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Modeling Focused Beam Reflectance Measurement and its Application to Sizing of Particles of Variable Shape
Author(s) -
Vaccaro Andrea,
Šefčík Ján,
Morbidelli Massimo
Publication year - 2007
Publication title -
particle and particle systems characterization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.877
H-Index - 56
eISSN - 1521-4117
pISSN - 0934-0866
DOI - 10.1002/ppsc.200600977
Subject(s) - sizing , optics , weighting , particle (ecology) , beam (structure) , chord (peer to peer) , convolution (computer science) , cylinder , mathematical analysis , mathematics , geometry , physics , materials science , computational physics , chemistry , computer science , acoustics , distributed computing , oceanography , organic chemistry , geology , machine learning , artificial neural network
A model for particle detection in focused beam reflectance measurement is presented in the general case of particles of any convex shape. Shape dependent convolution relationships between measured chord length distribution (CLD), particle size distribution (PSD) and particle mass distribution (PMD) are derived and an explicit formula for the weighting characteristic length is given in terms of particle shape. Based on the derived convolution relationships, equations relating moments of the CLD, PSD and PMD are obtained. Issues related to the definition of particle size of non spherical objects and its connection to the particle sizing technique are discussed. Based on the moment relationships, particle size is defined for focused beam reflectance measurement measurements in terms of a CLD equivalent sphere. CLD and characteristic length for a thin cylinder are obtained analytically and used as simple model in order to illustrate issues in sizing particles of variable shape. General conclusions regarding the role of the weighting characteristic length on the behavior of the measured CLD are drawn.