Modeling focused beam reflectance measurement and its application to sizing of particles of variable shape

Andrea Vaccaro, Jan Sefcik, Massimo Morbidelli

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

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.

LanguageEnglish
Pages360-373
Number of pages14
JournalParticle and Particle Systems Characterization
Volume23
Issue number5
DOIs
Publication statusPublished - Feb 2007

Fingerprint

Reflectometers
sizing
Convolution
Particle size analysis
Particles (particulate matter)
Particle size
reflectance
particle mass
particle size distribution
mass distribution
convolution integrals
moments

Keywords

  • chord length distribution
  • focused beam reflectance measurement
  • modeling
  • particle sizing
  • thin cylindrical particle

Cite this

@article{a3fa4b5cdae64450a6d371c860a141d1,
title = "Modeling focused beam reflectance measurement and its application to sizing of particles of variable shape",
abstract = "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.",
keywords = "chord length distribution, focused beam reflectance measurement, modeling, particle sizing, thin cylindrical particle",
author = "Andrea Vaccaro and Jan Sefcik and Massimo Morbidelli",
year = "2007",
month = "2",
doi = "10.1002/ppsc.200600977",
language = "English",
volume = "23",
pages = "360--373",
journal = "Particle and Particle Systems Characterization",
issn = "0934-0866",
number = "5",

}

Modeling focused beam reflectance measurement and its application to sizing of particles of variable shape. / Vaccaro, Andrea; Sefcik, Jan; Morbidelli, Massimo.

In: Particle and Particle Systems Characterization, Vol. 23, No. 5, 02.2007, p. 360-373.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Modeling focused beam reflectance measurement and its application to sizing of particles of variable shape

AU - Vaccaro, Andrea

AU - Sefcik, Jan

AU - Morbidelli, Massimo

PY - 2007/2

Y1 - 2007/2

N2 - 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.

AB - 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.

KW - chord length distribution

KW - focused beam reflectance measurement

KW - modeling

KW - particle sizing

KW - thin cylindrical particle

U2 - 10.1002/ppsc.200600977

DO - 10.1002/ppsc.200600977

M3 - Article

VL - 23

SP - 360

EP - 373

JO - Particle and Particle Systems Characterization

T2 - Particle and Particle Systems Characterization

JF - Particle and Particle Systems Characterization

SN - 0934-0866

IS - 5

ER -