Flux through a hole from a shaken granular medium

Abstract

We have measured the flux of grains from a hole in the bottom of a shaken container of grains. We find that the peak velocity of the vibration, v max , controls the flux, i.e., the flux is nearly independent of the frequency and acceleration amplitude for a given value of v max .The flux decreases with increasing peak velocity and then becomes almost constant for the largest values of v max . The data at low peak velocity can be quantitatively described by a simple model, but the crossover to nearly constant flux at larger peak velocity suggests a regime in which the granular density near the container bottom is independent of the energy input to the system. † We study the flux of grains emerging though a small hole in the bottom of a container of a vibrating granular sample. This flux has analogs both in the familiar act of shaking salt from a salt shaker and also in the important statistical mechanics problem of fluid flow through a hole. While the flux has been studied extensively for unvibrated grains, 18, , , 19 20 21 for vibrated grains the flux has only been studied in the case of flow from a vibrated hopper (in which the boundaries all slope toward an open bottom). , 23Our measurements complement these studies by examining the simpler case of flux from a vibrated granular medium through a hole in a flat boundary over a broader range of parameters, and we demonstrate that this quantity can be largely understood within a simple model. were large enough so that the effects of interstitial air could be neglected., 24The hole diameter (D) was sufficiently large that the grains would flow even in the absence ofThe vessel was supported by four aluminum posts connected to an electromagnetic shaker controlled by two feedback accelerometers mounted on the rim of the vessel. The vessel was vibrated sinusoidally (y vessel = Asinωt) at a desired frequency, f = ω/2π, and a peak acceleration, Γ = Aω 2 /g, which we normalize to the gravitational acceleration, g = 9.81 m/s 2 .Grains flowing out from the container landed in a stationary collector suspended below the vessel. The collector was attached to an electronic balance, allowing us to record the mass of the effluent as a function of time, m(t), and thus determine the time-averaged flux from the hole, Φ(t) = dm/dt. The mass of glass spheres in the shaking vessel was such that there were between 20 and 90 grain layers in the container while data were acquired. The flux was found to be almost independent of mass in the shaker for the range of masses used in the experiments (variation of less than 10%). The frequencies used in our experiment ranged from 6 Hz to 400 Hz with Γ ranging from 1.25 to 10. The range of the vibration parameters was limited by the maximum amplitude of the shaker ( ~ 12 mm). The acquisition time for each measurement was 120 seconds (720 -48000 cycles), and each of the flux values reported below was taken as an average of at least five measurements (error bars represent the standard deviation of the measurements). All data were acqui...

Glass transition associated with the jamming of vibrated granular matter

“…There is a wide consensus about the fact that α should play the role of the relevant control parameter in vibrated granular systems [1,8,9,[22][23][24][25][26][27], but the exact numerical value of the exponent α seems to vary, depending on the specific system considered. Our data, obtained with two different experimental techniques, agree with this general picture.…”

Three-dimensional discrete element models for the granular statics and dynamics of powders in cavity filling

“…Beverloo et al, 1961;Nedderman et al, 1982;Verghese and Nedderman, 1995;Humby et al, 1998;Chen et al, 2006;Huang et al, 2006;Mankoc et al, 2007;Pacheco-Martinez et al, 2008) and numerically (e.g. Langston et al, 1994Langston et al, , 1995Langston et al, , 1996Ristow, 1997;Hirshfeld et al, 1997;Cleary and Sawley, 2002;Pacheco-Martinez et al, 2008) for a long time, only very little attention has been paid to the onset of outflow immediately after opening the orifice .…”

Slow relaxation dynamics of clogs in a vibrated granular silo

“…Vibration is one of the most widely used perturbations to prevent or to break clogs. Regardless of whether the applied vibration is vertical [17][18][19][20][21][22][23] or if only the base on which the arch rests is vibrated horizontally [20,24], its aim is to allow the granular medium to explore different configurations and eventually reach one which may lead to the collapse of the arch. In this framework, robust clogs will be those that, in order to unclog them, it would require either a higher intensity or a longer duration of vibration.…”