Experimental velocity fields and forces for a cylinder penetrating into a granular medium

TL;DR

This study characterizes granular flow and force interactions for a cylinder penetrating a granular medium, revealing velocity independence of drag force, localization of flow and temperature profiles, and scaling laws for flow perturbation and temperature.

Contribution

It provides detailed measurements of velocity and force fields around a penetrating cylinder, introducing new scaling laws and insights into granular flow localization and temperature profiles.

Findings

Drag force is velocity-independent and proportional to cylinder diameter.

Flow perturbation decays exponentially with a length scale related to cylinder size.

Granular temperature near the cylinder forms a plateau scaling with flow parameters.

Abstract

We present here a detailed granular flow characterization together with force measurements for the quasi-bidimensional situation of a horizontal cylinder penetrating vertically at a constant velocity in dry granular matter between two parallel glass walls. In the velocity range studied here, the drag force on the cylinder does not depend on the velocity V_0 and is mainly proportional to the cylinder diameter d. Whereas the force on the cylinder increases with its penetration depth, the granular velocity profile around the cylinder is found stationary with fluctuations around a mean value leading to the granular temperature profile. Both mean velocity profile and temperature profile exhibit strong localization near the cylinder. The mean flow perturbation induced by the cylinder decreases exponentially away from the cylinder on a characteristic length \lambda, that is mainly governed by the cylinder diameter for large enough cylinder/grain size ratio d/d_g: \lambda ~ d/4 + 2d_g. The granular temperature exhibits a constant plateau value T_0 in a thin layer close to the cylinder of extension \delta_{T_0} ~ \lambda/2 and decays exponentially far away with a characteristic length \lambda_T of a few grain diameters (\lambda_T ~ 3d_g). The granular temperature plateau T_0 that scales as (V_0^2 d_g/d) is created by the flow itself from the balance between the "granular heat" production by the shear rate V_0/\lambda over \delta_{T_0} close to the cylinder and the granular dissipation far away.