The Fundamentals of Particle Size Analysis by Transmission Fluctuation Spectrometry. Part 1: A Theory of Temporal Transmission Fluctuations in Dilute Suspensions

Abstract

The extinction of radiation in suspensions is traditionally described by the Bouger-Lambert-Beer law (BLBL). Based on a quasicontinuum 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 signi®cant uctuations. The strength of¯uctuation 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 part of the series of papers provides a method for the temporal decomposition of the transmission's power spectrum, which permits the information on the particle size and concentration to be extracted from the seemingly irregular¯uctuation of the transmission signal.

The Fundamentals of Particle Size Analysis by Transmission Fluctuation Spectrometry. Part 2: A Theory on Transmission Fluctuations with Combined Spatial and Temporal Averaging

“…(11) shows that the logarithm of the expectancy of the transmission square (ETS) is linear with the particle concentration. Furthermore, it was shown in part one [1], that the effects from different particle size fractions superimpose linearly to form the resulting ln(ETS). This leads to conclude that particle size distributions and particle concentrations can be obtained by deconvolution from a simple measurement of transmission fluctuations.…”

“…As already applied successfully in previous theories on the transmission of radiation through concentrated disperse systems [1], or Eqs. (8) to (11) resp., the present model is based on a suspension monolayer, where the layer thickness corresponds to the diameter of the (maximum) particles.…”

“…The special case of temporal averaging with an infinitesimally small beam diameter and monodisperse particles corresponds to the situation considered previously in the thesis of Kräuter [1,3]. From Eq.…”

“…In the first part of this publication [1], a theory of temporal transmission fluctuations was developed for the case that a beam of radiation with a beam diameter much smaller than the particle diameter is transmitted through a suspension and that the transmission signal T hti originating from this arrangement is subject to averaging with a variable time constant t, leading to the averaged signal T t hti: In a first step, the signal statistics was studied for a monolayer, a two-dimensional arrangement of particles moving through the beam path with a flow velocity v. For monodisperse particles of diameter x forming a monolayer of thickness z ML ¼ ðP=1; 5Þx; the fraction of the monolayer area covered by particles is given by b ¼ P Á C v : Assuming ray optics and perfectly absorbent particles, the transmission value for a thin beam is jumping statistically between the values T ¼ 1 and T ¼ 0 and the average values (or expectancies e) of both the transmission T and the transmission square T 2 are identically found to be…”

Laserbasierte Strahler-Empfänger-Baugruppe mit integrierter Mikrooptik zur Messung von StreulichtLaser-based Emitter-Receiver-Device with Integrated Micro-Optics for the Measurement of Scattered Light

“…Durchlichtanordnungen benötigen für den Fall, dass Druckfestigkeit gefordert ist, zwei druckfeste Aufnahmen für optoelektronische Bauelemente [1]. Für den Fall, dass ein optisch reflektives Verfahren angewendet wird, können planare mikrooptoelektronische Strahler-Empfänger-Baugruppen als druckfeste Sensorelemente zum Einsatz kommen.…”