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The power-law PSD, n(D) = tD -s, where, t and s are positive constants and D is a non-dimensional particle size (see Power-law PSD), has been widely used to approximate experimental particle size distributions for numerous types of dispersions, since the introduction of this approximation by Junge CE 1963. Such an approximation is represented by a straight, descending line in the logn vs. logD plot.
Yet, experimental data on size distributions frequently exhibit curvature when plotted in such a scale, for example, Cavender-Bares K et al 2001, Jonasz M and Fournier 1996, Jonasz M 1983). Ceronio AD and Haarhoff 2005 examine an extension of the power-law approximation with the slope parameter s being a function of D:
| s(D) = b logD | (1) |
where parameter b was found by Ceronio AD and Haarhoff 2005 to be in a range of about 1.3 to 2 for nearly 1500 PSDs obtained for samples taken at water treatment plants. Ceronio and Haarhoff also provide a least-squares based procedure for estimating the parameters of so modified power-law approximation.
By making s a function of the particle size, D, one allows the PSD to curve in the log-log scale plots. Other functions used for approximating curved PSDs include:
| CITATION: Jonasz M. 2006. Variable-slope power-law PSD (www.tpdsci.com/Tpc/PsdPwLwVSlp.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published:17-Jan-2006 Modified: 19-Jun-2006 Peer-reviewed: PENDING |
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