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

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Figure 7.2 The fundamental nature of molecular diffusion. Here, N is the flux of chemical (mol/h), B is the diffusivity (m2/h), A is area (m2), C is concentration of the diffusing chemical (for example, benzene in water) (mol/m3), and y is distance (m) in the direction of diffusion. The group dC/dy is thus the concentration gradient and is characteristic of the degree to which the solution is unmixed or heterogeneous. The negative sign arises because the direction of diffusion is from high to low concentration, i.e., it is positive when dC/dy is negative. Here, we use the symbol B for diffusivity to avoid confusion with D values. Most texts sensibly use the symbol D. The equation is really a statement that the rate of diffusion is proportional to the concentration gradient and the proportionality constant is diffusivity. When the equation is apparently not obeyed, we attribute this misbehavior to deviations or changes in the diffusivity, not to failure of the equation. As was discussed earlier, there are differences of opinion about the word flux. We use it here to denote a transfer rate in units such as mol/h. Others insist that it should be area specific and have units of mol/m2h. We ignore their advice. Occa- ©2001 CRC Press LLC
sionally, the term flux rate is used in the literature. This is definitely wrong, because flux contains the concept of rate just as does speed. Flux rate is as sensible as speed rate. It is worthwhile digressing to examine how the mixing process leads to diffusion and eventually to Fick’s first law. This elucidates the fundamental nature of diffusivity and the reason for its rather strange units of m2/h. Much of the pioneering work in this area was done by Einstein in the early part of this century and arose from an interest in Brownian movement—the erratic, slow, but observable motion of microscopic solid particles in liquids, which is believed to be due to multiple collisions with liquid molecules. 7.3.2 Fick’s Law and Diffusion at Steady State We consider a square tunnel of cross-sectional area A m2 containing a nonuniform solution, as shown in the middle of Figure 7.2, having volumes V1, V2, etc., separated by planes 1–2, 2–3, 3–4, etc., each y metres apart. We assume that the solution consists of identical dissolved particles that move erratically, but on the average travel a horizontal distance of y metres in t hours. In time t, half the particles in volume V3 will cross the plane 2–3, and half the plane 3–4. They will be replaced by (different) particles that enter volume V3 by crossing these planes in the opposite direction from volumes V2 and V4. Let the concentration of particles in V3 and V4 be C3 and C4 mol/m3 such that C3 exceeds C4. The net transfer across plane 3–4 will be the sum of the two processes: C3 yA/2 moles from left to right, and C4 yA/2 moles from right to left. The net amount transferred in time t is then ©2001 CRC Press LLC C3yA/2 – C4 yA/2 = (C3 – C4) yA/2 mol Note that CyA is the product of concentration and volume and is thus an amount (moles). The concentration gradient that is causing this net diffusion from left to right is (C3 – C4)/y or, in differential form, dC/dy. The negative sign below is necessary, because C decreases in the direction in which y increases. It follows that The flux or diffusion rate is then N or (C3 – C4) = –ydC/dy N = (C3 – C4) yA/2t = –(y2A/2t) dC/dy = –BAdC/dy mol/h which is referred to as Fick’s first law. The diffusivity B is thus (y2/2t), where y is the molecular displacement that occurs in time t. In a typical gas at atmospheric pressure, the molecules are moving at a velocity of some 500 m/s, but they collide after traveling only some 10–7 m, i.e., after 10–7/500 or 2 ¥ 10–10 s. It can be argued that y is 10–7 m, and t is 2 ¥ 10–10; therefore, we
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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
Page 111 and 112: Compartment Definition of Fugacity
Page 113 and 114: 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: 5. Diffusion within soils, and from
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 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
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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8.5.2 Process Description The water
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learn the benefits of using fugacit
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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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