Stokes diameter determination

The approximation due to Kamack can be modified, for the scanning mode of operation, by replacing the constant r/S) with the variable r/S) where r is the position of the source and detector at time t i.e. equation (8.4) becomes  

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In particle-size measurement, gravity sedimentation at low soHds concentrations (<0.5% by vol) is used to determine particle-size distributions of equivalent Stokes diameters ia the range from 2 to 80 pm. Particle size is deduced from the height and time of fall usiag Stokes law, whereas the corresponding fractions are measured gravimetrically, by light, or by x-rays. Some commercial instmments measure particles coarser than 80 pm by sedimentation when Stokes law cannot be appHed. 

Many particle-measuring methods use STORE S LAW to determine particle distributions. By suitable mcUiipulation(see below), we obtain an equation relating the Stokes diameter, M, with the particle density, Pj, and the liquid... 

The size of a spherical particle is readily expressed in terms of its diameter. With asymmetrical particles, an equivalent spherical diameter is used to relate the size of the particle to the diameter of a perfect sphere having the same surface area (surface diameter, ds), the same volume (volume diameter, dv), or the same observed area in its most stable plane (projected diameter, dp) [46], The size may also be expressed using the Stokes diameter, dst, which describes an equivalent sphere undergoing sedimentation at the same rate as the sample particle. Obviously, the type of diameter reflects the method and equipment employed in determining the particle size. Since any collection of particles is usually polydisperse (as opposed to a monodisperse sample in which particles are fairly uniform in size), it is necessary to know not only the mean size of the particles, but also the particle size distribution. 

Many particles are not spherical and so will not have the same drag properties as spherical particles. The effective diameter for such particles is often characterized by the equivalent Stokes diameter, which is the diameter of the sphere that has the same terminal velocity as the particle. This can be determined from a direct measurement of the settling rate of the... 

The terminal velocity in the case of fine particles is approached so quickly that in practical engineering calculations the settling is taken as a constant velocity motion and the acceleration period is neglected. Equation 7 can also be applied to nonspherical particles if the particle size x is the equivalent Stokes diameter as determined by sedimentation or elutriation methods of particle-size measurement. 

The diameter of a sedimenting species determined from Stokes law assuming a spherical shape. Also referred to as the Stokes diameter or (divided by a factor of 2) the settling radius . 

Not to be confused with the effective diameter determined by Stokes law discussed earlier. 

If the particle-size distribution of a powder composed of hard, smooth s eres is measured by any of the techniques, the measured values should be identical. However, there are many different size distributions that can be defined for any powder made up of nonspheri-cal particles. For example, if a rod-shaped particle is placed on a sieve, its diameter, not its length, determines the size of aperture through which it will pass. If, however, the particle is allowed to settle in a viscous fluid, the calculated diameter of a sphere of the same substance that would have the same falling speed in the same fluid (i.e., the Stokes diameter) is taken as the appropriate size parameter of the particle. 

These equations are used to determine the grade efficiency of a classifier provided the total efficiency and the size distributions of two of the streams are known. Results are usually plotted as grade efficiency curves of G (jc) or Gj(x) against jc [3]. Since the classifier separates on the basis of Stokes diameter it is preferable to carry out the size determinations, for grade efficiency evaluations, on the same basis. 

This technique is a standard procedure since both the Stokes diameter and the mass undersize are determined from first principles. The method is versatile, since it can handle any powder that can be dispersed in a liquid, and the apparatus is inexpensive. The analysis is, however, time consuming and intensive. 

Since all the particles emanate from the same starting point, the Stokes diameter is determined using equation (8.4) with r as the measurement radius and 8 as the midpoint of the suspension layer... 

A change in conformation affects the apparent solute molecular weight versus M) as described eariier, so that for denatured proteins [Eq. (59)] can be substituted for M in Eq. (61). This assumes that and SEC retention are each determined by the Stokes diameter of the molecule (see discussion of Ref. 12). 

Fig. 2 Solute exclusion curves (static method) for water-swollen cellulosic materials determined with dextran-oligosaccharide series. Solid line never-dried samples. Broken line dried and reswollen samples. Abscissa stands for the Stokes diameter of polymers on the logarithmic scale (molecular weight is indicated on the top line), and ordinate the amount of water inaccessible to the solute divided by the dry weight of gel. (Reproduced from ref. 18 with permission.)...

Gravity and centrifugal sedimentation can be combined for the same sample in order to directly determine Stokes diameter for a wide range of particle sizes. In such a way conversion are avoided and a mass distributions, applicable to processes where gravimetric efficiencies are relevant, can be properly derived. Ortega-Rivas and Svarovsky (1994) determined particle sizes distributions of fines powders using a combined Andreasen Pipette-pipette centrifuge method. They derive relations useful to model hydrocyclone separations, which were later employed to describe apple juice clarification. 

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