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

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 V₀ and is mainly proportional to the cylinder diameter d. While the force on the cylinder increases with its penetration depth, the granular velocity profile around the cylinder is found to be 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 λ that is mainly governed by the cylinder diameter for a large enough cylinder/grain size ratio d/d_g: λ∼d/4+2d_g. The granular temperature exhibits a constant plateau value T₀ in a thin layer close to the cylinder of extension δ_T0∼λ/2 and decays exponentially far away with a characteristic length λ_T of a few grain diameters (λ_T∼3d_g). The granular temperature plateau T₀ that scales as V₀²d_g/d is created by the flow itself from the balance between the “granular heat” production by the shear rate V₀/λ over δ_T0 close to the cylinder and the granular dissipation far away.