the biofilm contributed to sediment stability and led to higher entrainment thresholds (Fig. 2). Figure 2 also shows that the sediment stability varied with the temporal development of biofilm. For the sediments cultured in the nutrient mixture, the incipient velocity increased by about 60%, 70%, 45% and 40%, respectively, after two, four, six and eight weeks of colonization compared with sediment without biofilm. Sediment stability therefore reached its maximum after four weeks, when the biofilm strength apparently reached its optimum as a function of its maturity and structural development. Subsequently, the armouring effect of biofilm weakened a little and maintained a relatively stable value after six weeks of cultivation.

Table 1. Incipient motion criteria for sediments colonized (a) and sediments not colonized (b) by biofilm
Sediment sampleTime (week)Discharge (l s−1)Depth (m)Mean velocity (m s−1)Shear velocity (m s−1)Re (×104)Fr
(a)
<0·05 mm116·10·10000·3240·01562·310·33
 217·20·09950·3470·01662·470·35
 318·00·09950·3660·01742·600·37
 418·00·10050·3670·01742·630·37
 516·50·09900·3580·01712·540·36
 615·20·10000·3190·01542·280·32
 715·40·10100·3170·01532·280·32
 815·20·10000·3170·01532·260·32
0·05 to 0·1 mm114·60·09900·2790·01352·010·28
 216·10·10100·3000·01492·160·30
 316·20·10100·3030·01512·180·30
 416·30·10100·3040·01532·190·31
 515·90·10100·2970·01432·140·30
 614·30·10000·2690·01301·930·27
 714·00·10000·2640·01231·900·27
 813·50·10050·2530·01181·820·25
(b)
<0·05 mm112·00·10100·2350·01171·690·24
 212·40·10050·2400·01191·720·24
 312·20·10000·2330·01161·660·24
 412·30·09950·2430·01211·730·25
 512·00·10050·2340·01171·680·24
 612·50·10100·2410·01201·730·24
 712·60·10100·2400·01191·730·24
 812·90·10000·2510·01241·790·25
0·05 to 0·1 mm19·50·09950·1880·00961·340·19
 29·80·10100·1820·00931·310·18
 310·00·10100·1890·00961·360·19
 49·60·10100·1870·00951·340·19
 59·40·10100·1810·00931·300·18
 69·70·10100·1870·00961·350·19
 79·50·10100·1820·00931·310·18
 89·80·10050·1810·00931·290·18
Figure 2.

Experimental results of incipient velocity for the sediment with or without biofilm.

Variation for different sediment size groups

The erosion processes of the two groups were quite different. For the coarser group, sediment erosion tended to be synchronous with failure of the mat-like biofilm. In contrast, for the finer group, the initiation movement tended to occur at higher velocities than those required for detachment of the matted biofilm. As a result, the armouring effect of biofilm is not quite so obvious for the finer group; here, additional stability is imparted by the network of filamentous biofilm formed between particles, permeating the void spaces and enhancing adhesion between particles.

Theoretical Analysis

Based on the experiment, theoretical analysis for achieving a formula for incipient velocity of sediment after biofilm colonization can be performed. The incipient motion conditions are usually expressed in three interchangeable forms: critical shear stress, mean velocity in section and incipient motion power.

For non-cohesive sediments, the well-known Shields curve (Shields, 1936) shows the relation between incipient motion condition Shields number and particle Reynolds number. Numerous additions, revisions and modifications have been applied to the Shields curve since its publication (Miller et al., 1977). In comparison with non-cohesive particles, the incipient motion of sediments consisting of cohesive particles, and methods of linking the threshold condition of cohesionless and cohesive sediments, are relatively less well-understood. To unify entrainment in a rigorous way is quite difficult. Lick et al. (2004) developed a threshold criterion formula which was uniformly valid for quartz particles ranging from cohesive to non-cohesive particles, but the application of the formula is restricted to conditions similar to the data sets from which they were generated. Cheng & Chiew (1999) formulated an incipient sediment motion with upward seepage. Several researchers took cohesive forces into consideration and developed formulas applicable to both cohesive and non-cohesive sediments. All of these formulas, which consider cohesive forces, and are applicable to both cohesive and non-cohesive sediments, are summarized in the book by Chien et al. (1999), and properly belong to the class of semi-theoretical and semi-empirical formulas, which calculate incipient velocity for sediments in agreement with experimental data. Recent research on incipient motion conditions generally focuses on the threshold criterion discussion (Rao & Sreenivasulu, 2009; Patel et al., 2010) and the interactions between sediment and the aquatic environment (Bobertz et al., 2009), especially between sediment and microbes, but few formulas have been proposed.

The problem becomes more complicated when biofilm exists. Microbial activities are especially obvious and intense at the interface of water and sediments. As a result, a biofilm can bind particles together and can be denoted as a biological adhesive force (Lick et al., 2004; Righetti & Lucarelli, 2007). Since the binding agents form in the sediment matrix, the sediment incipient motion is governed not only by hydrodynamic forces and by electrochemical forces between particles, but also by the forces generated by biofilm. Considering two cases of incipient sediment motion, sliding and rolling, the formulae calculating incipient velocity of biofilm-affected sediment are presented below.

Incipient velocity of sliding

In the critical condition of sliding, the drag force and the frictional force are under equilibrium. The forces acting on a single particle in fluid flow are shown in Fig. 3A: the effective gravity force FA, the drag force FD, the lift force FL, the frictional force Ff, the cohesive force F*, and the adhesive force due to biofilm FA. The force equilibrium equation of the incipient motion condition is:

display math(1)

in which:

display math(2)
display math(3)
display math(4)

where: u* is the shear velocity; ρs is sediment density; ρ is the water density; g is gravitational acceleration, L × T−2; C1 and ηC1 are the drag and lift coefficients, respectively; α3 is the volumetric shape factor, which can be considered equal to π/6 for spheres; and d is the particle diameter (L).

Figure 3.

Forces acting on a sliding (A) and rolling (B) particle in a fluid flow.

Israelachvili (1997) found that the cohesive inter-particle forces are mainly due to van der Waals forces, and that the cohesive force is directly proportional to particle diameter, which is consistent with the film water theory. Both van der Waals forces and film water theory are established on the basis of the electrical charge effect, but the calculations of film water theory are easier to determine. Therefore, the film water theory has been applied here. According to the film water theory, for a sediment particle immersed in water, a thin layer of water covers its surface, when two particles contact each other an interface forms between them, and a cohesive force of molecular scale is generated at the interface. Theoretical and experimental investigations enable the cohesive forces to be quantified in the form of Eq. (5). Dou (1960) developed an alternative formula (Eq. (6)) by detecting the frictional resistance of cross-quartz filaments. The current paper continues to use the formulas and hypotheses applied by Dou and Tang, (see Chien et al., 1999):

display math(5)
display math(6)

where: F* is cohesive force; H is the water depth (L); Ha is the head of water equivalent to the atmospheric pressure (L); Ak is the area of interface between two particles (L2); and ξ is the resisting moment per unit area due to cohesion (M T−2).

Dou (1960, see Chien et al., 1999) obtained the following expression for the effective contact area between particles:

display math(7)

where: δ is the diameter of a water molecule (= 3 × 10−8 cm); and k1 to k4 are constants that were determined from experimental measurements and th indicates the hyperbolic tangent function: th(x) = (ex − e−x)/(ex + e−x).

The adhesive force as a kind of surface force is usually assumed to be vertical downward, and it can be expressed with the square of particle diameter (Israelachvili, 1997; Lick et al., 2004):

display math(8)

where: FA is adhesive force produced by biofilm; and A is the adhesion coefficient (M L−1T−2).

Combining Eqs (2) to (4) and (6) to (8) with Eq. (1), the following relation is obtained:

display math(9)

Consider H ≪ Ha, therefore, th(H/Ha) ≈ H/Ha and (H/Ha)2 is negligible, Eq. (9) can be rewritten as:

display math(10)

The mean velocity in section Uc can be written as Eq. (11), where the coefficients a1 to a5 are proportional to those in Eq. (10):

display math(11)

where: γ = ρg is water bulk density (M L−2 T−2), A′ = a5 × A; a1 = 6.25, a2 = 41.6, a3 = 111, a4 = 740.

The parameter A′, which represents biofilm effects, is a function of time. When t = 0 there is no biofilm colonization and A′ = 0, then Eq. (11) can be rewritten as:

display math(12)

The adhesive force not only varies over time, but also relates to the substrate characteristic of the biofilm, which was assumed to be a function of particle size in this paper. It seems that the smaller the particle, the stickier the biofilms that form at the sediment–water interface, and this may be because the microbe colonization is greatly affected by the primary particle specific surface area. So, the particle size needs to be taken into account. The bell-shaped fitting formula A′(t) = β1 · t · exp(1 − β2t) taking time into consideration can be recomposed in the form of A′(t) = β1 · d−β2 · t · exp(1 − β2t), where β1 to β3 are the coefficients. Using the data of bio-sediment measured in this work, the resulting equation (R2 = 0.86) is:

display math(13)

where d is the particle diameter in centimetres, has units of unit g cm−1 s−2 and t represents the time (in weeks).

Substituting Eq. (13) into Eq. (11), the incipient velocity formula in the sediment–water interface is:

display math(14)

where Uc is the incipient mean velocity in cm s−1.

Incipient velocity of rolling

Forces acting on a single particle under the condition of rolling can be seen in Fig. 3B (‘u’ shows the direction of fluid flow). At initiation of movement of the particle, the balance between the overturning and restoring moments about the rotation point can be expressed as:

display math(15)

where a and b are the distances of the horizontal and vertical forces to the rotation point.

Based on the threshold criterion for incipient motion of sediments developed by Righetti & Lucarelli (2007), substituting Eqs (2) to (5) and Eq. (8) into Eq. (15), and noting that math formula then the Shields number is:

display math(16)

where τc is the critical shear stress (M L−1 T−2).

Following Righetti & Lucarelli (2007), for coarser particles, when the cohesion and adhesion can be ignored, the critical Shields number for non-cohesive sediment reduces to:

display math(17)

Equation (16) can then be rewritten as:

display math(18)

The critical Shields number for microbial affected sediments consists of three parts: the non-cohesive part ΘCO, the cohesive part ΘC* and the adhesive part ΘCA. Substituting the cohesive force Eq. (5) and adhesive force Eq. (8), then the last two parts can be written, respectively, as:

display math(19)
display math(20)

where C* is defined as the cohesive coefficient (see Righetti & Lucarelli, 2007).

By comparing formula Eq. (19) with Eq. (18), transformed from the equation of Tang (1963, see Chien et al., 1999), it can be derived that C* is dimensionless and is equal to 9·06 × 10−5/(ρs − ρ)d2):

display math(21)

where c is equal to 2·9 × 10−4 g cm−1, and all the parameters' units are denoted with units of grams and centimetres.

According to Eqs (18) to (20), regardless of whether the exponential law of velocity distribution or the logarithmic velocity distribution is used, the incipient velocity formula takes the following expression:

display math(22)

In the above, the adhesive coefficient A can be estimated with the experimental data. The fitting formula is Eq. (23) (as shown in Fig. 4, R2 = 0.85) using the same fitting formula as the sliding initiation condition:

display math(23)

where A(t) is the adhesive coefficient in g cm−1 s−2, and d in centimetres; t in weeks, ∈(0,8).

Figure 4.

Adhesion coefficient as a function of time and particle size: (A) and (B) represent <0·05 mm and 0·05 to 0·1 mm particle group, respectively.

Substituting Eq. (23) into Eq. (22) enables the calculation of critical shear stress and incipient motion velocity. The measured and calculated results fit well, and the fitting formula reflects the bell-shaped trend of adhesive force with time and the effect of the substrate on biofilm adhesion features. The bell-shaped response of adhesion to time is similar to results from Righetti & Lucarelli (2007), in which there was a bell-shaped dependence between adhesion coefficient and organic matter (OM) content.

Discussion

In order to study the applicability of the incipient velocity formulas thoroughly, it is necessary to analyze the relevant factors systematically. The incipient motion conditions for sediment are a function of the characteristics of the sediment (density, size, shape, etc.), the fluid (density and viscosity) and the flow conditions (average velocity or shear stress). Gravity, cohesive and adhesive forces are responsible for preventing particle movement while forces generated by the flow promote movement. The roles of the three resistant forces change with the particle size (Fig. 5). For particles bigger than 0·2 mm, gravity gradually takes the dominant role in resistance against particle movement. The value of gravity can be several orders of magnitude larger than that of cohesive and adhesive forces; for particles smaller than 0·01 mm, gravity can be ignored and the cohesive force plays the most important role as the particle size decreases. If 0.01 mm < d < 0.2 mm, the adhesive and cohesive force occupy the dominant position.

Figure 5.

Theoretical effect of particle size on entrainment forces calculated using Eqs (2), (5) and (8).

The drag force and lift force generated by water flow can be expressed as a function of shear stress; the shear stress changes with the average velocity and the sediment over which the water flows. Figure 6 shows calculated estimates of the shear stress for a range of particle sizes under different average velocity calculated by the logarithmic velocity distribution formula (see Eq. (24)); the conditions are: rectangular section, no bedforms, width of water surface = 50 cm, water depth = 10 cm, ρ = 1·0 g cm−3. Due to the viscous sublayer, the shear stress exerted on the bed does not change significantly until particles exceed ca 0·3 mm. For the same mean velocity, the shear stress increases with the increase of roughness when the particles protrude into the turbulent region. This is the reason why the smooth surface of matted biofilm can reduce the forces produced by water flow and provide initial protection for sediment before the failure of biofilm mats. After the failure of biofilm mats, particles with biofilm adhesion continue the resistance:

display math(24)

where: ks is the roughness size, ks = d for uniform sediment particles; R′ is hydraulic radius which corresponds to the grain friction and is equal to R when there are no sand waves; χ is the unique correction value (see Keulegan, 1938; Chien et al., 1999).

Figure 6.

Shear stress estimates calculated using Eq. (24) for different particle sizes under different mean velocities (U represents the mean velocity in section). See text for details.

The incipient velocities of particles for different biofilm cultivation periods, can be calculated using Eq. (22). For ρs = 2·65 g cm−3, water depth = 10 cm and ρ = 1·0 g cm−3. Figure 7 shows incipient velocities after about four weeks and eight weeks of biofilm colonization. The trend in Fig. 7 is consistent with the force analysis. For fine particles (d < 0.01 mm), cohesive force due to the electrochemical interactions plays the dominant role and the biofilm effects are relatively insignificant. However, for particles 0.01 mm < d < 0.2 mm, the adhesive forces due to biofilms play a more important role and, together with cohesive forces, affect the incipient velocity. With increasing particle size, gravity occupies the dominant role among the forces, thus the corrections to the traditional incipient velocity caused by cohesion and adhesion tend to vanish, especially when d > 0.2 mm.

Figure 7.

Incipient velocity versus grain size, estimated from Eq. (22), for different periods of biofilm cultivation (see text for conditions).

Although Eqs (14) and (22) relate the particle diameter directly to the velocity and offer advantages in application, it must be stressed that their application is less universal than the Shields relation. In order to compare the threshold between non-cohesive particles, cohesive particles and sediments colonized by biofilm, data was transformed in terms of Shields number (Θ) and particle Reynolds number (Re*), and the corresponding curves are presented in Fig. 8 where the modified Shields curve is according to Tang (1963) (see Eq. (21)). In Fig. 8, the solid lines show the band of non-cohesive sediment threshold, which is summarized by Miller et al. (1977). The left limb of each curve shows a rising trend with decreasing Re* but the reasons differ. For non-cohesive particles the rising trend is due to the shielding effect of the viscous sublayer, but for the cohesive particles it is because of the effect of cohesion between particles. Another additional rise is added after biofilm colonizing for a certain period. It is apparent that when Re* < 0·5, the differences between thresholds for non-cohesive particles and cohesive particles are quite large. For cohesive particles, at values of about Re* < 1·0, the Shields number rises very sharply due to the cohesive forces which bond grains together at discrete points of contact; as Re* increases, for the larger particles, the sediments behave in a non-cohesive manner, the cohesion effect trends towards vanishing, and this is consistent with the observations of coarser particles. At Re* > 500, the Shields number of the modified Shields curve becomes constant at about 0·045, which is quite close to the value of 0·041 calculated by the formula suggested by Tang (1963, see Chien et al., 1999). As analyzed above, the adhesive forces are affected by the substrate where the biofilm grows. Comparing the curve which considers cohesion only and the curves considering both cohesion and adhesion, it can be concluded that the adhesion effect can be of importance for the region of 0·2 < Re* < 1·0; for larger Re* and smaller, Re* gravity and cohesion dominate, respectively.

Figure 8.

Comparison of threshold curves for incipient motion.

Conclusion

Microbial activities produce biofilms in the water–sediment interface, and the presence of biofilm strongly changes the dynamic characteristics of sediment particles. In this paper, the incipient motion processes of two size groups were observed, comparative experiments were conducted to obtain the differences between samples without biofilm (soaked in deionized water) and samples with biofilm colonization (cultured in nutrient mixture).

The results indicated that the activities of microbes change the morphology and structure of sediments. Basically, the heterogeneous structure of biofilms consisting of a mat-like biofilm and filamentous elements that penetrate into the bed both shelters the substrate from the overlying flow and adds to adhesive forces. Biofilm colonization enhanced sediment stabilization and the impacts of the biofilm varied over time. A trend in incipient velocities over time indicated that biofilm strength increased to a threshold and then declined. Compared with the sediment without biofilm, the incipient velocity of sediment with biofilm was increased by 70% at maximum (after approximately four weeks), and remained 40% higher at eight weeks of colonization.

The experimental results are used to develop theoretical expressions of incipient velocity that include a biofilm effect for particle sliding and rolling. Both cohesion and adhesion are taken into account: film water theory is utilized to simulate the cohesive force and the microbial effect is schematized as an adhesive force. When fitting the cohesive coefficient, the time variation characteristics of biofilm strength and the bed material grain size are taken into consideration. The derived formulas can be used to calculate incipient velocity with biofilm colonization. Further work is needed to establish how biofilm growth and its effects are affected by nutritional conditions and other regional differences. Moreover, in the current paper, the experimental biofilms were cultured in standing water. Because the hydraulic flow condition is one important factor in biofilm growth, further studies considering different hydraulic conditions are also needed.

Acknowledgements

This research is supported by the National Nature Science Foundation (51139003) and National Science and Technology Project (2012AA112508). The authors would like to thank Professor Fu Renshou for very helpful discussions and instructions regarding the experiments. The authors thank the reviewers and editors very much for their constructive suggestions which helped to improve the manuscript.

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