Simulation of periodic mono-sized hard sphere systems under different vibration conditions and resulting compaction

This paper presents a simulation study of confined periodic mono-sized hard sphere systems under different vibration conditions and their influence on the final compaction. An initial random loose packing is submitted to a series of vibration cycles allowing to transform it into a “suspension” in which a given proportion of particles have the possibility to vibrate. This “suspension” is then let to settle down and brought to a new denser packing. Different random local rules are used for the simulation of the displacements of particles during vibration. Firstly, a symmetric vibration is applied in which particles attempt to perform vertical upwards and downwards displacements of equal length. Shocks between particles are simply simulated by random upwards or downwards displacements. It has already been shown that in these conditions, and when the whole system is vibrating, the final packing density can be related to the initial density and to the vibration amplitude (“suspension model”). We show here that for a periodic packing, this model can be extended to partial “suspensions” in which only a proportion of particles is vibrating. An excellent agreement is found between this model and the simulation results as long as the packing is disordered. For large vibration amplitudes, an order appears amongst the system allowing to reach high densities (up to 0.66). Then, the symmetric vibration is replaced by a random vibration in which particles attempt to perform alternatively random upwards and downwards displacements whose inclination with the vertical axis follows a normal distribution. It is shown that in these conditions, the vibration still allows transforming the initial packing into a partial “suspension” but the proportion of vibrating particles is lower than for the symmetric vibration previously used. However, the “suspension model” can be extended with a reasonable agreement to this kind of vibration