Ulrich Riebel

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

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.

Theoretical direct correlation function for two-dimensional fluids of monodisperse hard spheres

The direct correlation function plays an important role in describing the effects of the structure of particle systems with respect to light diffraction, x-ray diffraction as well as transmission and transmission fluctuations of radiation through a dense suspension. In this paper, the direct correlation function for a monolayer of monodisperse hard spheres or disks is derived theoretically. Based on the approximation of Baus and Colot [Phys. Rev. A 36, 3912 (1987)] and the equation of state for a fluid of hard disks by Santos et al. [J. Chem. Phys. 103, 4622 (1995)], we propose a new direct correlation function, which compares well to the approximate analytical expressions and gives a good prediction of the structure factor in a wide range of monolayer density or suspension concentration. The resulting radial distribution function also agrees well with Monte Carlo computer simulation data. The corresponding contact values of the radial distribution function compare well with the results of analytic approximations, numerical solutions, and computer simulations. Our proposed direct correlation function is applied to the transmission fluctuation spectrometric study. Experimental results show good agreement with the theory.

Comment on the Calculation of the Steady-State Charge Distribution on Aerosols < 100 nm by Three Body Trapping Method in a Bipolar Ion Environment

The theory of Fuchs (1963) is widely used for calculation of the steady-state charge distribution on (submicron) aerosol particles in a bipolar ion environment. Hoppel and Frick (1986) and others showed that the Fuchs theory is no longer valid for particle diameters in the order of magnitude of the ionic mean free path. In their 1986 and 1990 papers, Hoppel and Frick published a new calculation method based on the concept of thee-body trapping, which is applicable for small particles down to the size of ions. Some print and procedure mistakes were made in the named publications. Additionally some important calculation information was not given. In this article, the relevant equations are shown, corrected and appended. A recalculation of the charge distributions for small particles based on three-body trapping shows a pronounced difference in comparison to data calculated according to the theory of Fuchs.

Extinction by a Large Spherical Particle Located in a Narrow Gaussian Beam

In most extinction measurements, the laser beam is expanded and the particles are small enough so that the incident beam can be considered as a plane wave. With regard to particle size analysis by optical extinction counters or transmission fluctuation spectrometry, however, we are interested in the opposite situation, i.e. particle diameters which are larger than the beam diameter. This paper presents experimental results on the extinction by an absorbent or transparent spherical particle passing through a Gaussian beam. The experiments show that the extinction is sensitive to the particle location, especially when the particle is very near to the beam waist and the ratio of the beam to the particle diameter is close to or less than 1.

Measurements of particle-size distribution and concentration by transmission fluctuation spectrometry with temporal correlation

A new method of transmission fluctuation spectrometry with signal correlation was recently developed for particle-size analysis, whereby both particle-size distribution and particle concentration can be measured simultaneously. The measurements were realized with temporal correlation of the transmission fluctuation signals of a focused Gaussian beam.

Fundamentals of transmission fluctuation spectrometry with variable spatial averaging

Abstract Transmission signal of radiation in suspension of particles performed with a high spatial and temporal resolution shows significant fluctuations, which are related to the physical properties of the particles and the process of spatial and temporal averaging. Exploiting this connection, it is possible to calculate the particle size distribution (PSD) and particle concentration. This paper provides an approach of transmission fluctuation spectrometry (TFS) with variable spatial averaging. The transmission fluctuations are expressed in terms of the expectancy of transmission square (ETS) and are obtained as a spectrum, which is a function of the variable beam diameter. The reversal point and the depth of the spectrum contain the information of particle size and particle concentration, respectively.

An experimental investigation on corona quenching

Abstract Current–voltage characteristics of a wire-and-tube electrostatic precipitator were measured under conditions of corona quenching. It was found that corona quenching is associated with an increase or decrease of the corona onset voltage (depending on the discharge electrode diameter) and with a strong deformation of the current–voltage characteristic for voltages close to the corona onset voltage. The current state of knowledge, describing corona quenching as a simple shift of the current–voltage characteristic to higher voltages, apparently goes back to measurements of less resolution. Possible mechanisms leading to an understanding of the newly observed phenomena are discussed.

Signal Processing In Transmission Fluctuation Spectrometry With Band‐Pass Filter

Transmission fluctuation spectrometry is a recently‐developed method for particle size analysis, in which both the particle size distribution and particle concentration can be obtained simultaneously. This work presents a new technique of data processing of the fluctuating transmission signal. The 1st order band pass filter is employed to improve the resolution of the measurement. The analytical expression is obtained on the basis of the layer model. Numerical results and simulated results are given to make a comparison.

Particle analysis on concentrated particle suspensions by transmission fluctuation spectrometry with band-pass filters: part 1. Simulation

Transmission fluctuation spectrometry (TFS), as a new method of online and real-time particle analysis developed in recent years, can measure the particle size distribution and particle concentration simultaneously. In this work, TFS with band-pass filters is studied by numerical simulation in which the particle concentration varies in a large dynamic range. The results of the simulations show that the transmission fluctuation spectrum is related to the particle concentration of the suspension, the pathlength of the light beam within the particle system and the beam-to-particle diameter ratio. Empirical expressions to correct the effects of particle overlapping on the transmission fluctuation spectrum are obtained, which are found to be experimentally validated.

Particle analysis on concentrated particle suspensions by transmission fluctuation spectrometry with band-pass filters: part 2. Experimental results

Transmission fluctuation spectrometry (TFS), as a new method of online and real-time particle analysis developed in recent years, can measure the particle size distribution and particle concentration simultaneously. In the preceding paper, high concentration effects on the TFS using band-pass filters were investigated by numerical simulation, and empirical expressions to correct the effects were obtained. This paper presents a study on the TFS measurements in which the particle concentration varies in a very wide dynamic range. Finally, reasonable results on both the particle size distribution and particle concentration are obtained by introducing empirical corrections into the inversion algorithm.