Event driven simulations of translational and rotational dynamics of hard spheres with friction

Abstract

We analyze the hard sphere model with a rough surface using event driven simulation methods and study the impact of roughness on the rotational and translational particle dynamics of Newtonian and Brownian systems. Based on a collision algorithm proposed by Luding [Lud98], we considerbinary collisions with a Coulomb-type friction force, where energy is dissipated and it is possible to transfer linear to rotational momentum. We furthermore develop the algorithm by incorporating the conversation of the total energy for the system. In addition, the rotational and translational diffusion coefficients for Brownian systems are discussed for different friction and particle densities. Finally, the results also compared to simulation results from Tomilov [Tom+12] and experiments from Schütter et al. [Sch+17].We analyze the translational particle dynamics in terms of the mean squared displacement and the rotational dynamics in terms of the angle correlation and also consider the respective mean system energy. For Newtonian systems we observe that Luding's ansatz does not conserve energy for the translational and rotational particle dynamics and thus causes a slowing down of the system dynamics. For Brownian systems, no impact of friction on the system dynamics could be observed. First studies on the extended approach of an energy conserving collision algorithm for the limiting case of a smooth sphere system yield same results as our findings on the limit case of smooth spheres using Luding's ansatz. Our translational diffusion coefficients for different packing fractions agree with experimental data and simulations. The rotational diffusion coefficient of smooth spheres is independent of the packing fraction, whereas experiments indicate a slight decay of the diffusion coefficient approaching high packing fractions.