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The power-law (frequency or differential) particle size distribution (PSD) is expressed as follows:
| n(D) = tD -s | (1) |
where t [length-4] [see a note on the dimension of n(D)] and s [nondimensional] are positive constants (concentration factor and slope, respectively), and D is the nondimesional particle size. The concentration factor, t, represents the number concentration of particles with a particle size of unity.
The nondimensional particle size, D, is a ratio of the actual particle size Da [length] to D0, where D0 = 1 [length]. This way, the nondimensional ratio D / D0 is numerically equal to the actual particle size, Da, that is expressed in the chosen units of length. Such a trick avoids the need of raising units to an arbitrary power s, as it is done, for example, by Lerman et al (1977). However, as pointed out by Prothero (1986), by making the essentially empirical Eq. 1 dimensionally homogeneous one does not increase our understanding of the underlying processes. Such understanding must come from creating physical models of these processes (for example, Kiefer and Berwald 1992, Lerman et al 1977).
The power law has been widely used to fit experimental PSD for numerous types of dispersions, including naturally occuring dispersions, since the introduction of this approximation by Junge (1963). This type of PSD is sometimes referred to as the Junge distribution. Such an approximation is represented by a straight, descending line in the logn vs. logD plot.
Other functions used for approximating the PSD of naturally occuring particles include:
| CITATION: Jonasz M. 2006. Power-law PSD (www.tpdsci.com/Tpc/PsdPwLw.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 06-Jan-2006 Modified: 02-Feb-2007 Peer-reviewed: PENDING |
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