Sedimentation velocity decrease

Hindered Settling When particle concentration increases, particle settling velocities decrease oecause of hydrodynamic interaction between particles and the upward motion of displaced liquid. The suspension viscosity increases. Hindered setthng is normally encountered in sedimentation and transport of concentrated slurries. Below 0.1 percent volumetric particle concentration, there is less than a 1 percent reduction in settling velocity. Several expressions have been given to estimate the effect of particle volume fraction on settling velocity. Maude and Whitmore Br. J. Appl. Fhys., 9, 477—482 [1958]) give, for uniformly sized spheres,... 

With hydraulic residence times ranging from months to years, lakes are efficient settling basins for particles. Lacustrine sediments are sinks for nutrients and for pollutants such as heavy metals and synthetic organic compounds that associate with settling particles. Natural aggregation (coagulation) increases particle sizes and thus particle settling velocities (Eq. 7.1) and accelerates particle removal to the bottom sediments and decreases particle concentrations in the water column. 

The discussion so far relates to the motion of a single spherical particle in an effectively infinite expanse of fluid. If other particles are present in the neighbourhood of the sphere, the sedimentation velocity will be decreased, and the effect will become progressively more marked as the concentration is increased. There are three contributory factors. First, as the particles settle, they will displace an equal volume of fluid, and this gives rise to an upward flow of liquid. Secondly, the buoyancy force is influenced because the suspension has a higher density than the fluid. Finally, the flow pattern of the liquid relative to... 

Although the sedimentation velocity of particles tends to decrease steadily as the concentration of the suspension is increased, it has been shown by Kaye and Boardman11 that particles in very dilute suspensions may settle at velocities up to 1.5 times the normal terminal falling velocities, due to the formation of clusters of particles which settle in well-defined streams. This effect is important when particle size is determined by a method involving the measurement of the settling velocity of particles in dilute concentration, though is not significant with concentrated suspensions. 

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. 

Particle sinking rates are of considerable interest because the fester a particle can make the trip to the seafloor, the shorter the time it is subject to decomposition or dissolution and, hence, the greater its chances for burial in the sediments. The length of the trip is dictated by the depth to the seafloor, the horizontal current velocity, and the particle sinking rates. As shown in Figure 13.5, sedimentation rates decrease with increasing water depth. This relationship reflects the preservation issue and the feet that coastal waters tend to have larger sources of particles to the surfece zone. 

Equation (3) shows that the sedimentation velocity increases with the density difference between the particle and the medium. Any situation that brings the density of the settling unit closer to that of the solvent will decrease the sedimentation velocity. To an observer who is unaware of its derivation, however, the smaller velocity would be interpreted by Equation (4) as indicating a smaller value of (m/f). Since the actual mass of colloidal material is unaffected by the solvation, it is more correct to attribute the reduced sedimentation velocity to an increase in the value of the friction factor. 

Two-Layer Method. A suspension is spread in a thin layer on the surface of a clear, solids-free liquid. The particles then fall through the liquid in order of decreasing sedimentation velocity and reach the measuring plane in succession. 

It is evident from the above expressions that the appropriate diffusion coefficient must also be measured in order that molecular or particle masses may be determined from sedimentation velocity data. In this respect, a separate experiment is required, since the diffusion coefficient cannot be determined accurately in situ, because there is a certain self-sharpening of the peak due to the sedimentation coefficient increasing with decreasing concentration. 

Filtration is a physical separation whereby particles are removed from the fluid and retained by the filters. Three basic collection mechanisms involving fibers are inertial impaction, interception, and diffusion. In collection by inertial impaction, the particles with large inertia deviate from the gas streamlines around the fiber collector and collide with the fiber collector. In collection by interception, the particles with small inertia nearly follow the streamline around the fiber collector and are partially or completely immersed in the boundary layer region. Subsequently, the particle velocity decreases and the particles graze the barrier and stop on the surface of the collector. Collection by diffusion is very important for fine particles. In this collection mechanism, particles with a zig-zag Brownian motion in the immediate vicinity of the collector are collected on the surface of the collector. The efficiency of collection by diffusion increases with decreasing size of particles and suspension flow rate. There are also several other collection mechanisms such as gravitational sedimentation, induced electrostatic precipitation, and van der Waals deposition their contributions in filtration may also be important in some processes. 

For very dilute suspensions ((p <0.01), H decreases linearly to a constant level. The floes individually settle rather than as networked clusters. As the concentration of floes increases, the sedimentation velocity rapidly reduces and the increase in mixing boosts the settling rate, indicating that larger aggregated floes are produced. 

For more concentrated suspensions (q> >0.2), the sedimentation velocity becomes a complex function of At > 0.4, a hindered settling regime is usually entered whereby all of the particles sediment at the same rate (independent of size). A schematic representation for the variation of v with is shown in Figure 9.12, which also shows the variation of relative viscosity with rp. It can be seen from these data that v decreases exponentially with increase in approaches zero when cp approaches a critical value (the maximum packing fraction). The relative viscosity shows a gradual increase with increase in cp such that, when cp = the relative viscosity approaches infinity. 

Gel filtration may be used as a means of detecting different conformations of a protein. Kornfeld (137) has found that the elution of Fe3+-saturated transferrin through Sephadex G-100 is retarded relative to the apoprotein. Similar results have been reported by Charlwood (139) who appears to have been able to resolve the three species (O-Fe, 1-Fe and 2-Fe) of transferrin by this method, indicating a 0.7% decrease in the Stokes radius of the molecule per iron atom bound. Differential measurements of sedimentation velocity showed about 1.8% increase in S20W upon binding of 2 iron atoms per mole (139). 

The particle Reynolds number, given by dvpc/t]c, must be smaller than about 0.1, since otherwise turbulence will develop in the wake of the sedimenting particle, decreasing its velocity. Putting v = vs, it turns out that for an oil drop in water, the critical particle size is 140 pm. 

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