A packing algorithm for particles of arbitrary shapes

Particle packing is a subject of both academic and industrial importance, and a number of packing algorithms have been proposed and widely used. However, most of these packing algorithms can only deal with spheres and a few regular shapes. If applied to arbitrarily shaped particles, they would have difficulties in at least one of three aspects. First, arbitrary shapes are notoriously difficult to model mathematically. Secondly, efficient algorithms for collision and overlap detection of arbitrary shapes are difficult to derive and more difficult to implement. Thirdly, the packing program would be very computationally expensive for routine and practical use. This paper describes a new, digital approach to particle packing, which can avoid many of the difficulties suffered by conventional methods. The key innovation is digitisation of both particle shapes and the packing space. Thus, a particle is now just a coherent collection of pixels or voxels, regardless of its shape, moving on a square lattice, onto which the packing space is mapped. Using the digital approach, it is easy to pack particles of any shapes and sizes into a container of any geometry, generally requiring no more than an ordinary PC. Although, as yet, the packing algorithm does not involve physical forces explicitly, it can simulate some physical phenomena such as size segregation. The ability to pack particles in their real shapes, rather than approximated as spheres, opens up many new industrial and academic opportunities, some of which are discussed. Examples of packing density predictions of particles subject to various effects, including vibration and rotation, are given.