where x1 is the largest particle present in the initial sample withdrawn at time t1, when the mea-
surement radius is R and the surface is at radius S, whileω is the angular velocity. Allen (1981) presents a procedure for particle size evaluation, analogous to that of the Andreasen pipette, using Eq. (2.31).
Centrifugal sedimentation equipment can also use X-rays as a detection source. After passing through the suspension, particles are detected by a scintiliation counter. The signal is then processed to generate the size distribution. The attenuation is proportional to the mass concentration, which has to be converted to the size distribution by algorithms from a software.
Gravity and centrifugal sedimentation can be combined for the same sample in order to directly determine the Stokes diameter for a wide range of particle sizes. In such a way conversions are avoided and mass distributions, applicable to processes where gravimetric efficiencies are relevant, can be properly derived. Ortega-Rivas and Svarovsky (1994) determined particle size distributions of fine powders using a combined Andreasen pipette–pipette centrifuge method. They derived relations useful to model hydrocyclone separations, which were later employed to describe apple juice clar- ification. For more information on sedimentation equipment, refer to Allen (1997), who discussed different commercial gravimetric and centrifugal sedimentation particle analyzers in current use. Recently, the European Standards Organization of the European Community has prepared standards for centrifugal and gravity sedimentation methods.
2.3.6.4. Stream Scanning
Instruments used in stream scanning techniques have recently undergone significant develop- ments. Instrumentation in this category comprises a variety of different techniques with which to measure particle size. For example, during stream scanning of a liquid or gas, in which particles are
46 Food Powders suspended, the medium can either be subjected to a specific restriction or exposed to various light sources, obtaining a response that is a function of the concentration and number of particles present in the suspension being analyzed. In stream scanning, particles are examined one at a time and their interaction with an external field is taken as a measure of their size. Stream scanning methods utilize different principles, namely:
r laser beam diffraction caused by the particle;
r electrical resistance as the particles pass through a field (Coulter counter); r amount of particle cut off as a particle passes through a beam;
r signal created from rotating scanning beam through a particle; r time of flight between two laser beams; and
r interference pattern as a particle passes through the intersection of two laser beams (Doppler effect).
Instruments that utilize light as a means of detecting particles in suspension generally operate by making the stream flow through a cell across which a light beam is passed. As each particle passes through the beam, a portion of the beam is blocked by the particle’s cross-section. The number of particles in preset sizes is thus easily recorded. Instruments using a light-blocking tech- nique will, however, be problematic in measuring particles whose refractive indices are close to those of the carrier liquid. In general, instruments will have problems with particles smaller than 2µm.
Laser diffraction is the most widely used technique for particle size analysis. Instruments
employed in this technique are considered fast, reproducible, and easy to use and particularly attractive in their capability to analyze (over a broad size range) a variety of dispersion media such as liquids or air streams. The basic principle upon which these instruments work is shown in Fig. 2.18. In essence, the presence of particles in a light beam causes light diffraction, and the light intensity distribution for a single opaque spherical particle falls off rapidly as particle size is reduced. This action results in a set of light rings at various radii around the incident beam. The most common beams are produced from intense light of fixed wavelength He–Ne gas lasers (λ = 0.63 µm). When an array of sizes is
Laser beam
.
Small particle Large particle Ring detectorilluminated, a similar pattern emerges, but particles contribute to the intensities of more than one ring. Each set of diffraction rings is spaced radially at a distance fundamentally related to a specific particle diameter. This light scattering pattern must be deconvoluted in order to determine the size distribution from the scattered pattern measurement.
Representative samples can be as small as 4–10 g for dry powders and 1–2 g for liquid sus- pensions. During a test, the dry powder can be blown through the beam by means of pressure and sucked into a vacuum cleaner to prevent dust dispersion into the environment (may result in poorer dispersion than with liquid dispersing medium). Particles in suspension can be measured by recircu- lating the sample in front of the laser beam. This cloud or ‘ensemble’ of particles passes through a broadened beam of laser light and scatters the incident light onto a Fourier lens. The lens focuses the scattered light onto a detector array and, using an inversion algorithm, the particle size distribution is inferred from the collected diffracted light data. Sizing particles by this technique depends on accurate, reproducible, high resolution light scatter measurements and ensures full characterization of the sample. The size range covered by instruments employed is approximately 0.1–3,000µm according to ISO 13320. The method rapidly produces a measurement in less than 1 min and, thus, is ideally suited for process control operations where results are required quickly with minimal operator attention. Recent developments in the use of laser diffraction techniques have enabled particles in the sub-micron range to be analyzed.
Many commercial instruments that apply this principle are available, such as those manufactured by Leeds & Northrup, Cilas, Coulter, Seishin, Shimadzu, Sympatec, Malvern, Beckman, Fritsch, Insitec, and Horiba & Nitto (Allen, 1997). Polarization Intensity Differential Scattering (PIDS) is a technique that overcomes the limitations of conventional laser diffraction in order to give high resolution submicrometer analysis. PIDS uses three different wavelengths of light (450, 600, and 900 nm) in two planes of polarization (vertical and horizontal) to irradiate the sample. The resultant scatter patterns of various sized submicrometer particles are easily differentiated from each other, providing well-resolved particle size distributions. Modern laser diffraction instruments use Mie Theory as the basis of their size calculations. As Mie Theory covers all light scatter from spherical particles, both PIDS data and laser diffraction data can be processed into a particle size distribution using one continuous algorithm.
In instrumental particle counters, such as the well-known Coulter counter, the stream containing the particles is forced through a flow restriction, which is then subjected to an electric field. The normal flow of electrical current between the poles is altered by the particles passing through the restriction. These electrical flow changes, as a function of the size of particles passing through, are registered as pulses, and then counted and grouped according to size. This type of counter will count and size particles in the range 0.5–800µm, and since the basic response is directly related to particle volume, the instruments are for all practical purposes independent of problems associated with particle shape, color, or density, which affect most other methods.