Determining particle size distribution of non-spheres from chord length measurements

Derek Wilkinson, Mingzhong Li, Kumar Patchigolla

Research output: Chapter in Book/Report/Conference proceedingConference contribution


An algorithm has been developed by which chord length distribution (CLD) measurements, such as are obtained directly by Focussed Beam Reflectance Measurement (FBRM), may be transformed into the corresponding particle size distributions (PSD). Central to this transformation are general PSD to CLD and CLD to PSD translation models that are suitable for applications involving non-spherical particles. The superellipsoid shape has been used as a model particle as it can be formed in a wide range of shapes by adjustment of two parameters, aspect ratio and index. A numerical method is described to calculate the PSD to CLD transformation. The iterative non-negative least squares (NNLS) method has been found to be appropriate for the CLD to PSD transformation, being insensitive to moderate levels of noise in the measured data as well as being able to deal with measurements of non-pherical particles. This transformation has been validated by extensive simulations. These simulations have served to demonstrate that the particle aspect ratio is the only shape factor which has a significant effect on the PSD obtained from transformation of CLD measurements. CLDs of three different inorganic materials, spherical ceramic beads and non-spherical plasma aluminium and zinc dust particles, were measured using the Lasentec FBRM instrument. The particle shape and PSD of these materials were also investigated by Image Analysis (IA). Comparison of PSDs retrieved from FBRM data with PSDs measured using IA show that the PSD can be retrieved from a measured CLD successfully using the iterative NNLS method based on the PSD to CLD model. CLD measurements have been made during crystallisation of L-glutamic acid in both its prismatic a form and the acicular ß form. These CLD measurements have been transformed into PSDs of the crystals so that crystal growth data may be obtained.

Original languageEnglish
Title of host publicationAIChE Annual Meeting, Conference Proceedings
Subtitle of host publication2006 AIChE Spring National Meeting - 5th World Congress on Particle Technology; Orlando, FL; United States; 23 April 2006 through 27 April 2006
Publication statusPublished - 2006
Event2006 AIChE Spring National Meeting - 5th World Congress on Particle Technology - Orlando, FL, United States
Duration: 23 Apr 200627 Apr 2006


Conference2006 AIChE Spring National Meeting - 5th World Congress on Particle Technology
Country/TerritoryUnited States
CityOrlando, FL


  • Chord length distribution (CLD)
  • Focused beam reflectance measurement (FBRM)
  • Image analysis (IA)
  • Particle size distribution (PSD)


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