The sedimentation rate

Solute particles in a spinning rotor adopt a constant speed away from the rotational axis because the outward, centrifugal force is balanced by a retarding, frictional force. The sedimentation constant, S, a measure of the rate at which a particle migrates in the centrifugal field, is defined as 

Relation between the molar mass and the sedimentation constant 

A solute particle of mass m has an effective mass mes= bm in the solution. The solute particles at a distance r from the axis of a rotor spinning at an angular velocity experience a centrifugal force of magnitude r . The acceleration 

we draw on the Stokes-Einstein relation,/= kT/D, between the frictional coefficient,/, and the diffusion coefficient, D, to write 

The diffusion coefficient is related to the rate at which molecules migrate down a concentration gradient (it is treated in detail in Section 8.5) and can be measured by observing the rate at which a concentration boundary moves or the rate at which a more concentrated solution diffuses into a less concentrated one. The diffusion coefficient can also be measured by using laser light-scattering methods (Section 11.3). It follows that we can find the molar mass by combining measurements of sedimentation and diffusion rates (to obtain S and D, respectively). 

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Excessive volume of soHds may be retained in the bowl of conveyor centrifuges if (/) the conveyor volumetric displacement is not sufficient to handle the sedimentation rate of soHds (2) the sedimented soHds cannot be successfully conveyed and discharged over the soHds port until a sufficient layer has been built up inside the bowl and (3) soHds do not easily sHde outwardly on the underside of the disk of a disk centrifuge. 

Most surface waters contain varying amounts of suspended solids, including silt, clay, bacteria, and vimses and it is necessary to remove these before to distribution to the domestic or industrial consumer. Suspended soHds not only affect the acceptabiUty of the water but also interfere with disinfection. The principal treatment processes are sedimentation (qv) and filtration (qv). Sedimentation alone is rarely adequate for the clarification of turbid waters and is of htde or no value for the removal of such very fine particles as clay, bacteria, etc. Table 1 shows the effect of particle size on the sedimentation rate of a soHd having a specific gravity of 2.65 in water at 20°C. 

There are two essential consequences of this relation. Because larger droplets sediment or rise much faster (a 5-p.m drop rises 625 times faster than a 0.2-p.m droplet), the process is equal to shearing, leading to enhanced flocculation. The ratio between flocculation due to shear and to diffusion of droplets is proportional to the cube of the radius. Secondly, flocculation to droplet aggregates means an enhanced sedimentation rate. Sis drops ia an octahedral arrangement gives approximately four times the sedimentation rate. 

Thickener-Basin Depth The pulp depth required in the thickener will be greatly affected by the role that compression plays in determining the rate of sedimentation. If the zone-settling conditions define the area needed, then depth of pulp will be unimportant and can be largely ignored, as the normal depth found in the thickener will be sufficient. On the other hand, with the compression zone controlling, depth of pulp will be significant, and it is essential to measure the sedimentation rate under these conditions. 

If the feed rate exceeds the maximum of the design, particulate matter are unable to settle out of the normal clarification zone. Hence, there is an increase in the solids concentration, resulting in hindered settling. The result Is a corresponding decrease in the sedimentation rate below that observed for the feed slurry. 

For any section of the core, being known the in situ density and the sedimentation rate calculated from the radioisotope profiles, the pollutant... 

Stigter, D, Ionic Charge Effects on the Sedimentation Rate and Intrinsic Viscosity of Polyelectrolytes. T7 DNA, Macromolecules 18, 1619, 1985. 

If Vtii/Ptii = 1 then the accumulation of °Thxs in marine sediments would provide an assessment of their sedimentation rate. For instance, if Pm is N dpm m yr , and N dpm are found in the upper 1 cm of 1 m of seafloor, then the sedimentation rate must be lcmyr Sedimentation rate is an important variable in paleoceanographic reconstruction as it provides the timescale for the continuous record of environmental change recorded in marine sediments. Sedimentation rate is also a key geochemical variable as sediments are the major sink for most chemical species in the ocean. A tool allowing assessment of past sedimentation rates is therefore an appealing prospect. 

Where Ao is the activity at the sediment surface, w is the sedimentation rate (cm yr ), D is the mixing rate (cm yr ), is the decay constant for the nuclide of interest (yr ) and z is the depth in the sediment (cm). In some near-shore environments both sedimentation and bioturbation must be considered. But in most open marine environments the sedimentation rate is sufficiently slow that it can be ignored and the equation simplifies to ... 

The viscosity of water also changes with temperature. It decreases with an increase in temperature because of the reduction in the number of hydrogen bonds binding the molecules together. The viscosity of water has an influence on the movement of solutes in water and on the sedimentation rate of suspended solids. 

Between 1890 and 1902, the sedimentation rate identified as Region II of figure 3 averaged 1800 g m"2 yr-1 or 0.83 cm yr-1, i.e., greater than 10 times the pre-cultural rate. Historical records and photographs show that by 1895 most of the land comprising the watershed had been logged and the suburbs of Seattle had reached the lake shore. This rapid land development in the watershed occurred about the turn of the century. 

Since 1916 the sedimentation rate, Region III of Figure 3, has averaged 644 g m-2 yr-1 or 0.3 cm yr 1 or about 5 times the pre-cultural rate. The diversion of the Cedar River (average flow of 20 m3 s 1 into the lake in 1916 provided the water necessary to operate the ship and canal locks and contributes an estimated 4-5 x 107 kg-yr-1 of allochthonous material, Crecelius [7]. This riverine sediment input would contribute to the greater... 

A series of gravity cores was collected inside the inlet and at a control station located some 5 km north of the inlet in Port Orchard Passage, as shown in figure 2. The sedimentation rates as determined by 210Pb are shown in figure 4a where a least squares fit of the data gives an average sedimentation rate of... 

The simplest approach considers a perfectly mixed bioturbated layer of thickness L and homogeneous concentration C. If v is the sedimentation rate, the mass balance condition for element i reads... 

Analytical rotors are used to study the sedimentation rate of a sample. 

If the ratio of the diameter of the vessel to the diameter of the particle is greater than about 100, the walls of the container appear to have no effect on the rate of sedimentation. For smaller values, the sedimentation rate may be reduced because of the retarding influence of the walls. 

Provided that the walls of the vessel are vertical and that the cross-sectional area does not vary with depth, the shape of the vessel has little effect on the sedimentation rate. However, if parts of the walls of the vessel face downwards, as in an inclined tube, or if part of the cross-section is obstructed for a portion of the height, the effect on the sedimentation process may be considerable. 

In an initially uniform suspension of concentration C0, the interface between the suspension and the supernatant liquid will fall at a constant rate until a zone of composition, greater than C0, has propagated from the bottom to the free surface. The sedimentation rate will then fall off progressively as zones of successively greater concentrations reach the surface, until eventually sedimentation will cease when the Cmax zone reaches the surface. This assumes that the propagation velocity decreases progressively with increase of concentration. 

Because the concentration of particles is initially uniform and the sedimentation rate is a function solely of the particle concentration, the line APB will be straight, having a slope (—AH/At) equal to uc. 

For relatively coarse particles, the rates of fall of the interface between (a) and (b) and between (b) and (c) can be calculated approximately if the relation between sedimentation velocity and voidage, or concentration, is given by equation 5.76. Richardson and Shabi 65) have shown that, in a suspension of particles of mixed sizes, it is the total concentration which controls the sedimentation rate of each species. 

When the particles of two sizes are settling together, the upflow of displaced fluid is caused by the combined effects of the sedimentation of the large and small particles. If this upward velocity is up, the sedimentation rates uml and uMs will be obtained by deducting u F from the velocities relative to the fluid. 

Equation 5.113 gives the rate of fall of the interface between zones (b) and (c) that is the apparent rate of settling of the zone of mixed particles. The velocity of fall // of the interface between zones (a) and (b) is the sedimentation rate of the suspension composed only of fine particles, and will therefore depend on the free-falling velocity u<)S and the concentration Cf of this zone. ... 

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