Size Measurements

To measure the droplet size distribution of the primary emulsion (W/O in W/O/W or O/W in O/W/O) that has a micron range (with an average radius of 0.5-1.0 pm), a dynamic light-scattering technique (also referred to as photon correlation spectroscopy PCS) can be apphed. Details of this method are described in Chapter 19. Basically, the intensity fluctuation of scattered light by the droplets as they undergo Brownian diffusion is measured from this, the diffusion coefficient of the droplets can be determined, and in turn the radius can be obtained by using the Stokes-Einstein equation. 

To measure the droplet size distribution of the resulting multiple emulsion (with diameters 5 pm), optical microscopy combined with image analysis can be used. An alternative method to measure droplet size distribution is to use light diffraction and then to apply Fraunhofer s diflraction theory. Details of this method are provided in Chapter 19, but basically a laser beam that has been enlarged and 

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Reference 3 gives the equation log (a/ao) = l6/x, where a is the solubility activity of a crystal, ao is the normal value, and x is the crystal size measured in angstroms. Derive this equation. 

Aiien T 1981 Particie Size Measurement 3rd edn (New York Chapman and Haii) pp 246-66... 

The normal distribution of measurements (or the normal law of error) is the fundamental starting point for analysis of data. When a large number of measurements are made, the individual measurements are not all identical and equal to the accepted value /x, which is the mean of an infinite population or universe of data, but are scattered about /x, owing to random error. If the magnitude of any single measurement is the abscissa and the relative frequencies (i.e., the probability) of occurrence of different-sized measurements are the ordinate, the smooth curve drawn through the points (Fig. 2.10) is the normal or Gaussian distribution curve (also the error curve or probability curve). The term error curve arises when one considers the distribution of errors (x — /x) about the true value. 

T. Allen, "Particle Size Measurement , 2nd ed.. Chapman and Hall, London (1975). 

We saw in Chap. 1 that the random coil is characterized by a spherical domain for which the radius of gyration is a convenient size measure. As a tentative approach to extending the excluded volume concept to random coils, therefore, we write for the volume of the coil domain (subscript d) = (4/3) n r, and combining this result with Eq. (8.90), we obtain... 

Raman spectroscopy for [INFRARED TECHNOLOGY AND RAMAN SPECTROSCOPY - RAMAN SPECTROSCOPY] (Vol 14) -size measurement of particles for [SIZE MEASUREMENT OF PARTICLES] (Vol 22)... 

Size. The precise determination of particle size, usually referred to as the particle diameter, can actually be made only for spherical particles. For any other particle shape, a precise determination is practically impossible and particle size represents an approximation only, based on an agreement between producer and consumer with respect to the testing methods (see Size measurement of particles). 

Avera.ge Particle Size. Average particle size refers to a statistical diameter, the value of which depends to a certain extent on the method of deterniiaation. The average particle size can be calculated from the particle-size distribution (see Size measurement of particles). 

Size reduction (qv) or comminution is the first and very important step in the processing of most minerals (2,6,10,20—24). It also involves large expenditures for heavy equipment, energy, operation, and maintenance. Size reduction is necessary because the value minerals are intimately associated with gangue and need to be Hberated, and/or because most minerals processing/separation methods require the ore mass to be of certain size and/or shape. Size reduction is also required in the case of quarry products to produce material of controlled particle size (see Size measurement of particles). In some instances, hberation of valuables or impurities from the ore matrix is achieved without any apparent size reduction. Scmbbers and attritors used in the industrial minerals plants, eg, phosphate, mtile, glass sands, or clay, ate examples. 

Some particle size measuring techniques ate more particle shape sensitive than others. Data obtained by different methods can be significantly different, and whenever a particle size is reported, the measuring technique and conditions should always be mentioned. Even using the same equipment, the extremes of the distributions (low and high 10%) are usually not readily reproducible. 

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