Sedimentation under gravity

A basic limitation of all these methods is the narrow range of particle sizes that can be investigated by sedimentation under gravity. Therefore, we turn next to a consideration of centrifugation, particularly the ultracentrifuge, as a means of extending the applicability of sedimentation measurements. 

If we substitute the value for the rate of sedimentation under gravity, Equation (4), we obtain... 

The kinetic properties of colloids are characterized by slow diffusion and slow, often negligible, sedimentation under gravity. 

One usually performs simultaneous investigation of sedimentation and diffusion by analyzing changes in the distribution of particles on the z axis with time. For sedimentation under gravity such simultaneous (within the same experiment) analysis of sedimentation and diffusion can be carried out but with great difficulty and only within a limited particle size range. 

During sedimentation under gravity, particle velocity is given by the ratio of force, Fg, to friction coefficient, B. For spherical particles B is given by the Stokes equation, B=6m r, and hence the sedimentation flux and corresponding phenomenological coefficient, an, are given by... 

The morphology of floes is determined to a large extent by the nature of the interparticle forces involved. Thus, if the particles arc strongly repelling but sediment under gravity or centrifugation, they tend to form a close-packed structure because the particles can slide across one another under the influence of Brownian motion and seek out a configuration of minimum... 

Flocculation and deflocculation, followed by sedimentation under gravity will be the subjects of discussion in this chapter. Even though the microorganisms due to be treated here in each unit operation will be different and inconsistent from one to another, depending on the subject, the aspect underlying the discussion will be made consistent such that the difference, if any, of the separation will be silhouetted between the biochemical and chemical industries. Because of the idea not to include especially the filtration and consolidation in this chapter, some brief comment on the recent advance in connection with these separation techniques will be needed. 

When the particle size is too small to be measured by using sedimentation under gravity, its collisions with the molecules of the liquid will cause measurable displacement. This effect will increase the lower limit to about 1 pm, when the gravitational settling measurement is carried out using water as the liquid. If the... 

Particle Manipulation Using Ultrasonic Fields, Fig. 2 Enhanced sedimentation. Particles within an ultrasonic field left) are agglomerated by the field center) and then tend to sediment under gravity right)... 

Note that Equations (5.3)-(5.6) have been derived for the case of the onedimensional random walk. This is because these equations will be used later in analysis of sedimentation under gravity where motion only in one direction (one dimension) is of interest. Only motion of particles in the direction of the applied gravitational force field is of interest in sedimentation lateral motion in the other two orthogonal directions is not. In the case of the three-dimensional random walk, the analogy to Equation (5.3) would be L = V6af. 

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