A dynamic simulation of particle rearrangement in powder packings with realistic interactions

Abstract

A computer simulation of evolution of random structures of spherical particles has been performed by solving Newton’s equations of motion. The forces considered are gravity, Hertz contact force, frictional force, and van der Waals interaction (VDWI). 948 monosized particles were placed without overlapping inside a rigid cylindrical container by generating the coordinates of the centers of the particles with the help of a random number generator. The initial packing density was only 0.363. The particles were allowed to settle under gravity. When the coefficient of friction (μ) among the particles and between the particle and the wall of the container was 0.3, the packing density reached a value of 0.578. If there is no friction, the density reached 0.633 which is comparable to the random close-packed density obtained in the random structures of steel ball bearings. For small particles, VDWI can reduce the packing density by agglomeration of particles into local clusters. For example, with VDWI and μ of 0.3, the random structures of particles with diameter 100 and 50 μm had packing densities of 0.528 and 0.420, respectively. When μ was increased to 0.7, the packing density of 100-μm particles with VDWI was 0.505, compared to 0.528 in the case of μ equal to 0.3. The average velocity of the particles initially increased, and after reaching a maximum, started to decrease due to collisions amongst the particles. During the dynamic simulation, the trajectories of a few selected particles were traced. To study the rearrangement process, the average displacement of a few particles in a direction normal to the direction of gravity and the average angle of rotation of the straight line joining the centers of a few selected pairs of particles were calculated at various instants of time. It is seen that the rearrangement of 50-μm particles was smaller than that of 100-μm particles because of VDWI. The radial distribution functions of the computer-generated close-packed structure is similar to that of Finney’s close-packed structure of steel balls. In the case of 50-μm particles with VDWI, there were additional peaks close to the first peak, due to agglomerating effect of VDWI. The cumulative number of contacts was computed as a function of the radial distance and, in the case of 100-μm particles without friction and VDWI, it agreed with Mason’s data for steel balls.