Anomalous diffusion in vibration-induced spreading of a granular heap

Abstract The spreading of granular materials is a key phenomenon in various fields such as geophysics, additive manufacturing, batteries, and 3D printing. Understanding the dynamics of these materials, which behave like non-Newtonian fluids, is crucial for ensuring uniform distribution, precise layer formation, and surface quality. This study focuses on the influence of mechanical vibrations on the dynamics of granular heap spreading, initially at equilibrium at its angle of repose. We conduct experiments to characterize the effect of vibration amplitude and frequency on spreading dynamics and flow arrest. We observe two distinct regimes in the evolution of the heap radius: an early super-diffusive regime followed by a sub-diffusive regime, consistent with previous studies. Our results show that vibration intensity significantly impacts the long-term scaling exponents. We propose a spreading law based on scaling arguments and a simple model to explain the dependence of scaling exponents on vibration intensity.