We experimentally demonstrate that the flow rate of granular material through an aperture is controlled by the exit velocity imposed on the particles and not by the pressure at the base, contrary to what is often assumed in previous work. This result is achieved by studying the discharge process of a dense packing of monosized disks through an orifice. The flow is driven by a conveyor belt. This two-dimensional horizontal setup allows us to independently control the velocity at which the disks escape the horizontal silo and the pressure in the vicinity of the aperture. The flow rate is found to be proportional to the belt velocity, independent of the amount of disks in the container and, thus, independent of the pressure in the outlet region. In addition, this specific configuration makes it possible to get information on the system dynamics from a single image of the disks that rest on the conveyor belt after the discharge.
Sketch of the experimental setup. Disks, placed on a conveyor belt, which moves at a constant velocity V (white arrow), are forced to flow through an aperture in the confining frame. Observation of the grains—either remaining in the confining frame or forming the jet outside—makes it possible to study the dynamical properties of the discharge.
In addition, we measured the force exerted by the granular matter at the case in both 2D and 3D configurations.
Pressure Independence of Granular Flow
through an Aperture
Granular flow through an aperture : Pressure and flow rate are
Evolution of pressure profiles during the discharge of a silo.
The literature canonically presents granular materials as a bunch of athermal particles. Indeed, the energy necessary for the grains to hop one over another (a few tenths of a millimeter, for instance) is roughly 10 orders of magnitude higher than the ambient thermal agitation kBT. This is probably one of the reasons why the behavior of a granular assembly submitted to temperature fluctuations has received so little attention. Nonetheless, uncontrolled thermal dilations of a granular pile have been reported to generate stress fluctuations large enough to hinder reproducible measurements of the stress field inside the pile, and are even suspected of being the driving factor leading to large-scale ‘‘static avalanches’’. Indeed, the slow relaxation and compaction of a granular material, which has been hitherto produced by the input of mechanical energy, can be induced by periodically raising and then lowering the temperature of the granular assembly, as recently brought to the fore by Chen and co-workers. However, the compaction dynamics as well as the basic mechanisms at stake remain unknown. We address the following questions: What is the dynamic of the top of a granular column submitted to thermal cycling? Does this compaction process exhibit features analogous to aging, as other compaction processes (e.g., tapping, cyclic shear. . .) do? And finally, what is the behavior of the grain assembly in the limit of low amplitude temperaturecycles, i.e., well below a cycling amplitude of 40 °C.
First, we report a time-resolved study of the dynamics associated with the slow compaction of a granular column submitted to thermal cycles. The column height displays a complex behavior: for a large amplitude of the temperature cycles, the granular column settles continuously, experiencing a small settling at each cycle. By contrast, for a small-enough amplitude, the column exhibits a discontinuous and intermittent activity: successive collapses are separated by quiescent periods whose duration is exponentially distributed. We then discuss potential mechanisms which would account for both the compaction and the transition at finite amplitude [Divoux, 2008 & 2009, Blanc, 2013].
Left: Sketch of the experimental setup. Inset: picture of the upper part of the column. The granular level is indicated by the white dotted line. Right top: Height variation h vs number of cycles n. One observes first an exponential behavior at short time followed by a subsequent logarithmic creep at long time. Inset: Oscillations of the column height associated with the temperature cycles. For the chosen DT, the column settles slightly at each cycle (H = 140 cm, 1/f = 600 s, and DT = 10,8 °C). Right bottom: Characteristic number nc vs amplitude DT. The characteristic number of cycles nc increases drastically when DT is decreased and even seems to diverge for DT= 3 °C. Inset: For DT <DTc, the column settles, by jumps, linearly with time. For readability, we only display data obtained during the first half of the experiment duration (14 days, H = 140 cm, 1/f = 600 s, and DT = 2,8 °C).
Second, we evaluate in a simple model
the ability for the temperature changes to lead to aging of the
frictional contact between solids. The dry frictional contact between
two solid surfaces is well known to obey Coulomb friction laws. In
particular, the static friction force resisting the relative lateral
tangential motion of solid surfaces, initially at rest, is known to be
proportional to the normal force and independent of the area of the
macroscopic surfaces in contact. Experimentally, the static friction
force has been observed to slightly depend on time. Such an aging
phenomenon has been accounted for either by the creep of the material
or by the condensation of water bridges at the microscopic contact
points. By studying a toy model, we show that the small uncontrolled
temperature changes of the system can also lead to a significant
increase of the static friction force [Géminard, 2010]. We then
considered the reptation of a model frictional system, a achain of
sliders [Blanc, 2011].
Sketch of the situation - At rest, the contact between 2 sliders and the substrate is characterized by the static frictional coefficient. Due to the roughness of the surfaces in regard, the local static frictional coefficient might take, at random, different values for the two contact regions. By contrast, when the sliders in motion explore the surface of the substrate which is homogeneous in average, the contact is characterized by a single value of the dynamical frictional coefficient. The dynamics of the system is induced by temperature changes which, due the thermal dilation of the materials, lead to changes in the natural length of the spring.
Creep motion of a granular pile induced by thermal cycling,
Aging of a granular pile induced by thermal
Aging of the frictional properties induced by
Creep motion of a model frictional system
Intrinsic creep of a granular column subjected to temperature changes.
The friction of a sliding plate on a thin
immersed granular layer obeys Amonton-Coulomb law (You are encouraged to see my
former contributions here). We bring
to the fore a large set of experimental results which indicate that, over a few
decades of values, the effective dynamical friction coefficient depends neither
on the viscosity of the interstitial fluid nor on the size of beads in the
sheared layer, which bears out the analogy with the solid-solid friction in a
wide range of experimental parameters. We accurately determine the granular-layer
dilatancy, which dependence on the grain size and slider velocity can be
qualitatively accounted by considering the rheological behavior of the whole
slurry. However, additional results, obtained after modification of the grain
surface by a chemical treatment, demonstrate that the theoretical description of
the flow properties of dense granular matter, even immersed, requires the
detailed properties of the grain surface to be taken into account [Divoux,
2007]. We are now conisdering the effects of external vibrations (2014).
Left: experimental setup - A thin plate, the slider, is pushed at the free surface of an immersed granular layer by means of a steel leaf spring connected to a translation stage driven at constant velocity,Vs, by a computer-controlled stepping motor. Right: Total dilation of the layer vs slider velocity Vs for various grain size and fluid viscosity (see publication for détails).
Friction and dilatancy in
immersed granular matter,
Last update : 2012-06-26.