Decoupling Geometrical and Kinematic Contributions to the Silo Clogging Process

Based on the implementation of a novel silo discharge procedure, we are able to control the grains velocities regardless of the outlet size. This allows isolating the geometrical and kinematic contributions to the clogging process. We find that, for a given outlet size, reducing the grains velocities to extremely low values leads to a clogging probability increment of almost two orders of magnitude, hence revealing the importance of particle kinematics in the silo clogging process. Then, we explore the contribution of both variables, outlet size and grains velocity, and we find that our results agree with an already known exponential expression that relates clogging probability with outlet size. We propose a modification of such expression revealing that only two parameters are necessary to fit all the data: one is related with the geometry of the problem, and the other with the grains kinematics.

Figure 1

Experimental setup. The close up shows the orifice region with the conveyor belt placed below. The yellow arrow indicates the belt direction of movement. The origin of coordinates system is set at the center of the orifice.

Figure 2

Experimental data of the mean avalanche size as function of the belt velocity for the three outlet sizes indicated in the legend. In all cases we use spheres of diameter $d_p=4\mathrm{mm}$ and a gap between the belt and the silo of $h=3.2\pm 0.1\mathrm{mm}$. The horizontal lines correspond to the case where the silos are discharged only by gravity (without conveyor belt). Note the logarithmic scale in the $y$ axis.

Figure 3

(a) Mean flow rate $W$ and (b) mean vertical velocity $⟨{\mathbf{v}}_z⟩$ of the beads as function of the extraction belt velocity $v_{\mathrm{belt}}$ for the three orifice sizes indicated in the legend. The maximum $v_{\mathrm{belt}}$ investigated is given by the experimental limitations. The horizontal dashed lines indicate the values obtained for silos where the grains fall freely by gravity. (c) Probability density function (pdf) of ${\mathbf{v}}_z$ for an aperture size of $D=1.53\mathrm{cm}$ for the values of $v_{\mathrm{belt}}$ indicated in the legend and for the free fall discharge. Note the log-lin scale.

Figure 4

(a) Complementary cumulative distribution functions of the avalanche size for $D=1.53\mathrm{cm}$ and the values of the mean vertical velocity showed in the legend. (b) Experimental clogging probability as function of the absolute value of the mean vertical velocity for the three orifice sizes displayed in the legend. Empty squares represent the values obtained with a gap of $h=4.6\mathrm{mm}$, larger than the standard one ($h=3.2\mathrm{mm}$). (c) Clogging probability versus the outlet size for a very low extraction velocity ($v_{\mathrm{belt}}=0.1\mathrm{cm}/\mathrm{s}$) and for gravity discharged silos with particles of 1 and 4 mm diameter as indicated in the legend. In both (b) and (c) the solid and dashed lines correspond to Eq. (2) with the parameters indicated in the text. In (c) the expressions for the gravity discharged silos are obtained using the expected grains velocity $v=\sqrt{gD}$. Also, the solid circles in (c) correspond to Eq. (2), but use the actual experimental velocity.