Centrifugal Sedimentation Methods
These methods extend sedimentation methods well into the submicron size range. Alterations of the particle concentration may be determined space- and time resolved during centrifugation [T. Detloff, D. Lerche, “Determination of Particle Size Distributions based on Space and Time Resolved Extinction Profiles in Centrifugal Field”, Proceedings of Fifth World Congress on Particle Technology, Session Particle Measurement, Orlando USA, 23rd – 27th April 2006]. Sizes are calculated from a modified version of the Stokes equation:
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(1) |
where w is the radial velocity of the centrifuge. The concentration calculations are complicated due to radial dilution effects (i.e. particles do not travel in parallel paths as in gravitational sedimentation but move away from each other as they settle radially outwards). Particle velocities are given by
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(2) |
here both r the measurement radius, and s, the surface radius, can be varying: the former varies if the system is a scanning system, and the latter if the surface falls due to the extraction of samples.
Concentration undersize Dm is determined by
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(3) |
with |
 |
(4) |
where q3(x)=dQ3(x)/dx is the volume or mass density distribution and z is the integration variable.
The solution of the integral for measuring the concentration at constant position over time is only approximately possible. A common way is using Kamacks’s equation [Kamack,Br. J. Apll. Phys., 5, 1962-68 (1972)] as recommend by [ISO 13318 part 1 Determination of particle size by centrifugal liquid sedimentation methods].
An analytical solution is provided by measuring the concentration to at least one time at different sedimentation heights:
 |
(5) |
where ri is the measurement position and s the surface radius. Q3(x) is cumulative mass or volume concentration, (ri/si)² is the radial dilution correction factor.
The disc centrifuge, developed by Slater and Cohen and modified by Allen and Svarovsky [Allen and Svarowsky, Dechema Monogram, Nuremberg, Numbers 1589-1625, 279-292 (1975)], is essentially a centrifugal pipette device. Size distributions are measured from the solids concentration of a series of samples withdrawn through a central drainage pillar at various time intervals.
In the centrifugal disc photodensitometer concentration changes are monitored by a light point or line beam. In one high-resolution mode of operation, the suspension under test is injected into clear liquid in the spinning disc through an entry port, and a layer of suspension is formed over the free surface of liquid (the line start technique). The analysis can be carried out using a homogeneous suspension. Very low concentrations are used, but the light scattering properties of small particles make it difficult to interpret the measured data.
Several centrifugal cuvette photocentrifuges are commercially available. These instruments use the same theory as the photocentrifuges but are limited in operation to the homogeneous mode of operation [ISO 13318:2001 Determination of particle size distribution by centrifugal liquid sedimentation methods - Part 1: General principles and guidelines, Part 2: Photocentrifuge method]
The X-ray disk centrifuges is a centrifuge version of the gravitational instrument [ISO 13318-3:2004, Part3: Centrifugal X-ray method].
