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The Fundamentals of Particle Size Analysis by Transmission Fluctuation Spectrometry. Part 2: A Theory on Transmission Fluctuations with Combined Spatial and Temporal Averaging
Author(s) -
Breitenstein Marcus,
Riebel Ulrich,
Shen Jianqi
Publication year - 2001
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 - 10.1002/1521-4117(200110)18:3<134::aid-ppsc134>3.0.co;2-j
Subject(s) - transmission (telecommunications) , extinction (optical mineralogy) , computational physics , optics , particle (ecology) , physics , particle size , temporal resolution , image resolution , statistical physics , chemistry , geology , computer science , telecommunications , oceanography
Abstract The extinction of radiation in suspensions is traditionally described by the Bouguer‐Lambert‐Beer law (BLBL). Based on a quasi‐continuum approach, the BLBL does not account for the discrete nature of particles or their spatial extension and arrangement. If an extinction measurement is made with a high spatial and temporal resolution, the transmitted intensity signal shows significant fluctuations. The strength of fluctuation is related to the physical properties of the suspension and the process of spatial and temporal averaging. Exploiting this connection, it is possible to calculate the particle size distribution and the particle concentration from transmission measurements. This second part provides an analytical solution for the description of transmission fluctuations in terms of the expectancy of the transmission square, including both variations of the beam diameter to particle diameter ratio and variation of the temporal resolution of the signal capture. The result also provides the basis for describing the transmission fluctuations for beams of variable diameter and allows to define a measurement volume for the case of focussed beams.