Drag anisotropy of cylindrical solids in fluid-saturated granular beds

We study the direction-dependent drag acting on a cylindrical solid intruder with length $L$ and diameter $D$ as it moves in water-saturated granular beds at constant depth. Polysterene and hydrogel grains with diameter $d$ are used to investigate materials which have high contact friction and those which are nearly frictionless, respectively. The drag on the intruder is measured while oriented perpendicular $F_\perp$ and parallel $F_\parallel$ to its axis as a function of speed $U$ from the quasi-static to the rate-dependent regime. We find that the drag anisotropy $\xi = F_\perp/F_\parallel$ is not constant, and increases significantly with driving rate and $L/D$ in both mediums. In particular for $L/D = 40$, $\xi$ increases from 2.6 to 4.5, and from 7.0 to 8.2 in the high and low friction beds, respectively, as the nondimensional Froude number $Fr =U/\sqrt{g(D+d)}$ is varied between $10^{-4}$ and $2 \times 10^{-2}$. On average, $\xi$ is observed to increase logarithmically with $L/D$ for $L/D \gg 1$. Exploiting the index-matched nature of hydrogel grains in water, we further show that the sediment flow around the cylinder in the two orientations is consistent with skin friction dominated drag. The relative contributions of the cylindrical side and the circular flat-ends on $\xi$ are estimated with thin disks to understand the observed variation of drag with aspect ratio and surface friction.