Extinction of Radiation in Sterically Interacting Systems of Monodisperse Spheres. Part 2: Experimental results

Abstract

The Bouguer‐Lambert‐Beer law (BLBL), commonly used to describe the extinction of radiation in disperse systems, is known to be valid in the limit of low concentrations only. In Part [1] it was shown that steric particle‐particle interactions lead to important effects in the range of high particle concentration and two versions of a more general extinction equation including steric interactions were derived for the regimes of fraunhofer diffraction and ray propagation in this part experimental evidence for the effects of steric interactions on the extinction of radiation in suspensions of monodisperse spherical particles is given. Various experiments on light extinction and on ultrasonic extinction are combined to cover a broad range of particle size parameters, mechanisms of particle‐wave interaction and receiver apertures.

Investigations on the Capability of the Statistical Extinction Method for the Determination of Mean Particle Sizes in Concentrated Particle Systems

“…The Lambert–Beer's law gives a linear relationship between the measured extinction of a light beam and the concentration as well as the extinction cross section of the particles in the light beam for low particle concentrations and small optical path lengths . At higher particle concentrations additional effects, such as multiple scattering, appear, which are not taken into account in the derivation of the basic equations.…”

Transmission Fluctuation Spectrometry in Concentrated Suspensions Part One: Effects of the Monolayer Structure

“…The theory of TFS is basically that of a measurement method with close relations to extinction measurements. Therefore, we may assume that high concentration effects with TFS are similar to those encountered with extinction methods [6,7]. Notably, we might expect dependent scattering, steric interactions and multiple scattering as high-concentration effects which could be relevant for TFS as well.…”

“…This means that the PPCF is a result of statistics and is dependent on the monolayer density. The PPCF is also related to the particle-particle interactions [5,7,8]. The PPCF may also be written as:…”

“…A study of particle-particle interactions within the same monolayer was given by Riebel and Hickl in their work on the transmission and diffraction of radiation through dense monolayers of opaque particles [8], whereby the monolayer structure is described by means of a 2-dimensional particle pair correlation function (PPCF). Effects from steric interactions between particles from different monolayers were investigated in [6,7], in which one effect is described as a shielding effect or particle overlapping effect.…”

Particle Size Distribution Determination from Spectral Extinction Using Neural Networks

“…At high concentrations, the Beer−Lambert law fails because of multiple scattering and interaction effects. The maximum concentration for application of the Beer−Lambert law depends on the properties of the system, but for most cases, a practical upper limit is a particle volume fraction of 5% …”