Home | Survey | Topics | Index | References | Dictionary | Contribute | Gallery | Community | Search
| Particle shape parameters in 3D | Prev topic | Next topic |
Taylor MA 2002 proposed a generalized set of particle shape parameters defined by a set of moments of the 3D particle shape. The particle shape is understood here as a 3D distribution of the particle mass. This definition of the particle shape is especially attractive for these methods of calculating optical properties of small particles which "assemble" a particle from elementary volumes, as does the discrete dipole approximation (DDA), for example. Unfortunately, this approach to the particle shape characterization requires 3D techniques of the particle shape determination, which are generally more complicated than 2D techniques.
Traditionally, stereoscopic optical microscopy (for example, Kim NH et al 1990), stereoscopic scanning electron microscopy (for example, Laird D 2001), and stereoscopic transmission microscopy (Tanji T et al 2005) were used to determine 3D particle shapes. Note that the strikingly three-dimensional appearance of particle shapes viewed with a scanning electron microscope (SEM) allows to evaluate the particle height topography by using the "shape from shades" principle for a multi-detector SEM (Drzazga W et al 2006).
More recently, the 3D particle shape determination techniques include scanning optical microscopy (for example, Nagel Y and Ay 2000), x-ray microtomography (Lin CL and Miller 2005, Vincze L et al 2001), and electron tomography (for example, van Poppel LH et al 2005).
In 3D, the sphere is a convenient reference shape. The similarity to (or departure from) the spherical shape is frequently characterized with the sphericity parameter, S (for example, Allen T 1997):
| S | = (V / Vcs )1/3 | (1) |
| = dn / Dcs |
where V is the volume of the particle, Vcs is the volume of the circumscribed sphere, and dn is sometimes referred to as the nominal diameter of the particles. The sphericity assumes a maximum of 1 for the sphere. Diameter Dcs is frequently approximated by the length of the particle, following Krumbein WC 1941.
That definition of sphericity is a simplification, introduced by Wadell H 1933, following his original definition (Wadell H 1932):
| S = Aevs / A | (2) |
where Aevs is the area of a sphere having volume equal to that of the particle and A is the area of the particle surface. Given the difficulties in measuring the surface area of a particle, the original definition of sphericity has been only recently evaluated for a sample of gravel grains by Hayakawa S and Oguchi 2005 who found it to be well correlated to the visual particle roundness parameter introduced by Krumbein WC 1941.
Canham PB and Burton 1968 introduced a sphericity index to characterize the closeness of a red blood cell shape to that of a sphere. The sphericity index is defined as follows:
| sphericity index = a V 2/3 / A | (3) |
where a = 62/3 π1/3 ≅ 4.84 (which makes the sphericity index equal to 1 for a sphere), V is the particle volume, and A is the particle surface area.
Other shape factors characterizing the sphericity of a particle have been proposed and correlated with various physical properties of the particle, such as the settling velocity (for example, Le Roux JP 2002a, Dietrich WE 1982). These factor include:
with dl, di, and ds being the longest, intermediary, and shortest particle axes lengths, respectively, in an orthogonal reference frame.
Jonasz M 1987a defined the nonsphericity parameter (NSP) as the ratio of the projected area of a particle averaged, Ap, avg, over all orientations, to the projected area, Ap, eqs of the sphere with equal volume:
| NSP = Ap, avg / Ap, eqs | (4) |
This parameter was intented to assess the effect of particle nonsphericity on light scattering by dilute dispersions of particles larger than the wavelength of light. Indeed, for such dispersions, light scattering is proportional to the total projected area of the particles per unit volume of the dispersion. This latter area is a product of the average projected area of the particle and the number concentration of particles. NSP assumes a minimum of 1 for a disk. Aas E 1984 defined a similar parameter (shape factor), Ap, avg / V 2/3, where V is the particle volume. The shape parameter equals NSP to within a constant factor.
See also: Particle shape parameters in 2D
| CITATION: Jonasz M. 2006. Particle shape parameters in 3D (www.tpdsci.com/Tpc/PtSz.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 27-Aug-2007 Modified: 10-May-2010 Peer-reviewed: PENDING |
| Journals | Journals search | Contributing | | | Menu |
| Copyright 2005-2012 TPDSci Inc. All rights reserved. | Terms of use | |