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

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This flux of 0.002 mol/s can be regarded as a net flux consisting of k MAC 1 or 0.003 mol/s in one direction and k MAC 2 or 0.001 mol/s in the opposing direction. Worked Example 7.2 Water is evaporating from a pan of area 1 m 2 containing 1 cm depth of water. The rate of evaporation is controlled by diffusion through a thin air film 2 mm thick immediately above the water surface. The concentration of water in the air immediately at the surface is 25 g/m 3 (this having been deduced from the water vapor pressure), and in the room the bulk air contains 10 g/m 3 . If the diffusivity is 0.25 cm 2 /s, how long will the water take to evaporate completely? B is 0.25 cm 2 /s or 0.09 m 2 /h Dy is 0.002 m DC is 15 g/m 3 N = ABDC/Dy = 675 g/h To evaporate 10000 g will take 14.8 hours Note that the “amount” unit in N and C need not be moles. It can be another quantity such as grams, but it must be consistent in both. In this example, the 2 mm thick film is controlled by the air speed over the pan. Increasing the air speed could reduce this to 1 mm, thus doubling the evaporation rate. This Dy is rather suspect, so it is more honest to use a mass transfer coefficient, which, in the example above is 0.09/0.002 or 45 m/h. This is the actual net velocity with which water molecules migrate from the water surface into the air phase. 7.3.5 Sources of Molecular Diffusivities Many handbooks contain compilations of molecular diffusivities. The text by Reid et al. (1987) contains data and correlations, as does the text on mass transfer by Sherwood, Pigford, and Wilke (1975). The handbook by Lyman et al. (1982) and the text by Schwarzenbach et al. (1994) give correlations from an environmental perspective. The correlations for gas diffusivity are based on kinetic theory, while those for liquids are based on the Stokes–Einstein equation. In most cases, only approximate values are needed. In some equations, the diffusivity is expressed in dimensionless form as the Schmidt number (Sc) where where m is viscosity and r is density. ©2001 CRC Press LLC Sc = m/rB 7.4 TURBULENT OR EDDY DIFFUSION WITHIN A PHASE So far, we have assumed that diffusion is entirely due to random molecular motion and that the medium in which diffusion occurs is immobile or stagnant, with
no currents or eddies. In practice, of course, the environment is rarely stagnant, there being currents and eddies induced by the motion of wind, water, and biota such as fish and worms. This turbulent motion, illustrated in Figure 7.3, also promotes mixing by conveying an element or eddy of fluid from one region to another. The eddies may vary in size from millimetres to kilometres, and a large eddy may contain a fine structure of small eddies. Intuitively, it is unreasonable for an eddy to penetrate an interface, thus in regions close to interfaces, eddies tend to be damped, and only slippage parallel to the interface is possible. There may, therefore, be a thin layer of relatively quiescent fluid close to the interface that can be referred to as a laminar sublayer. In this layer, movement of solute to and from the interface may occur only by molecular diffusion. Under certain conditions, eddies in fluids may be severely damped, or their generation may be prevented. This occurs in a layer of air or water when the fluid density decreases with increasing height. This may be due to the upper layers being warmer or, in the case of sea water, less saline. An eddy that is attempting to move upward immediately finds itself entering a less dense fluid and experiences a hydrostatic “sinking” force. Conversely, a companion eddy moving downward experiences a “floating” force, which also tends to restore it to its original position. This inherent resistance to eddy movement damps out most fluid movement, and stable, stagnant conditions prevail. Thermoclines in water and inversions in the atmosphere are examples of this phenomenon. These stagnant or near-stagnant layers may act as diffusion barriers in which only molecular diffusion or slight eddy diffusion can occur. Conversely, situations in which density increases with height tend to be unstable, and eddy movement is enhanced and accelerated by the density field. An attractive approach is to postulate the existence of an eddy diffusivity, or a turbulent diffusivity, B T, which is defined identically to the molecular diffusivity, B M. The flux equation within a phase then becomes ©2001 CRC Press LLC N = –A(B M + B T)dC/dy The task is then to devise methods of estimating B T for various environmental conditions. We expect that, in many situations, such as in winds or fast rivers, B T Figure 7.3 The nature of turbulent or eddy diffusion in which chemical is conveyed in eddies within a fluid to a surface.
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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
Page 115 and 116: 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
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Page 165: ©2001 CRC Press LLC N = ABDC/ Dy m
Page 169 and 170: diffusivity, and some unknown layer
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
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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
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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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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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