Transition from clogging to continuous flow in constricted particle suspensions

When suspended particles are pushed by liquid flow through a constricted channel, they might either pass the bottleneck without trouble or encounter a permanent clog that will stop them forever. However, they may also flow intermittently with great sensitivity to the neck-to-particle size ratio $D/d$. In this Rapid Communication, we experimentally explore the limits of the intermittent regime for a dense suspension through a single bottleneck as a function of this parameter. To this end, we make use of high time- and space-resolution experiments to obtain the distributions of arrest times ($T$) between successive bursts, which display power-law tails ($\propto T^{-\alpha }$) with characteristic exponents. These exponents compare well with the ones found for as disparate situations as the evacuation of pedestrians from a room, the entry of a flock of sheep into a shed, or the discharge of particles from a silo. Nevertheless, the intrinsic properties of our system (i.e., channel geometry, driving and interaction forces, particle size distribution) seem to introduce a sharp transition from a clogged state ($\alpha \le 2$) to a continuous flow, where clogs do not develop at all. This contrasts with the results obtained in other systems where intermittent flow, with power-law exponents above two, were obtained.

Figure 1

Successive snapshots of a burst in a suspension of particles with a diameter $d$ that intermittently flow through a constriction—having a neck width $1.1D$ and height $D$—by a volume-driven flow ($D/d=3.03$). From top to bottom: Clog previous to the burst, burst, and clog after the burst.

Figure 2

Spatiotemporal diagrams at the constriction neck for various $D/d$. For $D/d\le 2.43$ only a few particles (which appear in the dark) escape before a permanent clog is formed. When increasing $D/d$, intermittent particle flow is observed, eventually reaching particle continuous flow for $D/d\ge 5.26$.

Figure 3

(a) Distribution of the normalized number of escaped particles $s/\langle s\rangle$ and burst duration $T_b/\langle T_b\rangle$ for $D/d=3.03$, for which $\langle s\rangle =270$ and $\langle T_b\rangle =55\tau$. The dashed line corresponds to the expected trend $\propto e^{-s/\langle s\rangle }$. Inset: Survival function $P(S>s/\langle s\rangle )$ limited to the range $s/\langle s\rangle <0.2$. The steeper slope indicates a high probability of having small particle bursts. (b) Typical particle burst showing the particle tracking employed for counting individual particles. The colors code for particles escaping during the same burst.

Figure 4

Distribution of the arrest time lapses normalized by the Stokes time $T/\tau$. The lines correspond to the best power-law fits with their exponent $\alpha$, as given by the Clauset-Shalizi-Newman method [34]. Inset: $\alpha$ as a function of the neck-to-particle size ratio $D/d$. The exponent can only be defined when the flow is intermittent and the values obtained (always below 2) reveal that the system is in the clogged regime when $D/d<5.26$. See values of $\alpha$ in Table 1.