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

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larger in mass and volume, but only a factor of 30 0.33 or about 3 in radius. The colloid diffusivity will thus be about one-third that of the dissolved molecule. But if 90% of the chemical is sorbed, the colloidal diffusion rate will exceed that of the dissolved form. As a result, is necessary to calculate and interpret the component diffusion processes, since it may not be obvious which route is faster. 7.7 DIFFUSION BETWEEN PHASES: THE TWO-RESISTANCE CONCEPT 7.7.1 Derivation Using Concentrations So far in this discussion, we have treated diffusion in only one phase, but in reality, we are most interested in situations where the chemical is migrating from one phase to another. It thus encounters two diffusion regimes, one on each side of the interface. <strong>Environmental</strong>ly, this is discussed most frequently for air-water exchange, but the same principles apply to diffusion from sediment to water, soil to water and to air, and even to biota-water exchange. An immediate problem arises at the interface, where the chemical must undergo a concentration “jump” from one equilibrium value to another. The chemical may even migrate across the interface from low to high concentration. Clearly, whereas concentration difference was a satisfactory “driving force” for diffusion within one phase, it is not satisfactory for describing diffusion between two phases. When diffusion is complete, the chemical’s fugacities on both sides of the interface will be equal. Thus, we can use fugacity as a “driving force” or as a measure of “departure from equilibrium.” Indeed, fugacity is the fundamental driving force in both cases, but it was not necessary to introduce it for one-phase systems, because only one Z applies, and the fugacity difference is proportional to the concentration difference. Traditionally, interphase transfer processes have been characterized using the Whitman Two-Resistance mass transfer coefficient (MTC) approach (Whitman, 1923), in which departure from equilibrium is characterized using a partition coefficient, or in the case of air-water exchange, a Henry’s law constant. We derive the flux equations for air-water exchange using the Whitman approach and following Liss and Slater (1974), who first applied it to transfer of gases between the atmosphere and the ocean, and Mackay and Leinonen (1975), who applied the same principles to other organic solutes. We will later derive the same equations in fugacity format. Unfortunately, the algebra is lengthy, but the conclusions are very important, so the pain is justified. Figure 7.6 illustrates an air-water system in which a solute (chemical) is diffusing at steady-state from solution in water at concentration C W (mol/m 3 ) to the air at concentration C A mol/m 3 , or at a partial pressure P (Pa), equivalent to C ART. We assume that the solute is transferred relatively rapidly in the bulk of the water by eddies, thus the concentration gradient is slight. As it approaches the interface, however, the eddies are damped, diffusion slows, and a larger concentration gradient is required to sustain a steady diffusive flux. A mass transfer coefficient, k W, applies over this region. The solute reaches the interface at a concentration C WI, then abruptly changes to C AI, the air phase value. The question arises as to whether there is a ©2001 CRC Press LLC
Figure 7.6 Mass transfer at the interface between two phases as described by the two-resistance concept. Note the concentration discontinuity on the right, whereas, in the equivalent fugacity profile on the left, there is no discontinuity. ©2001 CRC Press LLC
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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
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Therefore, ©2001 CRC Press LLC f =
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©2001 CRC Press LLC Z T = S(V i/V
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©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
Page 149 and 150: sulfate to sulfide or by dechlorina
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 and 168: no currents or eddies. In practice,
Page 169 and 170: diffusivity, and some unknown layer
Page 171 and 172: where ©2001 CRC Press LLC X = y/ U
Page 173: fraction of the total volume that i
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
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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
Page 215 and 216: learn the benefits of using fugacit
Page 217 and 218: where Figure 8.5 QWASI model: stead
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Page 221 and 222: C F ª Z Ff W ª 1.608 mol/m 3 ª 4
Page 223 and 224: 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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