Forces on a sphere suspended in flowing granulate

¹ Otto-von-Guericke-Universifat Magdeburg, Magdeburg, Germany
² Technische Hochschule Brandenburg, Brandenburg an der Havel, Germany
³ Universidad de Navarra, Pamplona, Spain
⁴ HUN-REN Wigner Research Centre for Physics, Budapest, Hungary

^* e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 1 December 2025

Abstract

We investigate the forces of flowing granular material on an obstacle. A sphere suspended in a discharging silo experiences both weight of the overlaying layers and drag of the surrounding moving grains. In experiments with frictional hard glass beads, the force on the obstacle was found to be practically flow-rate independent. In contrast, flow of nearly frictionless soft hydrogel spheres added drag forces which increased with the flow rate until reaching saturation at high flow speeds. The total force grew quadratically with the obstacle diameter in the soft, low friction material, while it grew much weaker, nearly linearly with the obstacle diameter, in the bed of hard, frictional glass spheres. In addition to the drag, obstacles embedded in the flowing hydrogel spheres experience a weight force from the top as if immersed in a hydrostatic pressure profile, but negligible counter-forces from below. In contrast, the frictional hard particles create a strong pressure gradient near the upper surface of the obstacle. Numerical simulations provide additional information that is difficult to access experimentally. They reproduce the experimental results and give hints for the origin of the different force contributions. The results have considerable practical importance for the discharge of storage containers with large objects suspended in flowing granular material.