Gravitational sedimentation, particle sizing

Sedimentation in liquids During gravitational sedimentation particles dispersed in a liquid settle with a velocity that is a function of their size. For a single, spherical particle in an infinite body of liquid the Stokes law is valid at low settling velocity (Reynolds number <0.2) ... 

The size of atmospheric particles ranges from molecular dimensions up to a diameter of above 10 m. Since particles with diameters below 0.1 fim (molecules and Aitken s nuclei) pre.sent no important problem and particles with diameters exceeding 10 fim are simply removed from the atmosphere by gravitational sedimentation, particles with diameters between 0.1 and 10 m are the main focus of interest. They can affect the reflection and scattering of the incident solar light, the local cloudiness and precipitation. 

Sedimentation (qv) techniques, whether based on gravitational forces or centrifugation, derive the particle size from the measured travel rates of particles in a Hquid. Before the particle analysis is carried out, the sample is usually dispersed in a medium to break down granules, agglomerates, and aggregates. The dispersion process might involve a simple stirring of the powder into a Hquid, but the use of an ultrasonic dispersion is preferred. 

Glassification. Classification (2,12,26,28) or elutriation processes separate particles by the differences in how they settle in a Hquid or moving gas stream. Classification can be used to eliminate fine or coarse particles, or to produce a narrow particle size distribution powder. Classification by sedimentation iavolves particle settling in a Hquid for a predetermined time to achieve the desired particle size and size distribution or cut. Below - 10 fim, where interparticle forces can be significant, gravitational-induced separation becomes inefficient, and cyclone and centrifugation techniques must be used. Classification also separates particles by density and shape. Raw material separation by differential sedimentation is commonly used in mineral processiag. 

Gravitational Sedimentation Methods In gravitational sedimentation methods, particle size is determined from settling velocity... 

Both particle size and the liquid viscosity affect the rate of particle settling. The rate of settling due to gravitational force decreases with decreasing particle size and increasing viscosity. The process mechanisms are sensitive to the relative rates of filtration and gravity sedimentation. 

Gravitational settlement is allowed to proceed for 4 to 10 minutes, according to the particle-size range of the sample. The sedimentation tube is then centrifuged to reduce the time required for the smaller particles to reach the bottom. By measuring the volume of particles accumulated as a function of time, the equivalent spherical size distribution of the sample may be computed from formulae based upon Stokes law. In addition to the specially designed sedi-... 

For the particle size measurements of boron and barium dichromate, components of pyrotechnic delay compns, Freeman (Ref 46) evaluated the MSA. Particle Size Analyzer versus microscopy, gravitational liq sedimentation,... 

Sedimentation analyses must be carried out at concentrations which are sufficiently low for interactive effects between particles to be negligible so that their terminal falling velocities can be taken as equal to those of isolated particles. Careful temperature control (preferably to 0.1 deg K) is necessary to suppress convection currents. The lower limit of particle size is set by the increasing importance of Brownian motion for progressively smaller particles. It is possible however, to replace gravitational forces by centrifugal forces and this reduces the lower size limit to about 0.05 p,m. 

It is dispersed by wind and removed by gravitational settling (sedimentation), dry deposition (inertial impaction characterized by a deposition velocity), washout by rain (attachment to droplets within clouds), and rainout (scrubbing action below clouds) (Schroeder et al. 1987). The removal rate and distance traveled from the source depends on source characteristics (e.g., stack height), particle size and density, and meteorological conditions. 

It is our objective in this chapter to outline the basic concepts that are behind sedimentation and diffusion. As we see in this chapter, gravitational and centrifugal sedimentation are frequently used for particle-size analysis as well as for obtaining measures of solvation and shapes of particles. Diffusion plays a much more prevalent role in numerous aspects of colloid science and is also used in particle-size analysis, as we see in Chapter 5 when we discuss dynamic light scattering. The equilibrium between centrifugation and diffusion is particularly important in analytical and preparative ultracentrifuges. 

The ultracentrifuge is an instrument in which a cell is rotated at very high speeds in a horizontal position. As we see below, the gravitational acceleration is easily increased by a factor of 105 in such an apparatus. Accordingly, the particle size that may be studied by sedimentation... 

It might be noted that sedimentation equilibrium is approached very slowly however, techniques that permit equilibrium conditions to be estimated from preequilibrium measurements have been developed by W. J. Archibald. Equations (86) and (87) predict a linear semilogarithmic plot of c versus x or x2 for gravitational and centrifugal studies, respectively. The slope of such a plot is proportional to the mass of the particles involved. Remember that monodispersity was assumed in the derivation of these equations. If this condition is not met for an experimental system, the plot just described will not be linear. If each particle size present is at equilibrium, however, each component will follow the equations and the experimental plot will be the summation of several straight lines. Under certain conditions these may be resolved to give information about the polydispersity of the system. In any event, nonlinearity implies polydispersity once true equilibrium is reached. 

Bomb products, rocket reentry bumup products, meteoritic dust, and other trace constituents will be redistributed rapidly within the mesosphere by large scale circulation, by eddy diffusion and, for particles of significant size, by gravitational sedimentation as well (1). Murgatroyd and Singleton (32) discuss the circulation of the mesosphere and indicate a meridional pattern, with ascent over the summer pole, descent over the winter pole, and a well defined flow from the summer hemisphere to the winter hemisphere above 50 km., with speeds of the order of meters sec."1 horizontally and cm. sec."1 vertically. 

As Martell has pointed out (30), in the region of the stratospheric large particle layer near 18-20 km. altitude, radioactive aerosol particles become attached to natural sulfate particles in the size range of about 0.1-0.4 jumeter radius. Subsequent upward transport of the radioactive aerosols is opposed by gravitational sedimentation. This combination of processes affords an explanation for the observed accumulation of 210Pb near 20 km. in the tropical stratosphere (2). At higher latitudes where slow mean motions are directed poleward and downward, no such accumulation is possible. 

Gravitational sedimentation causes a change in the particle size distribution anywhere in and below the cloud compared with the size distribution at stabilization time. Thus, to reconstruct the size distribution at stabilization time, corrections must be applied to the size distributions measured in the samples. These corrections were calculated by assuming Stokesian settling modified by a drag slip correction. It was assumed further that at stabilization time the cloud was axially symmetric and consisted of spherical particles. Wind and diffusion effects were neglected. 

In this chapter the thermal motion of dissolved macromolecules and dispersed colloidal particles will be considered, as will their motion under the influence of gravitational and centrifugal fields. Thermal motion manifests itself on the microscopic scale in the form of Brownian motion, and on the macroscopic scale in the forms of diffusion and osmosis. Gravity (or a centrifugal field) provides the driving force in sedimentation. Among the techniques for determining molecular or particle size and shape are those which involve the measurement of these simple properties. 

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 an estimate of the lower size limit, the displacement of the smallest particle by Brownian diffusion should be at least ten times smaller than its settling distance [10]. Other criteria could be selected since the error is both a function of the size and the spread of the distribution. It is reasonable however, for the sake of simplicity, to stipulate that if more than 10% of the distribution is smaller than the lower size limit, gravitational sedimentation should not be used. 

BS 3406, British Standard Method for determinig Particle Size Distribution is a comprehensive standard that includes methods for both incremental and cumulative methods of particle size deterination. Part 1, 1984, covers Recommendations for Gravitational Liquid Sedimentation Mehods for Powders and Suspensions. Part 5, 1985 covers... 

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