Discrete-Finite Element Modelling of Pharmaceutical Powder Compaction: A Two-Stage Contact Detection Algorithm for Non-Spherical Particles

Abstract

Granular flow, particle mixing and powder compaction are very important processes in many industrial applications such as pharmaceutical tabletting, minerals selection, casting, packing and transport of granular materials. Flow and deformation of particles has been typically treated as a continuum process, and thus the Finite Element Method (FEM) has been widely used. In reality, however, granular powder consists of millions of tiny particles of different sizes and shapes, the conventional continuum method cannot model these discrete features. Naturally, a discrete element method can provide more realistic results using uniform spherical particles. Furthermore, powder flow and deformation modelling involve rheology, particle size distribution, fracture, and mixture of different materials. The modelling of such processes is very difficulty due to their nonlinearity. Thus, the proper modelling of powder flow and compaction is of both industrial importance and scientific interest. The main issue in discrete element modelling is the contact detection of interacting particles during the flow and deformation processes. In fact, nearly two-thirds of the computing time is used for the contact detection purpose. Thus, the efficiency of the contact detection algorithms used in the discrete element analysis is crucially important to the whole modelling procedure. A number of good contact detection algorithms have been developed such as the direct check algorithm, binary tree algorithm, contact list and grid searching algorithms. However, most of these algorithms work well for rigid spherical or triangular particles. They generally do not apply well to the non-spherical particles, or at least there is no guarantee of their efficiency. So many existing studies have focused on the flow and transport of rigid spherical particles and soft particles. Recently, there have been new developments concerning flow of non-spherical particles such as elliptical shapes and/or triangular particles. In this paper, we present a two-stage contact detection algorithm for non-spherical particles using the contact list algorithm and direct polygon contact detection. This method combines the advantages of several existing contact detection algorithms so as to find an efficient way to deal with the interactions of non-spherical particles, and simply treating the spherical particle as a degenerated case of non-spherical shapes. In this way, we can essentially deal with any particle shape. In the next sections, we will give a brief description of the two-stage contact detection algorithm, and then provide some simulation results and compare the efficiency with other contact detection procedures.