McKay, Donald. "Front matter" Multimedia Environmental Models ...

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is much greater than B M, and the molecular processes can be ignored. In stagnant regions, such as thermoclines or in deep sediments, B T may be small or zero, and B M dominates. As we move closer to a phase boundary, B T tends to become smaller; thus, it is possible that much of the resistance to diffusion lies in the layer close to the interface. The roughness of the interface plays a role in determining the thickness of this layer. For example, grass may damp out wind eddies and retard the rate of diffusion from soil to air. Animal fur retards both diffusion of heat and water vapor. A complicating factor is that we have no guarantee that B T is isotropic, i.e., that the same value applies vertically and horizontally. In Figure 7.3, we postulate that some eddies may be constrained to form elongated “roll cells.” The horizontal B T will therefore exceed the vertical value. In practice, this nonisotropic situation is common and even leads to conditions in rivers where three B T values must be considered: vertical, upstream-downstream, and cross-stream. To give an order of magnitude appreciation of turbulent diffusivities, it is observed that a vertical eddy diffusivity in air is typically 3600 m 2 /h plus or minus a factor of 3, thus the time for moving a distance of 1 m is of the order of 1 s. Molecular diffusion is clearly negligible in comparison. In lakes, a vertical eddy diffusivity may be 36 m 2 /h near the surface, corresponding to a velocity over a distance of 1 m of 1 cm/s. At greater depths, diffusion is much slower, possibly by a factor of 100. To estimate eddy diffusivities, one can watch a buoyant particle and time its transport over a given distance. The diffusivity is then that distance squared, divided by the time. Turbulent processes in the environment are thus quite complex and difficult to describe mathematically. The interested reader can consult Thibodeaux (1996) or Csanady (1973) for a review of the mathematical approaches adopted. We sidestep this complex issue here, but certain generalizations that emerge from the study of turbulent diffusion are worth noting. In the bulk of most fluid masses (air and water) that are in motion, turbulent diffusion dominates. We can measure and correlate these diffusivities. Generally, vertical diffusion is slower than horizontal diffusion. Often, diffusion is so fast that near-homogeneous conditions exist, which is fortunate, because it eliminates the need to calculate diffusion rates. In the atmosphere and oceans, there is a spectrum of eddies of varying size and velocity. The larger eddies move faster. Consequently, when a plume in the atmosphere or a dye patch in an ocean expands in size, it becomes subject to dispersion by larger, faster eddies, and the diffusivity increases. If the velocity of expansion of the plume or patch is constant, this implies that diffusivity increases as the square of distance. At phase interfaces (e.g., air-water, water-bottom sediment), turbulent diffusion is severely damped or is eliminated, thus only molecular diffusion remains. One can even postulate the presence of a “stagnant layer” in which only molecular diffusion occurs and calculate its diffusion resistance. This model is usually inherently wrong in that no such layer exists. It is more honest (and less trouble) to avoid the use of diffusivities and stagnant layer thicknesses close to the phase interfaces and invoke mass transfer coefficients that combine the varying eddy diffusivities, the molecular ©2001 CRC Press LLC
diffusivity, and some unknown layer thickness, into one parameter, k M. We then measure and correlate k M as a function of fluid conditions (e.g., wind speed) and seek advice from the turbulent transport theorists as to the best form of the correlation equations. In some diffusion situations, such as bottom sediments, the eddy diffusion may be induced by burrowing worms or creatures that “pump” water. This is termed bioturbation and is difficult to quantify. Its high variability and unpredictability is a source of delight to biologists and irritation to physical scientists. The study of turbulent diffusion in the atmosphere includes aspects such as the micrometeorology of diffusion near the ground as it influences evaporation of pesticides, the uptake of contaminants by foliage, and the dispersion of plumes from stacks, in which case the plume is treated by the Gaussian dispersion equations. In lakes, rivers, and oceans it is important to calculate concentrations near sewage and industrial outfalls and in intensively used regions such as harbors. In each case, a body of specialized knowledge and calculation methods has evolved. ©2001 CRC Press LLC 7.5 UNSTEADY-STATE DIFFUSION Those who dislike calculus, and especially partial differential equations, can skip this section, but the two concluding paragraphs should be noted. In certain circumstances, we are interested in the transient or unsteady-state situation, which exists when diffusion starts between two volumes that are brought into contact. This is shown conceptually in Figure 7.4, in which a “shutter” is removed, exposing a concentration discontinuity. The two regions proceed to mix and chemical diffuses, eventually achieving homogeneity. <strong>Environmental</strong>ly, this situation is encountered when a volume of fluid (e.g., water) moves to an interface and there contacts another phase (e.g., air) containing a solute with a different fugacity. Volatilization may then occur over a period of time. There are now three variables: concentration (C), position (y), and time (t). If we consider a volume of ADy, as shown in Figure 7.4, then the flux in is –BA dC/dy, and the flux out is –BA(dC/dy + Dyd 2 C/dy 2 ), while the accumulation is ADyDC in the time increment Dt. It follows that or as Dy and Dt tend to zero, –BA dC/dy + BA(dC/dy + Dyd 2 C/dy 2 ) = ADyDC/Dt Bd 2 C/dy 2 = dC/dt This is Fick’s second law. Solution of this partial differential equation requires two boundary conditions, usually initial concentrations at specified positions. A particularly useful solution is the “penetration” equation, which describes diffusion into a slab of fluid that is brought into contact with another slab of constant concentration C S. The boundary conditions are
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McKay, Donald. "Front matter" Multi
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Multimedia Environmental Models The
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hensive, and reliable, and they hav
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Chapter 1 Introduction Chapter 2 So
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McKay, Donald. "Introduction" Multi
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It is now evident that our task is
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McKay, Donald. "Some Basic Concepts
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give the derived units directly wit
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Energy (joule, J) The joule, which
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particles (aerosols), or biota in w
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Worked Example 2.1 A three-phase sy
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(i) What is the concentration (C) i
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Answer ©2001 CRC Press LLC 5.1 kg,
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or or When t is zero, C is zero, th
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What is the absolute minimum piscic
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©2001 CRC Press LLC C 1 = C O/(1 +
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containing nonequilibrium quantitie
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1. Fallout of chemical from air to
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validated using real environments.
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©2001 CRC Press LLC CHAPTER 3 Envi
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of other, somewhat similar or homol
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Table 3.2 List of Chemicals Commonl
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elatively high concentrations. This
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exists between toxicologists and ch
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determine priority. This is a subje
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Another important classification of
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Figure 3.1 (continued) ©2001 CRC P
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Table 3.5 (continued) dichlorometha
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Table 3.5 (continued) total PCB 326
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Figure 3.2 Plot of log K AW vs. log
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chlorofluoro compounds are very sta
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3.3.2.7 Arsenic Compounds Arsenic,
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McKay, Donald. "The Nature of Envir
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Figure 4.1 Evaluative environments.
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are subject to two important deposi
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metals and organic chemicals from w
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carbon figure for deeper sediments
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flows. The quality of this groundwa
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Table 4.2 Evaluative Environments A
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McKay, Donald. "Phase Equilibrium"
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Figure 5.1 Some principles and conc
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likely using an equilibrium criteri
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Another useful quantity is the rati
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experimentally, but not directly, u
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©2001 CRC Press LLC 5.3 PROPERTIES
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1.0. This, then, is the fugacity or
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where ©2001 CRC Press LLC pH is -l
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In terms of solubilities, S iA and
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The temperature coefficient is the
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(1982), Baum (1997) and Leo (2000).
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Although it may appear environmenta
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Figure 5.4 Illustration of quantita
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5.5 ENVIRONMENTAL PARTITION COEFFIC
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C S = K PC W benzene = 1.1 ¥ 0.001
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Mackay (1986), in an attempt to sim
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Compartment Definition of Fugacity
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high concentration in the fish, but
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heat capacity of 0.38 J/g°C requir
Page 117 and 118: Therefore, ©2001 CRC Press LLC f =
Page 119 and 120: ©2001 CRC Press LLC Z T = S(V i/V
Page 121 and 122: ©2001 CRC Press LLC air Z = P S /R
Page 123 and 124: Table 5.1 Table 5.1 Summary of Defi
Page 125 and 126: Figure 5.7 Fugacity form 1 for dedu
Page 127 and 128: Calculate the following physical-ch
Page 129 and 130: ©2001 CRC Press LLC CHAPTER 6 Adve
Page 131 and 132: that all water will spend 100 days
Page 133 and 134: This enables us to conceive of, and
Page 135 and 136: ©2001 CRC Press LLC f = 15/0.5 = 3
Page 137 and 138: D AS dominates. A residence time of
Page 139 and 140: and Therefore, ©2001 CRC Press LLC
Page 141 and 142: eaction situation in which there is
Page 143 and 144: The rate constants in each case are
Page 145 and 146: ©2001 CRC Press LLC 1/t O = SD Ai/
Page 147 and 148: e achieved in 10 days. Detractors o
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Page 151 and 152: to Zepp and Cline (1977) for the or
Page 153 and 154: ©2001 CRC Press LLC 6.7 LEVEL II C
Page 155 and 156: Figure 6.3 Fugacity Level II calcul
Page 157 and 158: McKay, Donald. "Intermedia Transpor
Page 159 and 160: Figure 7.1 Illustration of nonequil
Page 161 and 162: 5. Diffusion within soils, and from
Page 163 and 164: sionally, the term flux rate is use
Page 165 and 166: ©2001 CRC Press LLC N = ABDC/ Dy m
Page 167: no currents or eddies. In practice,
Page 171 and 172: where ©2001 CRC Press LLC X = y/ U
Page 173 and 174: fraction of the total volume that i
Page 175 and 176: Figure 7.6 Mass transfer at the int
Page 177 and 178: partition coefficient. The signific
Page 179 and 180: and the series retains a similar ra
Page 181 and 182: ments of resuspension rates are par
Page 183 and 184: Figure 7.8 Movement of air phase (k
Page 185 and 186: ates can thus be used to estimate m
Page 187 and 188: Figure 7.9 Combination of D values
Page 189 and 190: Figure 7.10 Four-compartment Level
Page 191 and 192: Table 7.2 Order of Magnitude Values
Page 193 and 194: Unlike the Level II calculation, it
Page 195 and 196: Figure 7.12 Sample Level III output
Page 197 and 198: McKay, Donald. "Applications of Fug
Page 199 and 200: applications. Citations are given t
Page 201 and 202: Another approach is to employ Monte
Page 203 and 204: LEVEL1B A six-compartment Level I p
Page 205 and 206: Figure 8.1 Air-water exchange proce
Page 207 and 208: The total rates of transfer are thu
Page 209 and 210: Figure 8.2 Chemical transport and t
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Page 213 and 214: 8.5.2 Process Description The water
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Page 217 and 218: where Figure 8.5 QWASI model: stead
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are similar to those described by M
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C F ª Z Ff W ª 1.608 mol/m 3 ª 4
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y Mackay et al. (1983), and an appl
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accordingly, but the final solution
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Figure 8.10 Fish bioaccumulation pr
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The nature of the processes control
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iomagnification is more significant
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An alternative and more elegant met
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8.11.2 Model of a Chemical Evaporat
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Paterson et al. (1991), and Hung an
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8.14.1 Introduction ©2001 CRC Pres
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mated again in mg/day. Food, the ot
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models. Most interest is in LRT in
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available from the University of To
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McKay, Donald. "Appendix" Multimedi
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©2001 CRC Press LLC
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