Nonadditive drag of tandem rods drafting in granular sediments

TL;DR

This study investigates how the drag force on tandem rods moving through granular sediments varies with their separation and speed, revealing nonadditive effects and flow shielding phenomena that challenge existing force theories.

Contribution

It demonstrates that drag on multiple bodies in granular media is nonadditive at short separations and visualizes flow shielding effects using refractive index matching.

Findings

Drag on the leading rod is similar to a single rod.

The following rod experiences significantly less drag.

Flow visualization shows stagnant regions forming between rods.

Abstract

We examine the drag experienced by a pair of vertical rods moving in tandem through a granular bed immersed in a fluid as a function of their separation distance and speed. As in Newtonian fluids, the net drag experienced by the rods initially increases with distance from the value for a single rod before plateauing to twice the value. However, the drag acting on the two rods is remarkably different, with the leading rod experiencing roughly similar drag compared to a solitary rod, while the following rod experiences far less drag. The anomalous relationship of drag and the distance between the leading and following body is observed in both dry granular beds and while immersed in viscous Newtonian fluids across the quasi-static and the rate-dependent regimes. Through refractive index matching, we visualize the sediment flow past the two rods and show that a stagnant region develops in their reference frame between the rods for small separations. Thus, the following rod is increasingly shielded from the granular flow with decreasing separation distance, leading to a lower net drag. Care should be exercised in applying resistive force theory to multi-component objects moving in granular sediments based on our result that drag is not additive at short separation distances.