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

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. 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 T(0) in a thin layer close to the cylinder of extension δ(T(0))~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 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)/λ over δ(T(0)) close to the cylinder and the granular dissipation far away.

Unifying Impacts in Granular Matter from Quicksand to Cornstarch

“…Quantitative agreement is achieved by taking Aα 30. Such a value is consistent with experimental measurements of α and A for glass beads [21,35], for which α ≈ 4 and A ≈ 5 − 10. Furthermore, the Darcy-Reynolds model captures the impact dynamics for a wide range of physical parameters: using different suspension mixtures and different impact parameters, the data for the maximal indentation depth δ max , stopping time t end and maximal deceleration γ max collapse on the prediction when plotted as function of λ∆φ [ Fig.…”

“…Assuming a frictional rheology for the granular suspension [2] and neglecting the confining pressure due to gravity in front of the pore-pressure, the contact stress on the impactor is −AP f , where A is an effective friction coefficient [3,35] and P f is the pore-pressure (4), in which V p =δ, where δ is the penetration depth, and L = a the typical radius of the contact area of the projectile (consistent with our measurements of the pressure profile, see inset of lower panel of Fig. 2b).…”

Local rheological measurements in the granular flow around an intruder

“…This allows one to have local information in the granular medium up to at least 22 mm ≃ 5d g away from the intruder center. This should be a large enough zone of analysis as the radial extension of the velocity field perturbation is expected to be here of about 2d g + d/4 ≃ 13 mm ≃ 3d g [21]. The time evolution of the drag force F (t) extracted from the image analysis [Eq.…”

Dense flow around a sphere moving into a cloud of grains

“…In our simulation, we do not observe any quasi static regime at low velocity where the drag force would be velocity independent or would depend only weakly on the velocity. The existence of such a quasi-static regime which is the most often seen regime [3,4] arises from the existence of another natural scale of pressure in the system which may come either from gravity and solid friction. We found here that the drag force F increases linearly with the initial solid fraction φ 0 with the scaling law F 5φ 0 ρd g 2 V 2 0 φ 0 ρdd g V 2 0 /2.…”

“…Even in simple parallel shear flows, the existence of such a local rheology and the influence of solid walls is still under investigation [2]. As a matter of fact, the presence of far boundaries such as fixed or mobile solid walls has shown to have strong and non elucidated actions in different situations [3,4]. To examine this important question, one must have access simultaneously to the strain and stress fields in the bulk flow which e-mail: antoine.seguin@u-psud.fr is possible experimentally in some cases [5] but now easier with discrete numerical techniques.…”