Particle sedimentation model

Winters and Lee134 describe a physically based model for adsorption kinetics for hydrophobic organic chemicals to and from suspended sediment and soil particles. The model requires determination of a single effective dififusivity parameter, which is predictable from compound solution diffusivity, the octanol-water partition coefficient, and the adsorbent organic content, density, and porosity. 

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. )... 

In Chapter 21 on box models no distinction was made between a compound being present as a dissolved species or sorbed to solid surfaces (e.g., suspended particles, sediment-water interface). In Boxes 18.5 and 19.1, and also in Illustrative Example 19.6, we learned that several of the transport and transformation processes may selectively act on either the dissolved or the sorbed form of a constituent. For instance, a molecule sitting on the surface of a sedimentaiy particle at the lake bottom does not feel the effect of turbulent flow in the lake water, while the dissolved chemical species is passively moved around by the currents. In contrast, a molecule sorbed to a suspended particle (e.g., an algal cell) can sink through the water column because of gravity, unlike its dissolved counterpart. 

In the last step (Part 3), the sedimentary compartment (the surface mixed sediment layer , SMSL) was treated as an independent box (Table 23.7). The steady-state solution of the combined sediment/water system explained another characteristic of the observed concentrations, which, as mentioned above, could not be resolved by the one-box model. As shown in Table 23.8, for both congeners the concentration measured on particles suspended in the lake is larger than on sediment particles. The two-box model explained this difference in terms of the different relative organic carbon content of epilimnetic and sedimentary particles. This model also gave a more realistic value for the response time of the combined lake/sediment system with respect to changes in external loading of PCBs. However, major differences between modeled and observed concentrations remained unexplained. 

Compared to the situation in lakes, the sediment-water interactions in rivers are more complex. Because the flow velocity is constantly changing, particles may either settle at the bottom or be resuspended and deposited again further downstream. In order to adequately describe the effect of these processes on the concentration of a chemical in the river, we would need a coupled water-sediment model with which the profile of the chemical along the river of both the aqueous concentration in the river and the concentration in the sediment bed are described. This is a task to be left to numerical modeling. We choose a simpler approach by approximating the net deposition of the particles and the chemicals sorbed to them as a linear process (see Eqs. 23-16 and 23-17) ... 

Comparison of the depositional fluxes shows that diatoms were the most important particle component transporting P to the sediment surface, accounting for 50-55% of the flux (Table II). Terrigenous material and calcite were also important transport vectors. Deposition varied markedly with season, as shown by the time series plot of the major particle components (Figure 13). The total P flux calculated by using the particle components model agreed with the flux measured by sediment traps (157-227 versus 185 mg/m2). The close agreement indicated that the major particle vectors were represented and associated P concentrations were accurately quantified. 

To ensure that only the finer fraction of the sediment slurry was processed, a shipboard centrifugal cone separator was connected to the slurry transfer hose to remove the coarse-sediment fraction. The cone separator was a 101.6-mm diameter, urethane-coated centrifugal cone (Demco 275). Under a normal operational pressure of 221 kPa the cone separator is capable of delivering 57.0 L/min of sediment slurry, whose sediment particle size ranged from 2 to 32 jitm as measured on the particle data Model 111 analyzer. 

Fig. 22 Results of an investigation, by water modeling, of Kalgraf and Torklep, into transport of alumina particles (sediment) along the bottom of a cell. The parameters on the curves are the diameters (millimeters) of nylon particles (simulating alumina particles). Solid lines are calculated curves [64],...

Hinderliter PM, Minard KR, Orr G, Chrisler WB, Thrall BD, Pounds JG, Teeguarden JG (2010) ISDD a computational model of particle sedimentation, diffusion and target cell dosimetry for in vitro toxicity studies. Part Fibre Toxicol 7(1) 36... 

Sedimentation of PSC particles can be an effective process for removing water and nitrogen compounds from the atmosphere (dehydration and denitrification), and has to be taken into account when modeling PSC effects. The velocity at which particles sediment increases with the size of these particles. If the size distribution of the particles follows a lognormal law, the sedimentation flux for a given chemical compound can be expressed as (Considine et ai, 2000)... 

Fig. 2.2 Two types of sediment models, (a) The layered, volume-oriented model for bulk parameters only depends on the relative amount of solid and fluid components, (b) The microstructure-oriented model for acoustic and elastic parameters takes the complicated shape and geometry of the particle and pore size distribution into account and considers interactions between the solid and fluid constituents during wave propagation.

For particles, the model is identical to that for gases except that particle settling operates in parallel with the three resistances in series. The sedimentation flux is equal to the particle settling velocity, vs, multiplied by the particle concentration. It is usually assumed that particles adhere to the surface on contact so that the surface or canopy resistance rc = 0. In this case the vertical flux is... 

Particle concentration and size distribution in raw water have extensive and complex effects on the performance of individual treatment units (flocculator, sedimentation tank, and filter) and on the overall performance of water treatment plants. Mathematical models of each treatment unit were developed to evaluate the effects of various raw water characteristics and design parameters on plant performance. The flocculation and sedimentation models allow wide particle size distributions to be considered. The filtration model is restricted to homogeneous suspensions but does permit evaluation of filter ripening. The flocculation model is formulated to include simultaneous flocculation by Brownian diffusion and fluid shear, and the sedimentation model is constructed to consider simultaneous contacts by Brownian diffusion and differential settling. The predictions of the model are consistent with results in water treatment practice. 

The authors would like to express their appreciation to Harvey Jeffries, Associate Professor, and Michael Kuhlman, graduate student, in the Department of Environmental Sciences and Engineering, University of North Carolina at Chapel Hill, for their assistance in developing the computer programs for the flocculation and sedimentation models, and to Brian Ramaley, a graduate student in the same department, for his aid in calculating the effects of particle size distribution. 

Although these PANI-coated monodispersed particles are ideal for use as model ER materials, the particle size is micrometer-size and large particle settling problem is needed to overcome. Recently, using nanoparticles as the dispersal phase or filler has attracted considerable interest in the development of a non-conventional ER fluids [ 12-15,48-52]. In particular, significant attention has been paid to one-dimensional (ID) nanofiber suspensions because it has been foxmd that the nanofiber suspensions exhibit not only higher ER or MR effect, but also reduced particle sedimentation... 

The settling behaviour was described by Nakamura and Kuroda [1937], w4io assumed that onfy the downward dng surfrces accelerated sedimentation and that particles in the settling suspension tend to keep the same distance apart until they ali t on a solid surfrce or upon other particles. The model describes the settling process in a tilted square section tube on its edge. 

With regard to an effective use of catalyst it is necessary to realize a uniform distribution over the entire reactor. There are a number of experimental studies reported in the literature (1-5) which show that even for small particles well pronounced solid concentration profiles can be observed in the gas agitated bubble column slurry reactors (BCSR). A dispersion-sedimentation model has been proposed, which successfully describes measured data (2-4). 

The nonuniform catalyst distribution due to the settling of the particles is characterized in the balance equations by the variable ( ), which represents the ratio of the local solid concentration to the reactor mean value Ccat The catalyst concentration profile follows from the dispersion-sedimentation model (2-4). 

Joshi et al. (30) proposed reactor models based on the shrinking core mechanism. Since the particles take part in the reaction their role was evaluated based on the residence time distribution. For extremely fine pyrite particles, (< 100 ym), it has been shown (31) that the RTD of the solid and liquid phases can be asstimed to be identical and the RTD of the solid phase is given by the diffusion-sedimentation model. Various rate controlling steps that were considered are (1) gas-liquid mass transfer (2) liquid-solid mass transfer (3) ash diffusion (4) chemical reaction and, (5) intraparticle diffusional resistance (for particles encased in the coal matrix). 

A fairly complete model of the in bubble column slurry reactors has been presented by Joshi et al. [l5l]. It includes a dispersion-solids sedimentation model to describe the RTD of the reactive particles but solids accumulation is not included, hence g 1 L equation used is taken from Joshi [43] ... 

Successful application of dispersion-solids sedimentation models in continuous bubble column reactors has been achieved but it also has been shown that the solids sedimentation effects rapidly decrease with reactor diameter. For columns larger than 30 cm, solids settling effects usually can be neglected for particle sizes up to 200 pm. 

Of the 41 listed in Table 4.1 the 16 most common mass transport processes representing the air, water, and soil and sediment media appear in Table 4.2. The media of prime concern often dictate the most convenient phase concentration used in the flux equation. For example, water quality models usually have Cw as the state variable and therefore the flux expression must have the appropriate MTC group based on Cw and these appear in the center column of Table 4.2. Aquatic bed sediment models usually have Cs, the chemical loading on the bed solids, as the state variable. The MTC groups in the right eolumn are used. All the MTC groups in Table 4.2 contain a basic transport parameter that reflects molecule, element, or particle mobility. Both diffusive and advective types appear in the table. These are termed the individual phase MTCs with SI units of m/s. Examples of each type in Table 4.2 include for water solute transport and Vg for sediment particle deposition (i.e., setting). 

The concept of probability of deposition has been applied in transport models for fine-grained sediments that may exist in suspension as both aggregate and individual particles. Notable models include STUDH by Ariathurai and Krone (1976) and SEDZL by Ziegler and Lick (1986), which has also been extended to coarser-grained (noncohesive) sediments by Ziegler and Nisbet (1994), Gailani et al. (1991), and Jones and Lick (2001). 

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