CHABAY: But you don't get that actually. That arises simply from the amplitude of the ratio of the forward and backward Mie amplitudes rather than from the size of the Doppler shift itself, that is not from the motion of the particle. KNOLLENBERG: That's right. The amplitude is a function only of size. I'm sorry the modulation index is a function only of size. BILL YANTA: The spacing there is just due to velocity as it's going across. CHABAY: That was what I was was trying to find out. Whether the spacing or the depth itself is useful in getting the information. KNOLLENBERG: The frequency, let's say, gives you velocity. If you have particles that are very fast, you'll have a higher frequency. The only thing I said was that the number of waves across the beam is independent of velocity. So you can in a sense measure the beam width for each particle. NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 412 RAPID MEASUREMENT OF DROPLET SIZE DISTRIBUTIONS Ilan Chabay Department of Chemistry ABSTRACT A new technique which allows rapid, direct determination of particle size distributions by measurement of the Doppler shift of laser light scattered by falling particles will be discussed. The technique has been successfully applied to the measurement of parameters associated with cloud droplet growth (from 1 to 10 micrometer radius) in a diffusion cloud chamber. Applications to other types of particles in the size range 0.5-50 micrometers radius will be pointed out. Key words: aerosol cloud chamber; aerosol light scattering; aerosol size measurements; aerosol spectrometer; cloud droplet measurements; Doppler measurements of particle size; laser heterodyne; laser heterodyne; laser scattering by aerosol particles; particle sizing. I will describe first the general technique of determining particle size distributions by optical heterodyne spectroscopy and outline the method of measuring the spectrum. Then I'll briefly mention some results obtained on cloud droplets which will serve as an illustrative example. Finally, I'll comment on the limitations of this method and what extensions to a broader range of problems in particle measurement are possible. The experiment is performed by allowing the particles to fall through a laser beam which passes horizontally across a chamber containing the particles. The falling particles scatter light from the scattering volume which is defined and observed by apertures and a PMT. Scattering is observed at a small forward angle in the vertical plane. The frequency of the light scattered by the falling particles is Doppler shifted from the frequency of the incident light. The magnitude of this Doppler shift gives the instantaneous vertical velocity of the particles. These velocities in turn can be related to the particle sizes by means of the Stokes relation. Thus, the radii of the droplets passing through the beam is given by the Doppler shift frequencies, without regard to intensity. The calculated Mie scattering intensity for a specific scattering angle and beam polarization provides the relative intensity value for each particle size. One can obtain the particle size distribution simply by dividing the Doppler shift spectrum point by point by the relative Mie scattering intensities. The particular power of this technique is that the size distribution can be obtained unambiguously without any a priori assumptions of its form by using simultaneously the information available on scattered intensity and on particle velocity at a single angle of observation. Actual Doppler shifts that must be measured can be as small as a few parts in 1014. In order to achieve such high resolution, a stable laser with a minimum of low-frequency noise should be used. In the initial experiments on this technique, an Art ion laser was used. operated at 5145 Å with about 100 mW power. It was A part of the incident beam served as a local oscillator or reference signal after elastic scattering from walls and windows of the chamber into the collection apertures. The surface of the PMT acts as a mixer for the Doppler shifted radiation field and the unshifted reference field. Beat notes occur from mixing of the fields with different frequencies and these beat notes appear as amplitude fluctuations in the photocurrent. The photocurrent is the input to a real-time spectrum analyzer which is followed by a digital spectrum averager. The net result is that the information comes out as a plot of the power spectrum of the photocurrent. The information term in the power spectrum is given by Pj (w)= iLo<is (r1)>N(r)r. The first term on the right hand side is the local oscillator photocurrent. Angular brackets around the second term, i(r), indicate a timeaveraged quantity, which in this case is the photocurrent due to Mie scattering of a particle of radius r (and which has (and which has an associated Doppler shift w). The size distribution is given by the function, N(rw). As an illustration of the technique, I would like to discuss very briefly some key results of our studies of cloud droplets [1,2]. This work was done in the laboratory of Professor W. H. Flygare at the University of Illinois and was done in collaboration with Professor Jerry Gollub of Haverford College. A steady state, diffusion cloud chamber was used to produce the droplets under desired conditions. The scattering due to droplets falling through the horizontal laser beam was measured at 7° downward in the forward direction. An example of the spectra obtained is shown in figure 1. These three spectra were taken about 0.5 mm apart in the 4 cm high chamber. Each spectrum is the averaged result of 128 scans which required about 20 seconds total. The dip in the spectra at 530 Hz is due to a minimum in the Mie scattering the Mie scattering intensity which intensity which occurs for particles of 4.24 μm radius. The size distribution changed as different portions of the chamber were observed, but in the set of heights represented by the spectra shown, 4.24 um particles were present at each height. Therefore, the dip is present throughout and, of course, remained at the frequency characteristic of a particle of that size. From spectra such as were just shown, the size distribution was easily found at any height in the chamber. The mean size as a function of height was then used to determine growth curves for the droplets as a function of conditions in the chamber. These growth These growth curves then were compared to theories of droplet growth. The technique I've outlined here is directly applicable to particles with real or complex indices of refraction. The application is completely straightforward for particles which are spherical and range from 0.5 to 50 μm in radius. This range can be extended to smaller particles by more complex (and less unambiguous) data analysis. The lower limit on size is due to the fact that the velocity due to gravity and that due to Browning motion become equal for particles of about 0.5 um radius. Nonspherical particles can particles can be treated treated by more by more complex calculation of the falling velocity as a function of size parameters and by calculation of the Mie scattering intensities for more complex geometries. As I've indicated, this technique can be extended to a very broad range of particle sizes and materials. Information on particle size, size distribution, growth rates, and aggregation as a function of chemical and physical conditions can be readily obtained virtually in real time by this powerful technique. ACKNOWLEDGMENT Supported in part by the National Oceanic and Atmospheric Administrations Grant No. 04-4-022-10 to Haverford College and National Science Foundation Grant NSF-GH-33634 to the Materials Research Laboratory at the University of Illinois. REFERENCES [1] J. P. Gollub, I. Chabay, and W. H. Flygare, Applied Optics 12, 2838 (1973). [2] J. P. Gollub, I. Chabay, and W. H. Flygare, submitted to J. Chem. Phys. |