The simultaneous discharge of liquid and grains from a silo

Abstract

The flow rate of water through an orifice at the bottom of a container depends on the hydrostatic pressure whereas for a dry granular material is nearly constant. But what happens during the simultaneous discharge of grains and liquid from a silo? By measuring the flow rate as a function of time, we found that: (i) different regimes appear, going from constant flow rate dominated by the effective fluid viscosity to a hydrostatic-like discharge depending on the aperture and grain size, (ii) the mixed material is always discharged faster than dry grains but slower than liquid, (iii) for the mixture, the liquid level drops faster than the grains level but they are always linearly proportional to one another, and (iv) a sudden growth in the flow rate happens during the transition from a biphasic to a single phase discharge. These results are associated to the competition between the decrease of hydrostatic pressure above the granular bed and the hydrodynamic resistance. A model combining the Kozeny-Carman, Bernoulli and mass conservation equations is proposed and the numerical results are in good agreement with experiments.The clepsydra was an ancient device used to measure the passage of time based on the slow discharge of water through an orifice at the bottom of a graduated vessel. Its origin is unknown but presumably appeared in China about six thousands years ago [1]. The markings in this antiquity are non-uniformly separated since the flow rate depends on the hydrostatic pressure due to the water column above the orifice. On the other hand, the clepsammia, or sandglass, appeared millennia later probably in Alexandria [2] although evidence of its origin only dates from the middle ages [3]. In this device, the flow rate of grains through the bottleneck is independent of the granular column height because the stress acting on the material is redirected towards the container walls through contact force chains. This fact attracted scientists during the last 60 years, being the discharge of dry granular materials from hoppers widely investigated [4][5][6][7][8][9][10][11].The flow rate Q of dry grains through an orifice can be estimated using the Beverloo equation [4]:where D and d are the aperture and particle diameters, C and k are dimensionless fitting parameters related to friction and particle shape, ρ is the material density and g is the acceleration of gravity. The above equation must be modified by introducing an exponential factor when the ratio D/d is considerably increased [8]. More recently, experiments performed at different g's proved that the square root scaling proposed by Beverloo is relevant [10]. It has also been found that the initial packing fraction of the granular column does not affect considerably the flow rate [11][12][13] because the material under discharge is fluidized before reaching the silo aperture [11]. Even in unconventional systems of repelling particles, Q remains constant during the discharge [14,15]. In all the above studies, the interstitial medium is air and its presence was n...

Growth of clogs in parallel microchannels

“…The clogging of a microchannel follows three possible mechanisms depending on the size of the particles, their surface chemistry or charge and the concentration of the suspension [19]. For dense suspensions of particles without surface charges, bridging, i.e., the formation of an arch of particles is the main clogging mechanism [20][21][22][23][24][25][26][27]. This situation is similar to what is observed at a silo outlet with dry granular material [28].…”

Self-similar velocity profiles and mass transport of grains carried by fluid through a confined channel

“…Perhaps the most generic law describing such flow was proposed by Berverloo in 1961, concerning the gravity-driven flow of dry grains through an aperture, typical of that in a hopper or silo 6 . The empirical law is still the subject of new research [7][8][9][10] , notably with the "free-fall arch" concept being brought into question 11 and the reporting that the grain flow rate is not strictly constant with respect to filling height 12 . Entirely self-similar density and velocity profiles have also been found in the aperture of a silo and used to accurately obtain total grain flow rate 13 .…”

Subdiffusion model for granular discharge in a submerged silo

“…For the gravitational drainage of dry silos the mass flow rate of grains through an orifice is typically described by the empirical law proposed by Beverloo [1]. It chiefly depends upon the size of the outlet and the size and physical characteristics of the grains and is still the subject of new research [2][3][4][5][6][7]. Conversely in silos submerged in fluid the flow rate of grains has been seen to differ somewhat from Beverloo's law, exhibiting a considerable surge as the silo is emptied.…”