Particle size measurement centrifugal sedimentation

Schweyer (1942) compared various methods of particle-size measurement (except centrifuging). He found excellent agreement between pipette and hydrometer methods. He considers the former the best method for determining the particle-m/.c distribution of sub-sieve material by sedimentation, and prefers the hydrometer as a rapid control procedure. 

The solution of the integral for measuring the concentration at constant position over time is only approximately possible. A common way uses Kamack s equation [Kamack, Br. J. Appll. Phys., 5, 1962-1968 (1972)] as recommend by ISO 13318 Part 1 Determination of Particle Size by Centrifugal Liquid Sedimentation Methods). 

Sedimentation techniques are amongst the oldest methods of particle size measurement. Sizes are derived from the rate of settling of particles under the action of gravitational or centrifugal forces. One sedimentation technique is the disk centrifuge, which is used to measure particles in the range 0.1-50 pm. 

The concept of equivalence is well known and accepted in particle size measurement, and the paper applies this concept to the measure of the spread of the distribution. It characterises the actual distribution of particle size in the slurry by an equivalent, lognormal distribution described by a simple formula with two numerical parameters, the geometric mean (as a measure of the mean size) and the geometric standard deviation (as a measure of the distribution spread). The equivalence is by separation efficiency in a dynamic separator such as a hydrocyclone or a sedimenting centrifuge. 

Berg, S. Determination of particle size distribution by examining gravitational and centrifugal sedimentation to the pipett method and with divers. Symp. PSA, June 1958, Boston, ASTM STP 234 (1959), p. 143 - 171 /4/ Chung, H. S. Hogg, R. The effect of Brownian motion on particle size analysis by sedimentation. Powder Techn. 41 (1985) 3, p. 211 - 216 /5/ Allen, T. Sedimentation techniques of particle size measurement. Conf. PSA Sept. 1985, Bradford, Proceed, p. 24 - 45... 

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. 

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-... 

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. 

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. 

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. 

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. 

In operationally defined speciation the physical or chemical fractionation procedure applied to the sample defines the fraction isolated for measurement. For example, selective sequential extraction procedures are used to isolate metals associated with the water/acid soluble , exchangeable , reducible , oxidisable and residual fractions in a sediment. The reducible, oxidisable and residual fractions, for example, are often equated with the metals associated, bound or adsorbed in the iron/manganese oxyhydroxide, organic matter/sulfide and silicate phases, respectively. While this is often a convenient concept it must be emphasised that these associations are nominal and can be misleading. It is, therefore, sounder to regard the isolated fractions as defined by the operational procedure. Physical procedures such as the division of a solid sample into particle-size fractions or the isolation of a soil solution by filtration, centrifugation or dialysis are also examples of operational speciation. Indeed even the distinction between soluble and insoluble species in aquatic systems can be considered as operational speciation as it is based on the somewhat arbitrary definition of soluble as the ability to pass a 0.45/Am filter. 

---