From Long-Range Interaction to Solid-Body Contact Between Colloidal Surfaces During Forming

Abstract

A simulation method based on the discrete element method (DEM) has been developed for studying the particle packing dynamics and for optimizing the colloidal forming processes. The DEM needs explicit functions for the computation. The explicit van der Waals interaction functions derived by Hamaker between two surfaces (or spheres) become infinite if the surface distance approach zero. This is a numerical singularity problem due to the continuum assumption in the Hamaker theory and is inconsistent with the physical reality. The analytical solutions obtained by using the modern Lifshitz’s theory and solution by incorporating the non-continuum theories (e.g. Lennard–Jones potential) are too complex to be applied for the DEM process simulation. During consolidation processes, the colloids move from the long-range interaction region into the solid-body contact with other colloids or with the boundaries. The long-range interaction were described by the DLVO theory. Meanwhile, the Johnson–Kendall–Roberts (JKR) theory took the adhesion energy (or surface energy) into account for describing the elastic solid-body contact. Both the Derjaguin approximation and the JKR theory based on the continuum assumption have been successfully applied to solve the transition (or numerical singularity) problem from the DLVO long-range interaction to the elastic JKR solid-body contact for the DEM simulation. Solving the transition/singularity problem is the first step for simulating the consolidation processes. In this numerical model, the adhesion energy, the elastic deformation, the hard sphere diameter and the compact Stern layer were considered. The shortest surface distance (without external load) is calculated at a distance where the JKR adhesion force is equal to the DLVO interaction force. The interactions between two spheres, between sphere and surface plane and between two different materials were shown. The DEM simulation results show that the particle-pile-up is an essential mechanism for the particles to get into solid-body contact in stabilized suspensions.