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is valid, this diameter corresponds to the projected area diameter of the particle in random orientation. For particles ≤ 0.1 μm, the definition can be extended into volume-equivalent diameter. In this case, the cross-sectional area becomes nearly the same as that of a sphere with
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Of note, the ISO standards providing guidance for performing particle size determination by static and dynamic image analysis (respectively ISO 13322-1 and 13322-2) recommend to define particle size by a combination of 3 primary measurements, namely the area-equivalent diameter, the maximum Feret
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is based on the principle that light scattered by small particles (Rayleigh scattering) fluctuates as the particles undergo
Brownian motion. The equivalent spherical diameter for the technique is termed hydrodynamic diameter (HDD). This corresponds to the diameter of a sphere with the same
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The particle size of a perfectly smooth, spherical object can be accurately defined by a single parameter, the particle diameter. However, real-life particles are likely to have irregular shapes and surface irregularities, and their size cannot be fully characterized by a single parameter.
103:, also termed circular-equivalent diameter, is the diameter of a sphere having the same projected area as the particle’s projection. Enabled by the introduction of digital image analysis, this corresponds to a direct measurement of the projection area by pixel counting.
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in a simplified, homogenized way. Here, the real-life particle is matched with an imaginary sphere which has the same properties according to a defined principle, enabling the real-life particle to be defined by the diameter of the imaginary sphere.
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Since the particle’s orientation at the time of image capture has a large influence on all these parameters, the equivalent spherical diameter is obtained by averaging a large number of measurements, corresponding to the different particle orientations.
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Of note, the equivalent sieve diameter can be significantly smaller than the area-equivalent diameter obtained by optical methods, as particles can pass the sieve apertures in an orientation corresponding to their smallest projection surface.
66:, the analysis is made on the projection of the three-dimensional object on a two-dimensional plane. The most commonly used methods for determining the equivalent spherical diameter from the particle’s projected outline are:
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Hence, in a simplified way, the laser diffraction equivalent diameter is considered as a volume-equivalent spherical diameter, i.e., the diameter of a sphere of the same volume as that of the particle under investigation.
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Strictly speaking, the laser diffraction equivalent diameter is the diameter of a sphere yielding, on the same detector geometry, the same diffraction pattern as the particle. In the size regimen where the
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The principle used to match the real-life particle and the imaginary sphere vary as a function of the measurement technique used to measure the particle.
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of equivalent geometric, optical, electrical, aerodynamic or hydrodynamic behavior to that of the particle under investigation.
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Particle size analysis techniques based on gravitational or centrifugal sedimentation (e.g., hydrometer technique used for
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is based on the observation that the angle of the light diffracted by a particle is inversely proportional to its size.
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as the particle, in the same fluid and under the same conditions. The relationship between the diffusion coefficient
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diameter, and the minimum Feret diameter. The combination of these parameters is then used to define the
501:"Particle size analysis methods: Dynamic light scattering vs. laser diffraction :: Anton Paar Wiki"
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Jennings, B. R. and
Parslow, K. (1988) Particle Size Measurement: The Equivalent Spherical Diameter.
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equal volume. In addition, the favored mean particle size for laser diffraction results is the D or
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In that case the equivalent spherical diameter is appropriately termed
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252:{\displaystyle \mathrm {HDD} ={\frac {k_{\text{B}}T}{3\pi \eta D}}}
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Particle size measurements : fundamentals, practice, quality
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