Investigation of symmetric non-spherical particle shapes by applying low-resolution spherical harmonics

Abstract

The issue of mathematical modelling of non-spherical shapes of particles is considered. Thus, application of the spherical harmonics (SH) technique in modelling the simplest symmetric star-shaped particles is demonstrated by applying low-resolution functions. The investigation was restricted to a circular cylinder and a rectangular parallelepiped, geometrically primitive, but widespread oblate industrial shapes. The modelling quality was studied by considering selected error norms and the most important integral characteristics of a particle geometry, including the surface area and volume. The presented results discovered new features of the spherical harmonic technique and enhanced understanding of their applicability to describe non-spherical shapes.

Low-Resolution Spherical Harmonics Models in Application to Quasi-Quadric Particle Shapes

“…A general method for obtaining expressions for curvatures in terms of surface derivatives is provided in differential geometry while detailed description of curvature expressions for ellipsoid are given by Harris (2006) and Poelaert et al (2011) will be explored for further analysis of contact of quasi-ellipsoids. Differentiation of SH and analysis of ellipsoid's curvatures were considered by Garboczi (2002), while a more recently applied methodology is given in Radvilaitė et al (2017).…”

“…Desired accuracy of semi-analytical SH approximation is controlled by a suitable value of expansion degree L. It was found, however, see Feinauer et al (2015), Zhou et al (2015), that essential characteristics of the shape geometry are captured by a limited number of expansion terms, while the residual terms are responsible for the detailed description of the particle surface. Basic features of spherical harmonic modelling methodology, addressing the applicability of low-resolution spherical harmonics to describe symmetric particles with sharp edges shape were considered by Radvilaitė et al (2017).…”