Mathematical modeling sedimentation

The mathematical model chosen for this analysis is that of a cylinder rotating about its axis (Fig. 2). Suitable end caps are assumed. The Hquid phase is introduced continuously at one end so that its angular velocity is identical everywhere with that of the cylinder. The dow is assumed to be uniform in the axial direction, forming a layer bound outwardly by the cylinder and inwardly by a free air—Hquid surface. Initially the continuous Hquid phase contains uniformly distributed spherical particles of a given size. The concentration of these particles is sufftcientiy low that thein interaction during sedimentation is neglected. 

In this article, sampling methods for sediments of both paddy field and adjacent water bodies, and also for water from paddy surface and drainage sources, streams, and other bodies, are described. Proper sample processing, residue analysis, and mathematical models of dissipation patterns are also overviewed. 

Onishi, Y. Wise, S.E. "Mathematical Model, SERATRA, for Sediment - Contaminant Transport in Rivers and its Application to Pesticide Transport in Four Mile and Wolf Creeks in Iowa EPA-600/3-82-045, U.S. Environ. Prot. Agency, Environ. Research Lab. Athens, Georgia,1982 p. 56. 

A number of mathematical models have been developed in recent years which attempt to predict the behavior of organic water pollutants. >2>3 Models assume that compounds will partition into various compartments in the environment such as air, water, biota, suspended solids and sediment. The input to the models includes the affinity of the compound for each of the compartments, the rate of transfer between the compartments, and the rates of various degradation processes in the various compartments. There is a growing body of data, however, which indicates that the models to date may have overlooked a small but significant interaction. A number of authors have suggested that a portion of the compounds in the aqueous phase may be bound to dissolved humic materials and are not therefore truly dissolved. 

The quantitative water air sediment interaction (Qwasi) model was developed in 1983 in order to perform a mathematical model which describes the behavior of the contaminants in the water. Since there are many situations in which chemical substances (such as PCBs, pesticides, mercury, etc.) are discharged into a river or a lake resulting in contamination of water, sediment and biota, it is interesting to implement a model to assess the fate of these substances in the aquatic compartment [34]. 

Once the radionuclides reach the sediments they are subject to several processes, prime among them being sedimentation, mixing, radioactive decay and production, and chemical diagenesis. This makes the distribution profiles of radionuclides observed in the sediment column a residuum of these multiple processes, rather than a reflection of their delivery pattern to the ocean floor. Therefore, the application of these nuclides as chrono-metric tracers of sedimentary processes requires a knowledge of the processes affecting their distribution and their relationship with time. Mathematical models describing some of these processes and their effects on the radionuclide profiles have been reviewed recently [8,9,10] and hence are not discussed in detail here. However, for the sake of completeness they are presented briefly below. 

Solution of equation (10) which involves sedimentation in the presence of mixing and that of equation (11) which contains the sedimentation term only, are exponential in nature. The major conclusion which arises from this is that the logarithmic nature of the activity-depth profiles by itself is not a guarantee for undisturbed particle by particle sediment accumulation, as has often been assumed. The effects of mixing and sedimentation on the radionuclide distribution in the sediment column have to be resolved to obtain pertinent information on the sediment accumulation rates. (It is pertinent to mention here that recently Guinasso and Schink [65] have developed a detailed mathematical model to calculate the depth profiles of a non-radioactive transient tracer pulse deposited on the sediment surface. Their model is yet to be applied in detail for radionuclides. )... 

Geostatistical mathematical models can be used to assist investigators to target sampling locations and to avoid sampling in irrelevant areas. These models can be used to generate maps of soil, sediment, water, and groundwater contaminants. 

Reaction rates of nonconservative chemicals in marine sediments can be estimated from porewater concentration profiles using a mathematical model similar to the onedimensional advection-diffusion model for the water column presented in Section 4.3.4. As with the water column, horizontal concentration gradients are assumed to be negligible as compared to the vertical gradients. In contrast to the water column, solute transport in the pore waters is controlled by molecular diffusion and advection, with the effects of turbulent mixing being negligible. 

There are various mathematical models that can be used to describe and analyze experimental data (Scholze et al. 2001). In addition to these curve-fitting approaches, response surface models are also available (e.g., Greco et al. 1995), but these are suitable primarily for the analyses of experimental data, rather than for predictive purposes. As an example, Altenburger et al. (2004) applied both concentration addition and response addition and observed that the combined effect of a 3-compound mixture out of 10 identified sediment toxicants was sufficient to explain the observed combined effect of the more complex mixture. For identifying remediation priorities in site-specific assessment of complex contamination, this approach has great potential. 

Matisoff, G. (1982) Mathematical models of bioturbation. In Animal-Sediment Relations (McCall, P.L., and Tevesz, M.J.S., eds.), pp. 289-330, Plenum Press, New York. 

Jprgensen B. B. (1979) A comparison of methods for the quantification of bacterial sulfate reduction in coastal marine sediments 11. Calculation from mathematical models. Geomicrobiol. J. 1, 29-47. 

Van Cappellen P. and Berner R. A. (1988) A mathematical model for the early diagenesis of phosphorus and fluorine in marine sediments apatite precipitation. Am. J. Sci. 288, 289-333. 

There are also several methods to determine patterns of fate and transport of pollutants in the environment. In some cases, microcosms and me-socosms are used to study fate, biodegradability, bioavailability, and transport within compartments. Field surveys may also be used to study fate and transport of pollutants in contaminated environments. Such studies involve collection and analysis of biota, water, air, soil, or sediment. In some cases, radioactively labeled contaminants ( tracers ) may be introduced in mesocosms or noncontaminated environments in order to determine their fate and patterns of transport. Finally, mathematical models are often used to produce computer simulations to... 

The efficiency of the separation process, described as overall solids retention, was derived from particle-counting analyses through summation and integration. An attempt was also made to evaluate and interpret the observed removal behavior by analyzing data on specific microscopic suspension parameters such as floe shape. However, these latter data have not yet been incorporated into mathematical models. They have been used qualitatively to explain incongruencies observed in the performance of sedimentation and flotation tanks. 

Figure 6. Results of a mathematical model of organic acid generation from kerogen for two geothermal gradients (30 and 60 C/km). Sedimentation rate equals 500 m/m.y. in both cases. An arbitrary scale is used on X axes because of uncertainties in the accuracy of chosen kinetic parameters see text), a, Organic acid yield versus depth b, organic acid concentration versus depth. Continued on next page.

Nordin,C. F. (1975). Tidal data used to calibrate mathematical models for sediment transport in unsteady flows. EOS, Trans. Am. Geophys. Union 46, 981 (abstr.). 

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