TRANSPORT OF SUSPENDED PARTICLES

3.3 TRANSPORT OF SUSPENDED PARTICLES

The advection–dispersion equation, Equation 3.16, is appropriate for describing the fate and transport of dissolved contaminants that are advected with the same velocity as the ambient water. In the case of suspended particles, the settling of the particles is in fluenced by the size, shape, and density of the particles in addition to the ambient flow velocity. The process by which suspended particles settle to the bottom of water bodies is called sedi- mentation , and the settling velocity, v s , of suspended particles with diameters less than or equal to 0.1 mm (⫽100 µm) can be estimated by the Stokes equation, which is given by (Yang, 1996)

where α is a dimensionless form factor that measures the effect of particle shape (α ⫽ 1 for spherical particles), ρ s is the density of the suspended particle, ρ w is the density of the

119 TABLE 3.3 Typical Settling Velocities in Natural Waters

TRANSPORT OF SUSPENDED PARTICLES

Settling Velocity Particle Type

Diameter

(m/day) Phytoplankton

( µm)

Cyclotella meneghiniana 2 0.08 (0.24) a Thalassiosira nana

0.1–0.28 Scenedesmus quadricauda

8.4 0.27 (0.89) Asterionella formosa

25 0.2 (1.48) Thalassiosira rotula

0.39–0.21 Coscinodiscus lineatus

50 1.9 (6.8) Melosira agassizii

54.8 0.67 (1.87) Rhizosolenia robusta

84 1.1 (4.7) Particulate organic carbon

a Numbers in parentheses are for the stationary phase of microbial growth.

ambient water, g is gravity, φ is the particle diameter, and ν w is the kinematic viscosity of the ambient water. The form factor, α, sometimes called the sphericity, is defined as the ratio of the surface area of a sphere having the same volume as the particle to the surface area of the particle. Particles in natural waters have complex shapes, typically α ⬍ 1. The settling velocity given by Stokes’ equation (Equation 3.117) is called Stokes’ velocity. Settling velocities that are of interest in natural waters are given in Table 3.3 (Wetzel, 1975; Burns and Rosa, 1980; Chapra, 1997). As a general rule, settling is unimportant for parti- cles smaller than about 1 µm in diameter. Particles in water must be larger than about

10 µm in diameter to settle through distances of several centimeters in time scales of an hour or less, and particles in this class are sometimes called settleable solids (Nazaro ff and Alvarez-Cohen, 2001). In cases where the ambient water moves with a horizontal veloc- ity, V, suspended particles tend to move horizontally at the velocity, V, and vertically at the settling velocity.

Suspended solids in natural waters have two primary sources: surface runo ff from drainage basins and as products of photosynthesis. The suspended-solids concentration in natural waters typically range from below 1 mg/L in clear waters to over 100 mg/L in highly turbid waters. An example of a highly turbid stream resulting from surface runo ff is shown in Figure 3.11. Suspended solids derived from photosynthetic processes tend to

be higher in organic matter and less dense than suspended solids derived from surface runo ff. Caution should be used in applying the Stokes equation to calculate the settling velocity of living particles, since some phytoplankton, such as blue-green algae, can become buoyant due to the development of internal gas vacuoles.

Many contaminants sorb strongly onto suspended particles, so that prediction of the fate and transport of suspended sediments is essential for describing the fate and transport of these contaminants in natural waters. Heavy metals and hydrophobic organic compounds, such as PCBs, are two classes of contaminants that sorb strongly onto suspended sedi- ments.

FATE AND TRANSPORT IN AQUATIC SYSTEMS

FIGURE 3.11 Turbid runo ff in a stream. (From Town of Chapel Hill, 2005.)

Example 3.9 Analysis of water from a lake indicates a suspended-solids concentration of 50 mg/L. The suspended particles are estimated to have an approximately spherical

shape with an average diameter of 4 µm and a density of 2650 kg/m 3 . (a) If the water tem- perature is 20⬚C, estimate the settling velocity of the suspended particles. (b) If the sus- pended particles are mostly clay, compare your estimate of the settling velocity with the data in Table 3.3. (c) If there is 1 g of heavy-metal ion per kilogram of suspended parti- cles, determine the rate at which heavy metals are being removed from the lake by sedi- mentation.

SOLUTION (a) From the data given, α ⫽ 1 (spherical particles), ρ s ⫽ 2650 kg/m 3 , ρ w ⫽ 998 kg/m 3 at 20⬚C, φ ⫽ 4 µm ⫽ 4 ⫻ 10 ⫺6 m, and ν ⫽ 1.00 ⫻ 10 ⫺6 m 2 w /s. Substituting into the Stokes equation (Equation 3.117) gives

18(1.00 ⫻ 10 ⫺6 ) ⫽ 1.44 ⫻ 10 ⫺5 m/s ⫽ 1.25 m/day

(b) This result is consistent with the settling velocities for clay-sized particles shown in Table 3.3, which indicates that a 4- µm clay particle will have a settling velocity on the order of 1 m/day.

(c) Since the concentration, c, of suspended particles is 50 mg/L ⫽ 0.05 kg/m 3 , the rate at which sediment is accumulating on the bottom of the lake is given by

removal rate of suspended particles ⫽ v c⫽ 1.25(0.05) ⫽ 0.0625 kg/day · m 2 s

PROBLEMS

Since heavy metals are attached to the sediment at the rate of 1 g/kg, the removal rate of heavy metals is given by

removal rate of heavy metals ⫽ 1(0.0625) ⫽ 0.0625 g/day · m 2