Topics in Particle and Dispersion Science

Particle size distribution

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Particle size distribution (PSD), also referred to as body size distribution or body size - abundance distribution in biology and ecology, is a function relating the particle size, D [length], to the particle concentration. In the case of the number concentration of particles, i.e. the number of particles per unit volume of dispersion, the PSD, n(D) ≥ 0, with a unit of length^-4, also referred to as the differential particle size distribution or frequency particle size distribution, is defined by the following equation:

dN(D) = -n(D) dD

(1)

where N(D) [length^-3] is the concentration of particles with sizes greater than D, i.e. the cumulative particle size distribution, also referred to as the integral particle size distribution. The absolute value of the differential dN(D) is simply the number concentration of particles with sizes in a range of [D, D + dD].

A factor of length^-3 in the dimension of n(D), length^-4, refers to the unit volume of the dispersion and the remaining factor of length^-1 refers to the unit particle size interval. Thus, the dimension of n(D) is sometimes written, for example, as cm^-3µm^-1, i.e. by using different length units for each factor, instead of simply cm^-4 or µm^-4.

It follows that:

N(D) = ∫D∞ n(x) dx

(2)

Hence, N(0) is the total number concentration of the particles, N_tot. In reality, the upper limit of the integral in Eq. 2 is clipped at a finite particle size.

In atmospheric sciences, the PSD is frequently represented as:

nln(D) = dN(D) / dlnD

(3)

which is related to n(D) as follows:

n(D)	= - dN / dD
	= - (dN / dlnD) (dlnD / dD)
	= nln(lnD) (1 / D)	(4)

 

CITATION: Jonasz M. 2006. Particle size distribution (www.tpdsci.com/Tpc/PSD.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY: Published: 07-Jan-2006 Modified: 04-Jan-2008 Reviewed: PENDING

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