Sediment and Contaminant Transport in Surface Waters - Chapter 4 pptx

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Sediment and Contaminant Transport in Surface Waters - Chapter 4 pptx

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103 4 Flocculation, Settling, Deposition, and Consolidation Much of the suspended particulate matter in rivers, lakes, and oceans exists in the form of ocs. These ocs are aggregates of smaller, solid particles that may be inorganic or organic. The emphasis here is on the dynamics of aggregates that are primarily inorganic — that is, ne-grained sediments. These are especially prevalent in rivers, in the near-shore areas of lakes and oceans, and throughout estuaries. Because they are ne-grained, these sediments have large surface- to-mass ratios and hence adsorb and transport many contaminants and other substances with them as they move through an aquatic system. Flocculation is a dynamic process; that is, ocs both aggregate and disaggregate with time, and their sizes and properties change accordingly. The net rate of change of oc properties depends on the relative magnitudes of the rates of aggregation and disaggregation, with the steady state being a dynamic balance between the two. It is this dynamic nature of a oc that is particularly interesting and one of the major concerns in the present chapter. Section 4.1 considers the basic theory of the aggregation of suspended particles. This is useful for a preliminary understanding of the experimental results on the occulation of suspended particles presented in Section 4.2. As ocs are formed, their sizes and densities change with time and are quite different from the sizes and densities of the individual particles that make up a oc; this greatly modies the settling speed of the oc. Experimental measurements on the settling speeds of ocs are presented in Section 4.3. Based on the elementary theory of aggrega- tion presented in Section 4.1 and especially the experimental data presented in Sections 4.2 and 4.3, numerical models of the aggregation and disaggregation of suspended particles have been developed; these are discussed in Section 4.4. As sediments (both individual particles and ocs) are transported through surface waters, they tend to settle to the bottom. The rate at which they deposit on the bottom depends on the sediment concentration, the settling speeds of the particles and ocs, and the dynamics of the uid. This is discussed in Section 4.5. Finally, as particles and ocs are deposited on the bottom, the bottom sedi- ments consolidate; that is, the bulk density, water content, gas content, and ero- sive strength of the bottom sediments change with depth and time. Information on these processes is given in Section 4.6. © 2009 by Taylor & Francis Group, LLC 104 Sediment and Contaminant Transport in Surface Waters 4.1 BASIC THEORY OF AGGREGATION 4.1.1 C OLLISION FREQUENCY A general formula for the time rate of change of a suspended particle/oc size distribution will be developed later in Section 4.4. However, basic to this general formula and to a preliminary understanding of the experimental work is a knowl- edge of the collision frequency, N ij (the number of collisions occurring between particles in size class i and particles in size class j per unit volume and per unit time). If binary collisions are assumed, N ij can be written as Nnn ij ij i j B (4.1) where C ij is the collision frequency function (volume per unit time) for collisions between particles i and j, and n k is the number of particles per unit volume in size range k. The quantities C ij depend on the collision mechanisms of Brownian motion, uid shear, and differential settling. The original collision rate theories are due to Smoluchowski (1917), and additional work has been performed by Camp and Stein (1943). Ives (1978) presents the expressions for the different collision func- tions as follows. For Brownian motion, BB M ij b ij ij kT dd dd   2 3 2 () (4.2) where k is the Boltzmann constant (1.38 × 10 −23 Nm/nK), T is the absolute tem- perature (in Kelvin), µ is the dynamic viscosity of the uid, and d i and d j are the diameters of the colliding particles. For uid shear, BB ij f i j G dd  6 3 () (4.3) where G (s −1 ) is the mean velocity gradient in the uid. For a turbulent uid, G can be approximated by (F/O) 1/2 where F is the energy dissipation and O is the kine- matic viscosity (Saffman and Turner, 1956). For differential settling, BB P P M RR ij d i j si sj fwij ddw w g dd     4 72 2 () ()( )) 22 2 dd ij  (4.4) © 2009 by Taylor & Francis Group, LLC Flocculation, Settling, Deposition, and Consolidation 105 where w si is the settling speed of the i-th particle/oc, S f is the density of a par- ticle/oc, S w is the density of the water, and g is the acceleration due to gravity. The rst equality is generally true, whereas the second equality is only valid when the densities of all ocs are approximately the same and when Stokes law, Equation 2.4, is valid. A comparison of collision functions for collisions of an arbitrary-size par- ticle with a particle of 1 µm diameter is shown in Figure 4.1(a). For this compari- son, the following data used were: T = 20°C = 293K, G = 200/s, S f =2.65 g/cm 3 , and S w =1.0g/cm 3 . As can be seen, Brownian motion is only important for colli- sions of a 1-µm particle with particles less than 0.1 µm. For collisions of a 1-µm particle with particles between 0.1 and 50 µm, collisions are caused primarily by uid shear, whereas collisions of a 1-µm particle with particles greater than 50 µm are caused primarily by differential settling. As the applied shear decreases, C f will decrease and the range of diameters over which uid shear is dominant in causing collisions will decrease. As the oc density decreases, C d and the effects of differential settling will decrease. Figure 4.1(b) shows the collision functions for collisions of an arbitrary-size particle with a particle of 25 µm. Again, uid shear is the dominant mechanism for collisions of a 25-µm particle with other particles up to 50 µm, whereas differential settling is more important for larger particles. The effects of Brownian motion are negligible.                       FIGURE 4.1(a) Collision function C as a function of particle size: collisions with a 1-µm particle. C f is the collision function due to uid shear, C d is the collision function due to differential settling, and C b is the collision function due to Brownian motion. For these calculations, T = 298K, G = 200/s, and S p − S w =1.65 g/cm 3 . © 2009 by Taylor & Francis Group, LLC 106 Sediment and Contaminant Transport in Surface Waters 4.1.2 PARTICLE INTERACTIONS In the derivation of Equations 4.2 through 4.4 for the collision frequency func- tions, it was assumed that forces between particles were negligible. For predict- ing the rate of collisions between particles, this approximation is quite accurate. For a more accurate analysis of the entire collision process, these forces (which can be both attractive and repulsive) must be considered. It can be shown that these forces somewhat modify the rates of collisions (Friedlander, 1977), but, more importantly, they affect the probability of cohesion of particles during the collision process. The VODL theory by Verwey and Overbeek (1948) and Dar- jagin and Landau has been developed that includes these forces and assists in understanding the cohesion of colliding particles. This theory is only briey sum- marized here; for more details, extensions, and additional theories, see Hiemenz (1986) and Stumm and Morgan (1996). Figure 4.2 is a schematic of the potential energies between two interacting particles. The forces between the two particles are proportional to the slopes of the potential energy curves. The gure shows repulsive and attractive potential energies whose magnitudes decrease as the distance between particles increases. For small separations, on the order of twice the radius of the particles, more com- plex interactions occur; these forces are generally strongly repulsive. The attractive forces are of the van der Waals type. The resultant attractive force is the summation of the pairwise interactions of the molecules making up                       FIGURE 4.1(b) Collision function C as a function of particle size: collisions with a 25-µm particle. C f is the collision function due to uid shear, C d is the collision function due to differential settling, and C b is the collision function due to Brownian motion. For these calculations, T = 298K, G = 200/s, and S p − S w =1.65 g/cm 3 . © 2009 by Taylor & Francis Group, LLC Flocculation, Settling, Deposition, and Consolidation 107 the individual particles. It depends on the molecules making up the individual particles but does not depend signicantly on external parameters. Clay particles (as well as coated, nonclay particles) in solution are normally charged due to unbalanced cations at their surfaces; this leads to a repulsive force between particles. When ions are present in a system that contains an interface, there will be a variation in the ion density near that interface; an electrical double layer results. The net effect of this double layer is to reduce the repulsive force. This force is a function of the charge or potential of the particle as well as the ionic strength (salinity) of the solution. In particular, as the ionic strength of the solution increases, this repulsive force decreases. The net potential energy of two colliding particles is the sum of the repulsive and attractive potentials. In Figure 4.2, the net potential energy is positive at large distances and negative at small distances. A dashed curve has been added to show schematically the bottom of the potential well. Because of the variations in the repulsive and attractive potentials in magnitude and with distance, other forms of potential energy curves also can occur. Possible potential energies for differ- ent ionic strengths (low, medium, high) of the solution are shown in Figure 4.3. For low ionic strength, the maximum potential energy is relatively large and decreases slowly with increasing distance between particles. Because of the large potential energy, the speed of particle aggregation is relatively low because the particles cannot readily overcome this barrier. As the ionic strength increases, the maximum potential energy decreases and the speed of aggregation of particles should therefore increase. In some cases, there may be a secondary minimum (as shown); this is seldom very deep but could possibly explain some weak forms of occulation. For high ionic strengths, the potential energy is negative everywhere and the rate of aggregation should therefore be quite high. As constructed, the Repulsive (electrostatic double layer) Attractive (van der Waals) Distance Net Interaction Potential Energy 2R FIGURE 4.2 Schematic of potential energies between two interacting particles. © 2009 by Taylor & Francis Group, LLC 108 Sediment and Contaminant Transport in Surface Waters depths of the potential wells (the difference between the maximum and minimum potential energies) are approximately the same. 4.2 RESULTS OF FLOCCULATION EXPERIMENTS For aggregation to occur, particles must collide and, after collision, they must then stick together. As described above, the rates at which particles collide are reasonably well understood. However, as particles collide, usually only a small fraction of the collisions actually results in cohesion of the particles; this process is not well understood or well quantied. Because of this, experiments are needed to determine the probability of cohesion and the parameters on which this prob- ability depends. In addition, during transport, the disaggregation of ocs also can occur. This disaggregation is due to uid shear and, most importantly for many conditions, is due to collisions between ocs. The probability of disaggregation and the parameters on which it depends cannot be predicted from present-day theory and thus must be determined from experiments. To quantify the rates of aggregation and disaggregation and determine the parameters on which these processes depend, two types of occulation experiments have been performed. In the rst type of experiment, a Couette occulator was used to determine the effects of an applied uid shear on occulation; uid shear, sedi- ment concentration, and salinity were varied as parameters. In these experiments, differential settling of particles/ocs was inherently present. In the second type of experiment, a disk occulator was used to isolate and hence determine the effects of Potential Energy Low Medium High Distance FIGURE 4.3 Potential energies between two interacting particles for different ionic strengths. © 2009 by Taylor & Francis Group, LLC Flocculation, Settling, Deposition, and Consolidation 109 differential settling on occulation in the absence of an applied uid shear; sediment concentration and salinity were varied as parameters. The emphasis in both sets of experiments was to characterize occulation as a function of time and to determine the effects of uid shear, sediment concentration, and salinity on this occulation. 4.2.1 FLOCCULATION DUE TO FLUID SHEAR A typical Couette occulator is shown in Figure 4.4 (Tsai et al., 1987). It consists of two concentric cylinders, with the outer cylinder rotating and the inner cylinder stationary. In this way, a reasonably uniform velocity gradient can be generated in the uid in the annular gap between the cylinders. The width of the gap is 2 mm. The ow is uniform and laminar for shears up to 900/s, after which the ow is no longer spatially uniform and eventually becomes turbulent for higher shears. For the experiments reported here, the sediments were natural bottom sedi- ments from the Detroit River inlet of Lake Erie. These were prepared by ltering and settling so that the initial (disaggregated) size distribution had approximately 90% of its mass in particles less than 10 µm in diameter. The median diameter of the disaggregated particles was about 4 µm. The experiments were performed at different sediment concentrations; at shears of 100, 200, and 400/s; and in waters of different salinities. Because U = µG and µ is approximately 10 −3 Ns/m 2 , these shears correspond to shear stresses of 0.1, 0.2, and 0.4 N/m 2 . These shear stresses are typical of conditions in the nearshores of surface waters. In open waters, they would be less than this. Particle size distributions were periodically measured during the tests using a Malvern particle size analyzer. As shown by Camp and Stein (1943) and Saffman and Turner (1956), the occulation rate in a laminar ow can be related to the rate in a turbulent ow by replacing the laminar shear by an effective turbulent shear equal to (F/O) 1/2 , where F is the average turbulent energy dissipation rate per unit mass and O is the kinematic viscosity of water. This relation is valid as long as the size of the ocs is less than the size of the turbulent eddies. In isotropic turbulence in open water, Center Shaft End Piece Intake Port Annulus Stop Cock Bearing Seal 2.5 cm 25.4 cm 2.3 cm Hose Gear FIGURE 4.4 Schematic of Couette occulator. (Source: From Tsai et al., 1987. With permission.) © 2009 by Taylor & Francis Group, LLC 110 Sediment and Contaminant Transport in Surface Waters this size is given by the Kolmogorov microscale of turbulence. For estuaries and coastal seas, the eddies are on the order of a few millimeters or larger (Eisma, 1986). In the bottom benthic layer, the turbulence is no longer isotropic, but eddy sizes are generally 1 mm or larger. Because the sizes of the ocs in the present experiments are less than 400 µm, and generally much less, the above relation is generally valid and the conditions in the occulator can be related to turbulent ows in rivers, lakes, estuaries, and oceans. In occulation experiments, some investigators have used a tank with some sort of agitator or blade. Flows in this type of apparatus are turbulent but far from uniform, with very high shears produced near the agitator and generally quite low shears elsewhere. The high shears will dominate the aggregation–disaggregation processes. Because of this, the effective shear will be much higher (by an unde- termined amount) than the average shear, and therefore the use of the average shear in correlating the experimental results is not accurate. In the rst set of experiments described here (Tsai et al., 1987; Burban et al., 1989), tests were conducted with identical sediments in fresh water, in sea water, and in an equal mixture of fresh and sea water so as to mimic estuarine waters. In fresh water, the rst tests were double shear stress tests and were done as follows. The sediments in the occulator were initially disaggregated. The occulator was then operated at a constant shear stress for about 2 hr. During this time, the sediments occulated, with the median particle size initially increasing with time and then approaching a steady state in which the median particle size remained approximately constant with time. For the conditions in these experiments, this generally occurred in times of less than 2 hr. After this, the shear stress of the occulator was changed to a new value and kept there for another 2 hr. Again, after an initial transient of less than 2 hr, a new steady state was reached. The initial shears were 100, 200, and 400/s and these were changed to 200, 400, and 100/s, respectively. For each shear, the experiments were run at sediment concentrations of 50, 100, 400, and 800 mg/L. For fresh water and a sediment concentration of 100 mg/L, the median particle diameters as a function of time are shown in Figure 4.5. The initial diameters were about 4 µm. For each shear, the particle size initially increased relatively slowly. After about 15 minutes, the size increased more rapidly but then approached a steady state in about an hour. After the change in shear stress, a transient occurred, after which a new steady state was reached. For a particular shear stress, the median par- ticle size for the second steady state is approximately the same as the median particle size after the rst steady state. These results, along with results of other experiments of this type, indicate that the steady-state median particle size for a particular shear is independent of the manner in which the steady state is approached. From Figure 4.5 it can be seen that both the steady-state oc size and the time to steady state decrease as the shear increases. From observations of the ocs as well as measurements of settling speeds (see Section 4.3), it can be shown that the ocs formed at the lower shears are ufer, more fragile, and have lower effective densities than do the ocs formed at the higher shears. The steady-state size dis- tribution for each shear is shown in Figure 4.6. © 2009 by Taylor & Francis Group, LLC Flocculation, Settling, Deposition, and Consolidation 111 0 0 20 40 60 80 100 120 100 200 Time (min) Median Floc Diameter (µm) Stress change 100 s –1 100 s –1 200 s –1 200 s –1 400 s –1 400 s –1 FIGURE 4.5 Median oc diameter as a function of time for a sediment concentration of 100 mg/L and different uid shears. Detroit River sediments in fresh water. Fluid shears were changed at times marked by an . (Source: From Tsai et al., 1987. With permission.) 0 10 100 0 10 20 30 100 s –1 200 s –1 400 s –1 Floc Diameter (µm) Percent by Volume FIGURE 4.6 Steady-state oc size distribution for a sediment concentration of 100 mg/L and different uid shears. Fresh water. (Source: From Tsai et al., 1987. With permission.) © 2009 by Taylor & Francis Group, LLC 112 Sediment and Contaminant Transport in Surface Waters In most experiments, single shear stress tests were done rather than dou- ble shear stress tests. To illustrate the effects of sediment concentration on occulation, results for single shear tests in fresh water, a uid shear of 200/s, and sediment concentrations of 50, 100, 400, and 800 mg/L are shown in Fig- ure 4.7. For other shears and sediment concentrations, the results are similar and demonstrate that, as the sediment concentration increases, both the steady-state oc diameter and the time to steady state decrease. This dependence on sedi- ment concentration is qualitatively the same as the dependence on uid shear (compare Figures 4.5 and 4.7). Tests similar to those described above were done with the same sediments in sea water. The sediment concentrations ranged from 10 to 800 mg/L and the shears varied from 100 to 600/s. Results of one set of experiments at an applied shear of 200/s and different sediment concentrations are shown in Figure 4.8. In general, as for fresh water, an increase in uid shear and sediment concentration causes a decrease in the steady-state oc size and a decrease in the time to steady state. For tests with a 50/50 mixture of fresh water and sea water (Burban et al., 1989), results for the steady-state oc size and the time to steady state were approximately the average of those for fresh water and sea water. This indicates that these quantities in estuarine waters of arbitrary salinity between that of fresh water and sea water are approximately weighted averages of these same quantities for fresh and sea waters. 0 0 20 40 60 80 100 120 100 15050 Time (min) Median Floc Diameter (µm) 50 mg/L 100 mg/L 400 mg/L 800 mg/L FIGURE 4.7 Median oc diameter as a function of time for a uid shear of 200/s and differ- ent sediment concentrations. Fresh water. (Source: From Tsai et al., 1987. With permission.) © 2009 by Taylor & Francis Group, LLC [...]... at the end of this chapter that Equation 4. 43 can be transformed into the general form d d (1 ) (4. 46) where and are defined by Equations A.2 and A.3, respectively, and where depends on a2 and b2 When A* and D* are constants, = 2 Exact analytic solutions to Equation 4. 46 are possible when is an integer For = 1, 2, and 3, the solutions are given in Appendix A and shown in Figure 4. 21 It can be seen... comparison with the original formulation, Equation 4. 17, the above equation is quite simple and, in particular, the computation times are less by several orders of magnitude The present approach is therefore quite efficient and suitable for use in calculating sediment and contaminant transport in surface waters 4. 4.3 A VERY SIMPLE MODEL For exploratory purposes and as a first approximation in transport problems... described in Section 4. 2, analytic results for d(CG) and d(C) when fluid shear is dominant and when differential settling is dominant can be obtained from the experimental results and are shown in Figures 4. 10 and 4. 14, respectively An approximate analytic relation for d that is more general and includes these relations can be obtained from the steady-state results implied by Equation 4. 49, that is,... first evaluating D*/A* from the steady-state experimental results and then evaluating A*(d) from the time-dependent experimental results However, it should be realized that although fluid shear may be dominant in some experiments but not present in others, differential settling is inherently © 2009 by Taylor & Francis Group, LLC 138 Sediment and Contaminant Transport in Surface Waters present in all experiments... reciprocal seconds (s-1), and C is in grams per cubic centimeter (g/cm3) The above equation is uniformly valid for all values of C and CG It accurately reproduces all the experimental results (for fresh water) for d and Ts shown in Figures 4. 10 and 4. 11 (when fluid shear is dominant) and in Figures 4. 14 and 4. 15 (when differential settling is dominant) It also accurately describes the transition in experimental... settling, Equation 4. 4 gives d 4 (d i d j )2 wsi wsj (4. 31) where the settling speed can be approximated by Equation 4. 10 and is wsi ad im (4. 32) If all particles are exactly the same size and density and hence have the same settling speed, then d = 0 and there is no contribution of differential settling to dN/dt in this limit As the difference in particle sizes increases, the difference in settling... on salinity is unlikely as a cause in the formation of a turbidity © 2009 by Taylor & Francis Group, LLC 122 Sediment and Contaminant Transport in Surface Waters maximum in estuaries; see Eisma (1986) for a similar conclusion Of much more importance in causing changes in flocculation in an estuary are the changes in shear stress (turbulence) and sediment concentration, both generally decreasing as... 0 200 40 0 G (s–1) FIGURE 4. 19 Settling speeds of steady-state median diameter floc produced at a concentration of 100 mg/L as a function of shear © 2009 by Taylor & Francis Group, LLC 126 Sediment and Contaminant Transport in Surface Waters zero, the settling speed first decreases rapidly and then increases slowly Similar curves are obtained for different sediment concentrations For different sediment. .. determined so as to give the correct time to steady state Equation 4. 43 can then be written as d(d) dt A Cd1.2 [1 B Cd1.18 ] (4. 48) where A+ = 3.0 × 102 Integration of this equation gives essentially the same results as those shown for the steady-state diameter in Figure 4. 14 and for the time to steady state shown in Figure 4. 15 When fluid shear is dominant, the terms in Equation 4. 43 can be evaluated in. .. terms on the right-hand side of Equation 4. 17) is then given by dn k dt 1 Ad 2 ni n j b nk Ad ni b i j k (4. 20) i 1 By summing the terms in this equation over all states, one obtains nk N (4. 21) k dN dt © 2009 by Taylor & Francis Group, LLC 1 Ad 2 ni n j b k 1 i j k NA d ni b i 1 (4. 22) 132 Sediment and Contaminant Transport in Surface Waters It can be shown that ni n j k 1 ni n j i j k i (4. 23) j By means . near-shore areas of lakes and oceans, and throughout estuaries. Because they are ne-grained, these sediments have large surface- to-mass ratios and hence adsorb and transport many contaminants. Group, LLC 106 Sediment and Contaminant Transport in Surface Waters 4. 1.2 PARTICLE INTERACTIONS In the derivation of Equations 4. 2 through 4. 4 for the collision frequency func- tions, it was assumed. these processes is given in Section 4. 6. © 2009 by Taylor & Francis Group, LLC 1 04 Sediment and Contaminant Transport in Surface Waters 4. 1 BASIC THEORY OF AGGREGATION 4. 1.1 C OLLISION FREQUENCY A

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  • Table of Contents

  • Chapter 4: Flocculation, Settling, Deposition, and Consolidation

    • 4.1 BASIC THEORY OF AGGREGATION

      • 4.1.1 COLLISION FREQUENCY

      • 4.1.2 PARTICLE INTERACTIONS

      • 4.2 RESULTS OF FLOCCULATION EXPERIMENTS

        • 4.2.1 FLOCCULATION DUE TO FLUID SHEAR

        • 4.2.2 FLOCCULATION DUE TO DIFFERENTIAL SETTLING

        • 4.3 SETTLING SPEEDS OF FLOCS

          • 4.3.1 FLOCS PRODUCED IN A COUETTE FLOCCULATOR

          • 4.3.2 FLOCS PRODUCED IN A DISK FLOCCULATOR

          • 4.3.3 AN APPROXIMATE AND UNIFORMLY VALID EQUATION FOR THE SETTLING SPEED OF A FLOC

          • 4.4 MODELS OF FLOCCULATION

            • 4.4.1 GENERAL FORMULATION AND MODEL

            • 4.4.2 A SIMPLE MODEL

            • 4.4.3 A VERY SIMPLE MODEL

              • 4.4.3.1 An Alternate Derivation

              • 4.4.4 FRACTAL THEORY

              • 4.5 DEPOSITION

                • 4.5.1 PROCESSES AND PARAMETERS THAT AFFECT DEPOSITION

                  • 4.5.1.1 Fluid Turbulence

                  • 4.5.1.2 Particle Dynamics

                  • 4.5.1.3 Particle Size Distribution

                  • 4.5.1.4 Flocculation

                  • 4.5.1.5 Bed Armoring/Consolidation

                  • 4.5.1.6 Partial Coverage of Previously Deposited Sediments by Recently Deposited Sediments

                  • 4.5.2 EXPERIMENTAL RESULTS AND ANALYSES

                  • 4.5.3 IMPLICATIONS FOR MODELING DEPOSITION

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