Undulatory forcing of an intruder through granular media: effects of frequency and packing fraction

We investigate the motion amid grains of an intruder undergoing an imposed force that oscillates with a given frequency. For that, we made use of discrete numerical simulations where the intruder was a larger disk on which a force oscillating in direction was applied, and the grains consisted of smaller disks. All disks were placed on a surface with basal friction over which they could slide, the system was confined in the sliding directions, and we varied the system packing fraction, oscillation frequency, and magnitude of the forcing. The results show intermittent and very complex motions of the intruder depending on both the packing fraction and frequency of oscillation: It can move sideways while slowly progressing forward, it can be blocked during a long period after and/or before start moving, or it can simply be blocked after a given time. Interestingly, we find that the displacement velocity is much higher when the system packing fraction is above a given threshold, contrary to intuition. The results show that there is an optimal frequency that minimizes the transit time for some ranges of packing fraction, and we propose a model based on the system elasticity that explains this behavior and agrees with the numerical simulations. Our findings shed new light on how to better explore oscillating motion to move objects within granular media.