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Power-law PSD for natural dispersions

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The power-law reasonably approximates the PSD characteristic of naturally occuring suspensions and aerosols. The slope, s, of the differential particle size distribution (see Particle size distribution), n(D) = dN / dD, is about 4 in a particle size range above ~0.1 µm for both atmospheric aerosols (for example, Clark WE and Whitby 1967) and aquatic suspensions (for example, Stramski D and Kiefer 1991, Jonasz M 1983, Simpson WR 1982, Brun-Cottan JC 1971, Bader H 1970). See also Jonasz M 1996a for a representative data collection regarding aquatic dispersions). Note that the log-normal function has been subsequently found to fit the PSD of atmospheric aerosol much better than the power-law function (for example, Schuster GL et al 2006, Whitby KT 1978, Davies CN 1974).

The estimate of the average slope of the PSD of aquatic particles is based on an extensive set of in vitro data obtained with the electrical resistance measurement (ERM) particle counters. Disturbance caused by sampling and the hydrodynamic characteristics of these particle counters (for example, Kachel V and Menke 1979) is known to disrupt delicate aggregates which may constitute a significant fraction of particles in the large-size range (for example, Kranck K and Milligan 1988). This would contribute to the high slope of the PSD obtained with the above method.

Slopes of the PSDs of aquatic particle measured in situ with imaging methods are lower (~2.5 to ~3.5, for example, Hou W 1997) than those obtained with ERM instruments. However, with an imaging method, one determines the ECD of a particle, while with the ERM method one determines the ESD of the particle. These two particle size definitions yield equal values only for spheres. For identical randomly-oriented solid nonspherical particles, an imaging method would yield a distribution of the ECD, while in principle, the ERM method would yield a single value of the ESD. For natural particles with varying shapes and sizes, the situation is even more complex. In order to compare the PSDs obtained with these two types of methods, one needs a relationship between the ECD and ESD, such as one derived by Jonasz M 1987a from experimental data for coastal marine particles. Please also see Jonasz M and Fournier 2007 (p. 278) for an in-depth discussion of transformation of the PSD between various particle size scales.

CITATION: Jonasz M. 2006. Power-law PSD for natural dispersions (www.tpdsci.com/Tpc/PsdPwLwNat.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY: Published: 16-Jan-2006 Modified: 08-Jul-2011 Peer-reviewed: PENDING

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