Pollution cloud

Box 19.2 Dilution of a Finite Pollutant Cloud Along One Dimension (Advanced Topic)... 

In this section we will develop the mathematical tools to describe mass transfer at diffusive boundaries. Again, it is our intention to demonstrate that diffusive boundaries have common properties, although the physics controlling them may be different. We will then apply the mathematical tools to the process of dilution of a pollutant cloud in an aquatic system (ocean, lake, river). Here the boundary is produced by the localized (continuous or event-like) input of a chemical that first leads to a confined concentration patch. The patch is then mixed into its environment by diffusion or dispersion. Note that in this case the physical characteristics on both sides of the... 

Strictly speaking, equations 19-52 and 19-53 are valid only if the pollutant cloud is infinitely long. A more realistic situation is treated in Box 19.2 here a pollutant patch of finite length L along the x-axis is eroded on both edges due to diffusion processes (turbulence, dispersion, etc.). Again, the boundary is of the diffusive type since the transport characteristics on both sides of the boundary are assumed to be identical. 

We consider a pollutant cloud which at time t = 0 has the concentration C° in the segments = —L/2, + L/2 and zero outside. The cloud along the x-axis is eroded by diffusion (or dispersion) in thex-direction. The effective diffusivity is D. According to Crank (1975), the concentration distribution at time t is ... 

The growth rate of the patch size a2(t) determines the dilution of a chemical into the environment and thus the drop of the maximum concentration of the chemical. Therefore, the power law relating a2(t) and t is of great practical importance, for instance, to predict the behavior of a pollutant cloud in the environment. As it turns out, the specific power law which follows from Okubo s theory, Eq. 22-42, greatly exaggerates the effect of dilution compared to observations made in the field. The shear diffusion model which will be discussed next gives a more realistic picture. 

If the water currents transport the pollutant cloud directly to the intake of the water plant, the transport time would be about ... 

Since the vertical spreading of the pollutant cloud can be neglected, the maximum concentration of atrazine at t = 10s s would be ... 

In Illustrative Example 24.5 we look again at the atrazine spill in River G of Illustrative Example 24.3 and ask how strongly dispersion would reduce the maximum atrazine concentration while the pollution cloud is moving downstream. 

What is the physical meaning of the time rskewed of Eq. 24-53 In what respect does a pollution cloud behave differently for times t < tskewed than for t > Skewed ... 

Consider the case of a pollution cloud in the river passing by the infiltration location during time At, which shall be very short compared to the time tw needed for the ground-water to travel from the river to the wells. During the event, the concentration in the river is Cin before and after the event, the riverine concentration is approximately zero. 

Note As discussed in Chapter 24, a pollution cloud caused by an accidental spill and traveling along a river often has the shape of a normal distribution (see Fig. 24.76). In order to keep the following considerations simple, it is assumed that the variance of the cloud in the river is still small at the time when infiltration takes place. Otherwise, the following considerations would have to be modified in a similar way as explained in Eqs. 24-55 and 24-56. 

The fate of the pollutant moving in the aquifer along the streamlines is determined by the advection-dispersion equation, Eq. 25-10 or 25-18. For Pe 1, that is, for locations x dis / if, the concentration cloud can be envisioned to originate from an infinitely short input atx = 0of total mass (a so-called5 input) that by dispersion is turned into a normal distribution function along the x-axis with growing standard deviation. Since the arrival of the main pollution cloud at some distance x is determined... 

In River R a pollution cloud of 2,4-dinitrophenol (see Illustrative Example 25.2) of duration At = 1 h and concentration Cin =50 ng L-1 is passing by Groundwater System S. Calculate the maximum concentration reached at the wells for the three regimes. Compare these values to the maximum concentrations reached 3 m away from the river. 

Remember that according to the approximation made for the dispersion coefficient, dis (Eq. 25-12), the Peclet Number does not depend on it. Therefore, the influence of the pump regime on the concentration at the well is not caused by a change of the transport conditions in the aquifer (e.g., flow time tw), but simply by the fact that more dinitrophenol enters the groundwater during the passage of the pollution cloud if u is large. 

In order to prevent polluted river water from reaching your drinking-water system, you want to know how much time you have to turn off the pumps once a pollution cloud in the river has reached the location adjacent to the well. In your considerations you assume that the concentration of the pollutant suddenly increases from 0 to a value 10 times above the maximum tolerable drinking-water concentration and then remains at this level. (1) Take the worst-case scenario and calculate how much time you have to turn off the pumps. (2) How much does this time change if you assume that the concentration in die river reaches 1000 times the maximum tolerable drinking-water concentration ... 

Perhaps a bit more visionary, many of the everyday materials of the future may be grown — self-assembled from a purpose-designed genetic blueprint — rather than hammered out in Blake s satanic mills. And doubtless, as with GM foods, some latter-day Blakes will see this as even more satanic, the polluting clouds made more frightening by their invisibility. This too, both benefits and worries, will be the province of Chemical Engineering. 

Owing to the lack of knowledge about the impact on man and animals of the barely perceptible substance in the polluted cloud, it was some time before a definitive assessment of the damage could be made, thus naturally exacerbating the anxiety and concern in the population affected. 

Hudson, J. G.. and Li, H. (1995) Contrasting microphysics between clean and polluted clouds, AMS Conference on Cloud Physics, Dallas, TX, January 15-20. 

The lifetime of OH in the river water, based on the reciprocal of the consumption rate constant, was in the range 2.6-6.0 x 10 s (Table 4). This value is similar to OH lifetimes reported in dew (Arakaki et al., 1999b) and cloud waters (Arakaki and Faust, 1998), while those in polluted cloud waters based on a modeling study were in the range 3-66 X 10 s (Jakob, 1986). Based on the photochemical formation rate and the total consumption rate constant of OH, steady-state OH concentrations were calculated to be in the range 3.3-8.4 X 10 M (Table 4), which is similar to reported values in river water (Brezonik and Fulkerson-Brekken, 1998), and in rain and dew water (Arakaki et al., 1999b). 

As should be evident, this survey has dealt on the whole with idealized models of aerosols and aerosol particles which are different from the complex aerosols of practical interest in such fields as air pollution, cloud physics, aerosol therapeutics, military science, industrial technology, etc. Indeed this complexity presents great difficulties in establishing a science of aerosols. 

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