the behavior of small particles in aquatic systems An introduction to the processes involved in the transport and removal of particles that have major effects on water quality
Charles R. O’Melia The Johns Hopkins Unioersity Baltimore, M d . 21 21 8
transport and fate of solid particles in aquatic systems, and (2) to illustrate, using case studies, our understanding of these processes and the extent of their effects.
Solid particles exert substantial effects on the chemical composition of fresh, estuarian, and marine waters. For example, Turekian (1977) stated that such particles control the concentrations of trace metals in water from initial weathering reactions on land to final deposition in marine sediments. La1 (1977) indicated that solid particles play a vital role in ocean chemistry, scavenging several elements and providing a source for others. Most pollutants of concern to human health and environmental quality are associated with solid particles. The treatment of wastewaters and water supplies primarily involves the removal of particles. Consequently, the physical processes involved in the transport and removal of particles in natural aquatic systems and in water and wastewater treatment plants can be expected to hdve major effects on water quality. The purposes of this feature article are twofold: (1) to describe certain physical processes that affect the
Processes and effects Three physical processes are considered throughout this article. The first is Brownian or molecular diffusion, in which random motion of small particles is brought about by thermal effects. The driving force Lor this transport is a function of k T , the product of Boltzmann’s constant and absolute temperature. The kinetic energy of water molecules is transferred to small particles during the continuous bombardment of these particles by the surrounding water molecules. Transport by Brownian diffusion depends on these thermal effects only and is independent of such factors as fluid flow and gravity forces. The second process affecting particle transport in aquatic systems is fluid shear, either turbulent or laminar. Velocity differences or gradients occur in all real flowing fluids. Hence, particles that follow the motion of the suspending fluid will travel at different velocities. These fluid and particle velocity differences or gradients can produce interparticle contacts among particles suspended in the fluid. Particle transport in this case depends upon the mean velocity gradient, G. The third force considered here is gravity, which produces vertical
Featirrr articles i n ES&T hare by-lines, reprr.rent the c i w s o f t h e authors. and are edited hj. the Washington stafJ I f y o u are interested i n contributing an article, contact the managing editor.
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Environmental Science & Technology
transport of particles and depends upon the buoyant weight of these particles, represented here by d i ( p p- p)g in which d , is particle size, pp and p are the densities of the particles and the fluid respectively, and g is the gravity acceleration. These physical processes are few in number and are simple in concept. They are also numerous in occurrence and complex in effects. Four case studies will be summarized. Two are examinations of particle deposition a t water-solid interfaces: filtration by packed beds in laminar flow, and deposition on pipe walls in turbulent flow. Two examples will consider particle transport within aquatic systems: a water treatment plant and a lake.
Deposition at water-solid interfaces Packed-bed filtration. We examine here the performance of packedbed filters as used extensively in water and wastewater treatment for the removal of particles. The approach is adapted from the early work of Friedlander (1958) which deals with the filtration of aerosols. Consider a single spherical grain of filter media as illustrated in Figure l . The flow of fluid around the collector is laminar, depicted by the streamlines. Particles in the flowing fluid may be transported to the spherical collector by three mechanisms: Brownian diffusion (molecular effects), interception (a form of velocity gradient), and sedimentation (gravity effects).
0013-936X/80/0914-1052$01.00/0
@ 1980 American
Chemical Society
The problem, expressed in mathematical form, is:
FIGURE 2
Effects of suspended particle size on the efficiency of a single collector in a typical packed-bed filter. 10-1
+ (Pp - P ) gm oc ( I )
3W d , Here C is the concentration of particles a t some location and time: t is time; v is the velocity of the fluid at some location and time, assumed to follow Stokes' equations for laminar flow around a sphere; D is the Brownian or molecular diffusion coefficient of the particle: I-L is the viscosity of the fluid; and n7 the mass of particles in suspension. A steady state is assumed so that the first term on the left side of Equation 1 equals zero. The second term on the left side of Equation 1 describes the advective flow of fluid towards the collector. Suspended particles that follow the flow of suspending fluid exactly may, depending upon their size and the size of the collector, be intercepted by the media grain. This interception can be visualized as a form of velocity gradient coagulation where one particle with a velocity equal to that of the fluid collides with a second stationary particle with a velocity of zero. The effects of molecular diffusion are described by the first term on the right side of Equation 1 , and the effects of the gravity force are described by the second term on that side. Integration of Equation 1 has been accomplished by several investigators. Depending upon boundary conditions and simplifying assumptions used, analytical and numerical solutions with different complexities a r e achieved. The results describe the concentration distribution of particles in the flowing, fluid in the region around the sphlere. By differentiating
-7
L
0 01
Particle trainsport to a single collector in a packed-becl filter.
r
I
/
01
1
10
Suspended particle size ( d p ,p m ) I
FIGURE 3
Effects of suspended particle size and filtration time on the performance of a typical packed-bed filter.
U
65 400
C, = 20 mgiL
350 FIGURE 1
1 = 25 "C d = 0.05 cm v, = 5 mlh
v
pp = 2.65 glcm3
v, = (5 mlh)
300
d = 0.5 mm 250
L = 60 cm U = 0.40
u)
_o
200
U
m 150
lh 100
50
I
0
0.1
I 10
1
Suspended particle size (pm)
Volume 14,Number 9,September 1980
1053
this result and solving for the concentration distribution a t the surface of the collector, the local or microscopic flux of particles to the collector can be determined. The next step is to estimate the removal efficiency ( q ) of this single collector, defined as follows: Rate at which particles strike a collector 17” Rate at which particles approach a collector Some available solutions are illustrated by Equations 2 a, b, and c, taken from the work of Yao et al. (1971):
Here TD, 71, and q~ are the singlecollector removal efficiencies for diffusion, interception, and gravity considered separately as transport processes; Pe is the Peclet number; d is the diameter of the collector; and uo is the approach velocity of the fluid. The significance of these particle transport processes is depicted graphically in Figure 2, in which the singlecollector efficiency is plotted as a function of the size of the particles in suspension for conditions representative of water and wastewater filtration. An important conclusion here is that small particles, in this case smaller than about 1 y m in diameter, are transported and removed predominantly by Brownian diffusion. Larger particles are transported by interception and gravity. Analogies between these effects of suspended particle size on removal from suspension in packed-bed filters and phenomena that occur in certain other aquatic systems are to be expected. The efficiency of zooplankton feeding in natural waters is one such case. W e continue our scale-up from the microscopic flux at a point on a single media grain through the total efficiency of such a single grain to consider the total removal efficiency and head loss of a complete filter bed of length L. The removal efficiency of a clean bed has been described by: - = e-(3/2).(1-0)dL/d)
(3)
C O
Here C , and C, are the influent and effluent concentrations of suspended particles, respectively; u is the porosity 1054
Environmental Science & Technology
of the d e a n filter bed; and cy is the collision or sticking efficiency of the water-solid system. This latter factor reflects the aqueous and surface chemistry of the system and is defined as the number of contacts between suspended particles and filter media that successfully result in attachment and removal divided by total number of contacts that occur. The effects of suspended particle size and filtration time are illustrated in Figure 3. These results are based on the work of O’Melia and Ali (1978) and Tobiason (1979). The filtration efficiency and the head loss development of a typical packed-bed filter are presented as functions of suspended particle size and filtration time. The influence of the three transport mechanisms on removal efficiency is illustrated in Figure 3a. A window or region of minimum removal efficiency exists for particles in the size range of 1 pm. Effective removal of submicron particles can be accomplished, including viruses. Removal efficiency increases appreciably as time proceeds. This increased efficiency is accompanied by an increased head loss (Figure 3b). An important conclusion is that small particles exert much more substantial head losses than larger ones when comparisons are based on similar masses of material removed from suspension. In this filtration analysis, the improvement in filtration efficiency with time is based on a consideration that particles removed from suspension early during a filter run can act as filter media and accomplish the removal of additional particles later in the run. Deposition in pipes. Particle deposition from the suspending fluid to pipe walls has important effects in many systems of engineering interest. Examples include a reduction in the carrying capacity of transmission mains due to increased pipe friction, and reduction in the heat-transfer capabilities of condenser tubes in power plant cooling systems. The approach here is similar in structure to that used in considering packed-bed filtration. W e begin by considering a small section of the pipe and evaluating a local mass-transfer coefficient which is analogous to the single-collector efficiency developed for filters. Following this, we scale up the results to a pipe of some total length L. Important particle transport mechanisms are Brownian diffusion and sedimentation. The approach is again patterned after earlier work by Friedlander (1957) in aerosol systems.
Brownian diffusion is considered first. Schematic representations of the velocity and the concentration distributions during turbulent flow in a circular pipe are presented in Figure 4. The velocity distribution is the result of processes affecting the transport of momentum within the fluid. This momentum may be transported by turbulent eddies and by molecular or viscous effects, represented by the coefficients of turbulent diffusivity ( E ) and kinematic viscosity ( u ) with typical dimensions being cm2/s. Within the turbulent core, E is much greater than v, and the fluid velocity, u , is almost constant. In the region near the pipe wall, u is much greater than E and a laminar sublayer or velocity boundary layer exists in which u increases linearly with the distance from the wall. Between these two regions, a buffer zone exists in which momentum can be transported by both turbulent and viscous effects. Similarities exist when considering the concentration distribution within the pipe. In the turbulent pipe core, transport of mass by turbulent eddies is considerably greater than the transport of mass by molecular diffusion. These processes are characterized by E ~ the , turbulent mass diffusivity, and D, the Brownian or molecular diffusion coefficient. Within the turbulent core, E , is considerably greater than D, and a uniform concentration is observed. In the region near the wall, turbulent eddies become weaker and transport by Brownian diffusion becomes significant. Here it is important to consider differences in water between the molecular coefficients for the transport of momentum, u, and of mass, D. The kinematic viscosity of water, u, is in the order of 10-2 cm2/s, while molecular diffusion coefficients, D, are in the order of cm2/s or smaller. The ratio ( u / D ) is termed the Schmidt number (Sc) and is in the order of 1000 or greater in water. In contrast, coefficients of turbulent momentum and mass diffusivity ( E and E , ) are similar. The result is that turbulent eddies too weak to affect momentum transport in the laminar sublayer (Le., E < cm2/s) can significantly affect mass transport up to a very small distance from the wall. There exists at water-solid interfaces a concentration boundary layer which is significantly thinner than the corresponding velocity boundary layer and within which both turbulent and molecular transport can be significant. Using Friedlander’s analysis for Brownian diffusion (1977) and for-
mulating a separate analysis for the effects of gravity, Bliss and O'Melia (1979) presented and tested the following equations for the local masstransport coefficients describing depposition on pipe walls in turbulent flow due to diffusion (kD) and sedimentation ( k s ) .
FIGURE 4
Schematic velocity and concentration distributions within a circular pipe in turbulent flow.
(4a)
tm
(D
>>D
- 10-5 crn'k)
I
Concentratio Rni inriarw
Here Re is the F!eynolds number of the pipe; f is the Fanning friction factor; d is the pipe diameter; and 4 is the angle that the pipe axis makes with the horizontal direction. Integrating the local flux along a pipe of length L, the following equation is obtained: - = e-4nkL/L'2
co
YUIICI
LUllC?
Velocity, u
layer ( u and 1 significant)
-
Concentration,C
-
P
(5) FIGURE 6
Here Co and C, are the influent and effluent particle concentrations for the pipe system; U is average fluid velocity; and k is the appropriate mass-transport coefficient.
Effects of particle size on collision rate coefficients for coagulation processes.
FIGURE 5
Effects of suspended particle size on mass-transport coefficients for deposition on horizontal pipe walls.
d,
= 1 pn T =5%
G
=
0.1
S-1
pp = 1.02 gicrn3
10-20
LU lo-'
Suspended particle size (dD,w m )
lo-'
Size of
1 d2
10
102
particles (pm)
Volume 14, Number 9, September 1980
1055
It is instructive to examine the effects of the size of the particles suspended in the water on the local mass-transport coefficient for deposition. These are illustrated in Figure 5. The results are remarkably similar in form to the results obtained for the transport of particles to spherical collectors within packed beds in laminar flow. A region about 1 p m in size exists for which particle transport to the pipe walls is a minimum. For smaller particles, transport by Brownian diffusion is effective; for larger particles, transport by gravity is effective when the pipes are horizontal. Very extensive effects of the density of the suspended particles on the deposition of the larger particles are predicted and observed. It is expected that analyses of this type have considerable application in evaluating the head loss in transmission mains, the fouling of condensers in power plants, and the design of fixed-film biological reactors in wastewater treatment plants. Transport within aquatic systems We proceed now to some concepts about coagulation within aquatic systems; then we will examine the effects of coagulation in water and wastewater treatment plants and in lakes. The basic developments describing coagulation rates in aquatic systems were presented by Smoluchowski in 1917. Since that time these have been applied primarily to homodisperse colloids, Le., those in which the particles have only one size a t the onset of coagulation. Note here that particles in natural waters span a size range of several orders of magnitude. Again following the lead of Smoluchowski, let us examine how coagulation rates become more rapid when suspensions are heterodisperse. Collisions between suspended particles in water can occur by three different processes, viz., Brownian diffusion (thermal effects), fluid shear (flow effects), and by differential settling (gravity effects). The particle size distribution of the suspension being coagulated has important effects on the significance of these three processes. Equations for the coagulation of heterodisperse suspensions are cumbersome; for didactic purposes the collisions between particles of two different sizes are considered first. The rate at which particles of sizes dl and d2 come into contact by the j t h transport mechanism is given by:
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Environmental Science & Technology
the “bimolecular” rate coefficient for the j t h mechanism (volume/time); and n ( d l ) and n ( d 2 ) are the number concentrations of particles of sizes d l and dZ, respectively (volume-’). The rate coefficients for the three transport processes are given by Equations 7 a, b, and c.
Here kg, kSH, and kDs are the bimolecular collision rate coefficients for transport by Brownian diffusion, fluid shear, and differential settling, respectively. These rate coefficients are compared in Figure 6 for a case that is illustrative of a sedimentation tank in a water treatment plant during the winter season and the hypolimnion of a lake during the summer season. Results are presented for the collisions of particles with a size d2 ranging from 0.01 p m to 100 pm with particles of size dl = 1 pm. Values of T = 5 ‘C, pp = 1.02 g/cm3, and G = 0.1 s-l have been assumed. The collision rate by Brownian motion is a minimum for d l = d2 = 1 pm; i.e., it is a minimum for a homodisperse suspension. Collisions by differential settling do not occur in homodisperse suspensions, since when d l = dZ, kDs = 0 (Equation 7c). Coagulation by Brownian diffusion dominates in this example for particles in the micron and submicron range. For particles larger than about 7 p m , coagulation by gravity forces predominates. A general model for the transport of particles in aquatic systems that includes the effects of coagulation and gravity is described by Equation 8.
f wk,l
+ q o ’ nk,o - qo * nk,l
into a number of size compartments, denoted as h, i, j, k, 1 . . . etc. Equation 8 is a general equation for the particles of size k in, for example, box I. Here n k , l denotes the concentration of particles of size k in box I; k ( i j ) l denotes a collision frequency function that depends on the mode of interparticle contact; W k , H is the settling velocity of particles of size k in box H located directly above box I; ZIis the depth of box I; wk,[is the rate of production or destruction of particles by biological and chemical processes in box I; and qo is the areal hydraulic loading or overflow rate into and out of box I. The left side of Equation 8 describes the rate a t which the number concentration of particles with size k and location I changes with time (particle/ m3.s). The first term on the right side expresses the rate of formation of particles of size k (or volume Ck) from particles having the total volume U k . The condition i j = k under the summation denotes the condition that Ui + U j = uk. The factor l/2 is needed since collisions are counted twice in this summation. The second term on the right side of Equation 8 describes the loss of particles of size k by growth to form large aggregates; this occurs when a size k particle collides with and attaches to a particle of any size i. The third term describes the addition of particles of size k to box I by settling from above (box H). The fourth term expresses the loss of size k particles from box I by settling into box J. For the bottom box, this corresponds to removal of particles from the system. w k , J is described above. The sixth and seventh terms on the right side express the input and output of the nk particles by hydraulic inflow and discharge. Before turning to applications of these concepts, it is important to consider inputs of particles to the systems under evaluation and the methods employed to describe these inputs. Investigations of both atmospheric and aquatic systems have provided useful information about particle size distributions in these environments. Observations frequency follows a power law of the form:
+
(8)
The aquatic system is segmented into a number of vertical boxes, denoted here as H, I, J, K, L . . . etc. These could correspond to the epilimnion, thermocline, and hypolimnion ( 3 boxes) in a lake, or various depths in a settling tank in a treatment plant. The particles in the water are subdivided
where dN is the concentration of particles in the size range d, to d, d ( d p ) and n(d,) is defined as a particle size distribution function. A is a coefficient related to the total concentration of particulate matter in this system. Measurements indicate that for aquatic particles larger than about 1
+
FIGURE 7
Performance of flocculation, sedimentation, and filtration processes. 3
Diffusion and shear
Diffusion, differential settling, and settling
h
4
-z
-
c
Diffusion, interception, and settling
0 I E 05U
C
-
0
+
a,
r
s 2
h
W
-
L
0
L
W
W
5
._ U
W 0,
I
25
> W
-5 s
1
6
150
8
3
100
I
50 0 1
Flocculation
2
0
3
Sedimentation
24
L
Filtration Time (h)
p m in size (Le., those detectable by present electronic or optical measurements), values o'f the exponent range from 2 to 5 . Often, a value of P of 4 is observed. For example, Lerman et al. (1977) reported measurements of size distributions a t four locations in the north Atlantic. Fifty-three size distributions derived from samples taken a t depths ranging 30-5100 m yielded a mean value of p = 4.01 f 0.28. In part because of observations such as these, a value of p = 4 is used in much of the analysis presented subsequently. Model f o r wtrter treatment plants. A model for the performance of coagulation, sedimentation, and filtration processes in water treatment plants has been developed by Lawler et al. (1980). The model for the coagulation basin is a simplification of Equation 8: One well-mixed box is assumed; collisions are restricted to Brownian diffusion and fluid shear processes only; and the removal of mass from the system by sedimentation is not permitted. The model for the settling basin divides
TABLE 1
The water source and the treatment system System component
Raw water
Parameter
Volume concentration Mass concentration Particle density Particle size range
Assigned value
50 PPm
Temperature
132 mgIL 2.65 g/cm3 0.3-30 p m 4.0 25 OC
Flocculation tank
Collision efficiency factor Flow type Detection time Velocity gradient
1.o Plug flow I h 10 s-1
Settling tank
Flow type Detention time Tank depth Overflow rate
Plug flow 2h 4m 2 m/h
'Filter
Filtration rate Media size Media depth Clean bed porosity
5 m/h 0.5 mm 60 cm 0.4
P
Volume 14, Number 9, September 1980
1057
FIGURE 8
Particle size distribution functions in a model lake without coagulation ( a = 0).
I
'"I
I t1
-Hypolimnion
-5
0.3
I
I
I
1
3
10
I 30
I
Particle size (Fm) FIGURE 9
Particle volume distributions in a model lake without coagulation (a = 0). Inflow = 5
I
pprn, 10-6 rn3/rn*'s
I
Particle size ( p m )
I
TABLE 2
Parameters in lake examplea Parameter
(m) T(OC) p (g/cm. s)
P (g/cm3) P p (g/cm3)
G (6) 90 (m/s)
a a
Thermocline
Eplllmnlon
10 25 0.8915X 0.997 1.05 10 10-6 b 0,10-3
lop2
5 15 1.146 X 0.999 1.05 0.1 0
0,104
Hypollmnion
50 5 1.515 X 1.ooo
1.05 1 .o 0 0,10-3
The river input is assumed to contain 5.0 ppm by volume of particles or 5.25 mg/L of particles with a density of 1.05 g/cm3. The particles are distributed over a size range of 0.3-30 pm, and
p = 4.
This corresponds to the Stokes' settling velocity of a 5.6-pmparticle having a density of 1.05 g/cm3 in water at 25 O C .
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Environmental Science 8 Technology
that tank into four vertical boxes, considers collisions by Brownian diffusion and differential settling only, and permits removal of mass by sedimentation at the bottom of the tank. The filtration model is based on the work of O'Melia and Ali (1978). Because modeling of filtration is still restricted to considerations of monodisperse suspensions, the heterodisperse effluent from the settling tank is converted to a monodisperse suspension with an equivalent volume average diameter for assessing filtration performance. A representative set of results is presented in Figure 7. These are based on selected water source and treatment system characteristics summarized in Table 1. On the left side of Figure 7, the increase in volume average diameter of the suspended particles is plotted as a function of time in the flocculation basin. Particle growth occurs as expected, brought about in this case by contact opportunities provided by Brownian diffusion and fluid shear. In the middle of Figure 7 , the volume average diameter and the mass concentration of solids remaining in suspension are plotted as functions of time in the sedimentation tank. The volume average diameter continues to increase substantially during the first portion of the settling tank. Average particle size then decreases during the last portion of the tank as larger particles are removed from the system by gravity settling. Overall settling performance results in the removal of about 85% of the particles on a mass basis. The effects of Brownian diffusion, differential settling, and simple gravity sedimentation are responsible for extensive coagulation and removal of particles in such settling tanks. The performance of a packed-bed filter is illustrated on the right side of Figure 7. Brownian diffusion, interception, and gravity settling within the filter enable effluent concentrations from the plant to be reduced to less than 0.1 mg/L. Particle removal within the filter is accomplished at the expense of an increase in head loss, but a filter run of more than a day in length is expected. These and other results permitted Lawler et al. to reach the following conclusions. First, particle concentration and size distribution have extensive, complex, predictable, and dominant effects on the performance of individual treatment units and on overall performance in water treatment plants. Second, flocculation basins which are designed to cause coagulation by fluid shear also induce extensive coagulation by Brownian
diffusion. Third, settling basins actually act as flocculation basins with differential settling and Brownian diffusion producing extensive aggregation. Fourth, Brownian diffusion, interception, and settling produce effective removal in filtration processes. Finally, present knowledge about these processes is not utilized effectively and can have significant conceptual and practical advantages. Particles in h k e s . The results described here are preliminary. They are taken from a study to evaluate the extent and significance of coagulation and settling processes in lakes. The general approach is to take the model for particles in aquatic systems as presented in Equation 8 and apply it to limnetic systems. To facilitate the analysis, a model lake was chosen. Appropriate descriptive information is presented in Table 2. The lake is divided into three vertical compartments during the stratification period: the epilimnion or well-mixed zone, the thermocline or region of rapid temperature and density changes with depth, and the hypolimnion representing the bottom waters of the lake. The analysis was conducted by Bowman and Clark (1979). The particle concentrations that would result in such a lake in the absence of coagulation are represented in Figures 8 and 9. 'I'he coagulation process is eliminated by setting CY = 0 in Equation 8. Under these conditions, particles enter the lake in the river inflow, are discharged downstream in the river outflow, and also settle by gravity from the epilimnion through the thermocline and hypolimnion into the lake sediments. The results are expressed in terms of the particle size idistribution function as related to particle size (Figure 8) and as the particle volume concentration as a function of particle size (Figure 9). Effects are seen most easily in the volume distribution, Figure 9. The river inflow contains 5 ppm of particles; for p = 4 this corresponds to a n equal distribution of particle volume with every logarithmic size interval. Hence, 2 5 ppm in volume is contained in the particle size range 0.3-3 p m and the remaining 2.5 ppm is contained in the size range 3-30 p m (note the horizontal line for the river inflow in Figure 9). One expected result is observed; particles larger 'than about 5 p m in size, Le., those with settling velocities greater than the hydraulic loading or the overflow rate of the lake, are removed to a considerable extent from all of the lake compartments. Similarly, submicron particles which have
FIGURE 10
Particle size distribution functions in a model lake with slow coagulation (CY = 0.001).
'"I
I
Inflow = 5 ppm 10-6 m31mz.s I I Thermocline
0.3
3
1
10
30
Particle size (prn) FIGURE 1 1
Particle volume distributions in a model lake with slow coagulation (a = 0.001). Inflow = 5 ppm, 10-6 m3/mZ. s , Epilimnion -Thermocline -Hypolimnion 3
River inflow 2
1
0
0.3
10
3
1
30
Particle size (prn)
TABLE 3
Illustrative effects of coagulation in lakes Locatlon
Number concentration (parttcies/cm3)
River inflow
3.41 x 107
Epilimnion Thermocline Hypolimnion
3.39 x 107 4.51 x 107 6.08x 107
Epilimnion Thermocline Hypolimnion
1.53x 107 1.81 X lo6 2.6 x 105
Surface area concentration (m*/L)
2.29 X
Mass concentratlon (mglL)
5.25
a = (No coagulation) 2.14 X 2.85 X 3.85 X
3.25 4.36 5.89
a = 0.001 (Slow coagulation) 1.52X 0.76X 0.30 X
lo-* lo-* lo-*
3.12 2.17 2.01
Volume 14, Number 9, September 1980
1059
settling velocities significantly smaller than the hydraulic loading are not removed from any lake compartment. This second observation is instructive. The steady-state concentrations of particulate materials increase from 3.28 mg/L in the epilimnion through 4.36 m g / L in the thermocline to 5.89 mg/L in the hypolimnion (Figure 9). The concentration of particles in the hypolimnion in this case is higher than in the influent to the lake. These results are brought about by the significant effect of temperature on fluid viscosity and hence on Stokes’ settling velocity. As the temperature decreases from the epilimnion to the hypolimnion, the fluid viscosity approximately doubles and the Stokes’ settling velocity is correspondingly halved. The result is that steady-state particle concentrations must increase with depth, so that mass concentrations at the bottom of the lake are approximately twice those that result in the epilimnion. This vertical distribution is a direct consequence of the balance between hydraulic loading and gravity forces on the particles in the lake. W e do not usually observe such particle distributions in the lakes. Some other processes must occur. One possibility, not discussed here, is zooplankton feeding and the production of fecal pellets. This would further reduce the concentration of particles in the epilimnion, but still would require that mass concentrations increase with depth. A second possibility is coagulation with the lake compartments. Coagulation can cause particles to aggregate, increasing their settling velocities and speeding their removal from the lake. This possibility is examined in Figures 10 and 1 1. These results are for a system identical to the one previously examined, save that Q = 0.001. Stated another way, one out of every 1000 contacts predicted by Smoluchowski’s equations are considered to result in successful attachment and the formation o f an aggregate. Coagulation is seen to have extensive effects on the particle size distribution function (Figure 10) and on the volume distribution (Figure 1 1 ) . The results indicate that coagulation occurs in all three lake compartments: epilimnion, thermocline, and hypolimnion. Removal of submicron particles is accomplished in all compartments; coagulation occurs by Brownian diffusion, fluid shear, and differential settling and permits removal of aggregates by gravity settling. Particle concentrations no longer increase with depth; in this case the steady-state particle concentrations decrease from 1060
Environmental Science 8 Technology
the epilimnion to the thermocline and the hypolimnion. These predicted results are more consistent with observations in the natural systems. Effective removal of submicron particles is indicated. There are efforts underway at present to develop measurement techniques for detecting submicron particles in water. The results of this analysis indicate the possibility that when such instrumentation is developed, we may find that very few particles are actually present, because coagulation has incorporated them into larger aggregates. These and other results are summarized in Table 3. The effects of coagulation are illustrated by comparing model predictions for N = 0 with those when cy is assumed = 0.001, In addition to the effects on mass concentration as described in Figures 9 and 11 and summarized in the last column of Table 3, it can be seen that the influence of coagulation on number and surface concentrations are even more extensive. In the absence of coagulation, steady-state particle number and surface area concentrations are predicted to increase with depth in the lake in the same manner as for particle mass Concentrations. In the presence of coagulation, however, where mass concentrations are reduced by about 50% from 3 mg/L to 2 mg/L, surface area concentrations are reduced by 80% and number concentrations are lowered by almost two orders of magnitude. It is concluded that coagulation can profoundly affect the concentration and flux of particles in limnetic systems which in turn exert significant controls on the transport and fate of pollutants associated with these particles.
Concluding remarks First, available evidence indicates that most pollutants in water are particles or are associated with particles. Second, the transport and fate of particles (and the pollutants associated with them) are controlled in aquatic systems by physical processes, i.e., Brownian diffusion, fluid motion, and gravity. Third, present knowledge permits description and control of these processes in treatment and transport systems for water supply and wastewater disposal. Fourth, extension of these concepts to natural aquatic systems can be expected to provide significant new insights into the functioning of these natural systems and the flow of materials (including nutrients and pollutants) through them, and to permit improved management and control of man’s impacts on these systems.
Acknowledgments T h e author is pleased to acknowledge the ideas and assistance of Waris Ali, Margaret Bliss, Kathleen Bowman, Sheldon Friedlander, Desmond Lawler, James Morgan, Werner Stumm, John Tobiason, and Kuan-Mu Yao, among the many teachers, co-workers, and students who have contributed to this work.
Additional reading Bliss, M. J.; O’Melia, C. R. “Physical Aspects of Biofouling,” Presented at 34th Annual Purdue Industrial Waste Conference, West Lafayette, Ind., 1979. Bowman, K.; Clark, M: Unpublished results, DeDartment of Environmental Sciences and En’gineering, University of North Carolina, Chapel Hill, 1979. Friedlander, S.K. “Theory of Aerosol Filtration,” Ind. Eng. Chem. 1958, 50, 116164. Friedlander, S. K.“Smoke, Dust, and Haze”; John Wiley and Sons: New York, 1977. Friedlander, S. K.; Johnston, H. F. “Deposition of Suspended Particles from Turbulent Gas Streams,” Ind. Eng. Chem. 1957, 49, 1151-56. Lal, D. “The Oceanic Microcosm of Particles,” Science 1977,198, 997-1009. Lawler, D. F.; O’Melia,C. R.; Tobiason, J. E. “Integral Water Treatment Plant Design: From Particle Size to Plant Performance,” In “Particulates in Water: Characterization, Fate, Effects, and Removal”; Kavanaugh M.; Leckie J. O., Eds:; ACS Advances in Chemistry Series, 1980. Lerman, A,; Carder, K. L.; Betzer, P. R. “Elimination of Fine Suspensions in the Oceanic Water Column,” Earth and Planetary Science Letters 1977,37, 61-70. O’Melia, C. R.; Ali, W. “The Role of Retained Particles in Packed Bed Filtration,” Prog. Water Technol. 1978,lO (5/6), 123-37. Smoluchowski, M. “Versuch einer Mathematischen Theorie der Koagulations-Kinetiks Kolloider Usungen,” Z. Physik. Chem. 1917, 92, 129-68. Tobiason, J. “Packed Bed Filtration: Experimental Investigation and Conceptual Analysis of a Filter Ripening Model,” Unpublished master’s report, Department of Environmental Sciences and Engineering, University of North Carolina, Chapel Hill, 1979,136 pp. Turekian, K. Geochim. Cosmochim. Acta 1977,41, 1139-44. Yao, K. M.; Habibian, M. T.;O’Melia, C. R. “Water and Wastewater Filtration: Concepts and Applications,” Enuiron. Sci. Technol. 1971,5, 1105-12.
Dr. Charles R.O’Melia is professor o f e n cironmental engineering at T h e Johns Hopkins Unicersity. Dr. O’Melia’s research interests are in aquatic chemistry, water and wastewater treatment, and predictice modeling o f natural waters.
