Topics in Particle and Dispersion Science

Moments of particle size distribution

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An r-th cumulative moment, M_r, of the particle size distribution (PSD), n(D) is defined by the following equation:

Mr = ∫0∞ D r n(D) dD

(1)

For example, the 0-th moment, M₀, is simply the total particle concentration [length^-3]. The 0-th and the 1-st moment, M₁, define the (arithmetic) mean particle diameter, D_m, as follows:

Dm	=	∫0∞ D n(D) dD ∫0∞ n(D) dD
	=	M1 M0	(2)

Similarly, the 0-th, 1-st, and 2-nd moments define the variance, Var(D) of the particle diameter as follows:

Var(D)	= Avg[ ( D - Dm ) 2 ]
	= Avg[ D 2 ] - Dm2
	= M2 / M0 - Dm2	(3)

where, Avg(x) denotes the average of x. The importance of the moments of particle size distribution stems from their use in:

• defining various measures of the average or effective particle size
  Indeed, one use of the moments in this capacity is shown in Eq. 2, another is the definition of the optically effective particle diameter, D_eff = D₃₂:

  D32 = M3 / M2

  (4)

  Incidentally, in the above notation, D_m = D₁₀.
• defining an optimum particle size grid for the PSD measurements (for example, Jonasz M and Fournier 2007, p. 274)
• reconstruction of the PSD from a finite number of the PSD moments (for example, John V et al 2007, 2005)

In respect of the latter use of the moments of PSD, note that some analytical approximations to the PSD can, in principle, be reconstructed exactly from the knowledge of the first few moments (see, for example, Moments of a log-normal distribution

CITATION: Jonasz M. 2006. Moments of particle size distribution (www.tpdsci.com/Tpc/PsdMom.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY: Published: 27-Aug-2007 Modified: 04-Jan-2008 Reviewed: PENDING

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