TPDSci Particle shape parameters in 2D

Particle shape parameters in 2D

The convenience of characterizing the shape of a particle with a single parameter, with a view towards relating that parameter to other properties of particle, for example, a cross section for light scattering, stimulated defining of a number of particle shape parameters. Such parameters refer mostly to a projection of the 3D particle shape onto a plane, i.e. are suitable for the characterization of particles by using optical or electron microscopy. These latter two techniques are still used in the vast majority of the particle characterization tasks.

The following 2D particle shape parameters have been defined, referencing the particle shape (projection onto a plane) to the disk shape:

aspect ratio (AR)
the ratio of the maximum to the minimum Feret's diameters (for example, Hentschel ML and Page 2003):

AR = D_{F, max} / D_{F, min} (1)

This parameter assumes a minimum of 1 for a circle.
area-to-perimeter-squared ratio (AP2R)
also referred to as the form factor (FF):

AP2R = FF = 4πA / P² (2)

where A is the projected area of the particle onto a plane, and P is the length of the particle perimeter (for example, Hentschel ML and Page 2003, Kindratenko V 1997). The AP2R assumes a maximum of 1 for the disk. The inverse of AP2R is called the circularity or circularity factor (for example, Kindratenko V 1997).
circulatity (C) or circularity factor

C = 1 / AP2R = P² / 4πA (3)

where AP2R is the area-to-perimeter-squared ratio, A is the projected area of the particle onto a plane, and P is the length of the particle perimeter (for example, Kindratenko V 1997). The circularity assumes a minimum of 1 for a disk.
roundness (R)
is defined as follows (for example, Chakrabarty RK et al 2006, Hentschel ML and Page 2003):

R = 4A / [π D_{F, max}²] (4)

where A is the projected area of the particle onto a plane, D_{F, max} is the maximum Feret's diameter (see Particle size). Roundness assumes a maximum of 1 for a disk.

The above shape parameters are ratios of attributes of the particle shape projection onto a plane. Given the limited accuracy of determining these attributes and digital imaging effects (for example, Zeidan M et al 2007, Schäfer M 2002), the shape parameters, when used for comparing particles, are most representative for particles of similar sizes (Hentschel ML and Page 2003). Hentschel ML and Page (2003) point out that a single shape parameter is not a unique shape descriptor.

CITATION:
Jonasz M. 2006. Particle shape parameters in 2D (www.tpdsci.com/Tpc/PtSz.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY:
Published: 27-Aug-2007
Modified: 27-Aug-2007
Peer-reviewed: 03-Sep-2007

Topics in Particle and Dispersion Science