Drag Force Regime in Dry and Immersed Granular Media

The drag force acting on an intruder colliding into the granular media is typically influenced by the impact velocity and penetrating depth. In this study, the investigation was extended to the dry and immersed scenarios through coupled simulations at different constant intrusion velocities. The drag force regime was clarified to exhibit velocity dependence in the initial contact stage, followed by the inertial transit stage with a F~z² (force-depth) relationship. Subsequently, it transitioned into the depth-dependent regime in both dry and immersed cases. The underlying rheological mechanism was explored, revealing that in both dry and immersed scenarios, the granular bulk underwent a state relaxation process, as indicated by the inertial number. Additionally, the presence of the ambient fluid restricted the flow characteristics of the perturbed granular material, exhibiting a similar rheology framework as observed in the dry case.