On the determination of log-normal particle-size distributions using half widths and detectabilities of scattered laser power spectra

Abstract

We present the theoretical curves needed to define log-normal particle-size distributions from the measured power spectra of scattered laser radiation. (i) We show how to make estimates of the particle sizes of monodisperse systems using only the measured half-widths of the observed, scattered laser-power spectra. This technique has been employed by us before on flat-flame burners and does not involve the optical properties of the scattering centers. Number densities of particles may also be determined readily for monodisperse systems but require use of the index of refraction for the scattering centers. (ii) We define procedures for making estimates of the count-median diameters and standard deviations in log-normal size distributions using (a) measured half-widths of scattered laser-power spectra and (b) measured ratios of detectabilities determined for a given laser at two different scattering angels. We find that it is not possible to achieve adequate sensitivity for experimental utilization of this technique. (iii) We describe techniques for estimating the count-median diameters and standard deviations in log-normal size distributions using (a) measured half-widths of scattered laser-power spectra and (b) measured ratios of detectabilities determined at the same or at different scattering angles for two different laser wavelengths. Our calculations indicate that these procedures will also not yield adequate sensitivities for the determinations of particle-size distributions. (iv) The use of two linearly polarized beams [one polarized in the plane defined by the direction of laser-beam propagation and the vertical direction (1) and the other defined by the direction of laser-beam propagation and the horizontal (2)] in making half-width and detectability measurements has been studied. Although acceptable sensitivities for the determination of σ g and ♂r are achievable for selected particle-size ranges, the use of polarized laser radiation will not always lead to satisfactory characterization of log-normal particle-size distributions. Experiments involving detectabilities do not offer clear-cut advantages over those involving half-widths insofar as measurement sensitivities are concerned. (v) We describe procedures for determination of the total number of particles contained in the log-normal particle-size distributions using measured absolute values for the detectabilities observed for the power spectra of scattered laser radiation, after prior definition of the count-median diameters and standard deviations in log-normal size distributions.