Micromechanics of intruder motion in wet granular medium

We investigate the effective friction encountered by an intruder moving through a sedimented medium which consists of transparent granular hydrogels immersed in water, and the resulting motion of the medium. We show that the effective friction $\mu_e$ on a spherical intruder is captured by the inertial number $I$ given by the ratio of the time scale over which the intruder moves and the inertial time scale of the granular medium set by the overburden pressure. Further, $\mu_e$ is described by the function $\mu_e(I) = \mu_s + \alpha I^\beta$, where $\mu_s$ is the static friction, and $\alpha$ and $\beta$ are material dependent constants which are independent of intruder depth and size. By measuring the mean flow of the granular component around the intruder, we find significant slip between the intruder and the granular medium. The motion of the medium is strongly confined near the intruder compared with a viscous Newtonian fluid and is of the order of the intruder size. The return flow of the medium occurs closer to the intruder as its depth is increased. Further, we study the reversible and irreversible displacement of the medium by not only following the medium as the intruder moves down but also while returning the intruder back up to its original depth. We find that the flow remains largely reversible in the quasi-static regime, as well as when $\mu_e$ increases rapidly over the range of $I$ probed.