Jamming of particles in a two-dimensional fluid-driven flow

The jamming of particles under flow is of critical importance in a broad range of natural and industrial settings, such as the jamming of ice in rivers, or the plugging of suspended solids in pipeline transport. Relatively few studies have been carried out on jamming of suspended particles under flow, in comparison to the many studies on jamming in gravity-driven flows that have revealed various features of the jamming process. Fluid-driven particle flows differ in several aspects from gravity-driven flows, particularly in being compatible with a range of particle concentrations and velocities. Additionally, there are fluid-particle interactions and hydrodynamic effects. To investigate particle jamming in fluid-driven flows, we have performed both experiments and computer simulations on the flow of circular particles floating over water in an open channel with a restriction. We determined the flow-rate boundary for a dilute-to-dense flow transition, similar to that seen in gravity-driven flows. The maximum particle throughput increased for larger restriction sizes consistent with a Beverloo equation form over the entire range of particle mixtures and restriction sizes. The exponent of ∼3/2 in the Beverloo equation is consistent with approximately constant acceleration of grains due to fluid drag in the immediate region of the opening. We verified that the jamming probability from the dense flow gave a geometric distribution in the number of particles escaping before a jam. The probability of jamming in both experiments and simulations was found to be dependent on the ratio of channel opening to particle size, but only weakly dependent on the fluid flow velocity. Flow entrance effects were measured and observed to affect the jamming probability, and dependence on particle friction coefficient was determined from simulation. A comprehensive model for the jamming probability integrating these observations from the different flow regimes was shown to be in good agreement for experimental data on average times before jamming.

Figure 1

Diagram illustrating the three different states of particle flow. From left to right: Dilute flow, dense flow, and jammed state.

Figure 2

Schematic of flow channel flume for jamming studies of disks.

Figure 3

Left: Initial arrangement of particles in flow channel with the restriction closed. Right: Image of a stable jamming arch spanning the restriction. The accumulation distance, $L$, of particles is shown before being released (left) and after jamming (right).

Figure 4

Jamming probability for 400 $\frac{5}{8}$-in. particles in the flow channel as a function of restriction opening for several values of friction coefficient as simulated using pfc2d. The jamming probability from flow channel experiments at a fluid velocity of 0.21 m/s is included with a line to guide the eye, and was used to fit the friction coefficient.

Figure 5

Plot of the maximum particle output flow rate, ${\dot{N}}_{\mathrm{out},\max }$, versus $R$, the ratio of opening width to average particle diameter, for 400, 800, and 1200 $\frac{5}{8}$-in. particles and also for five different mixtures of $\frac{3}{8}$-in. and $\frac{5}{8}$-in. particles. The dashed line is the model based on the Beverloo equation. The flow rate is scaled by the nondimensionalized root average particle diameter, ${\overline{d_p}}^{1/2}$, to account for different particle areas in a constant area flow rate.

Figure 6

Jamming probability for 400 $\frac{5}{8}$-in. particles in the flow channel at a fluid velocity of 0.21 m/s as a function of the location of the restriction opening (1.875 in.). The location is indicated as the distance upstream from the channel bend.

Figure 7

(a) Jamming probability for 400 $\frac{5}{8}$-in. particles in the flow channel as a function of the restriction opening and flow velocities (experiments and simulations). Error bars are 95$\%$ confidence intervals assuming a binomial distribution [18]. (b) Comparison of the jamming probability in experiment with 0.21 m/s average flow velocity to simulations of particles moving under different accelerations of gravity without fluid. Lines are guides to the eye only.

Figure 8

Comparison of the jamming probability for 400 $\frac{5}{8}$-in. particles to 1111 $\frac{3}{8}$-in. particles plotted against the ratio, $R$, of restriction opening to particle diameter, for 400 $\frac{3}{8}$-in. particles in a (a) 4-in. and (b) geometrically similar 2.4-in. channel. Error bars are 95$\%$ confidence intervals assuming a binomial distribution [18]. Lines are guides to the eye only.

Figure 9

Comparison of the observed and the calculated jamming probability assuming jamming of different groups of particles are statistically independent for (a) $\frac{5}{8}$-in. particles and (b) $\frac{3}{8}$-in. particles.

Figure 10

Block flow diagram for the jamming model based on the comparison between the maximum throughput of a restriction and the number of particles passing through the same restriction. The primary parameter for this model is the ratio of the restriction size versus the particle diameter.

Figure 11

(a) Histogram of the jamming times for 2000 $\frac{5}{8}$-in. particles through the 1.875-in. restriction. (b) Plot of the experimental results and model predictions for the jamming time for 5555 $\frac{3}{8}$-in. and 2000 $\frac{5}{8}$-in. particles at various restriction sizes. Inset shows the jamming time plotted versus $R$, the ratio of restriction opening to particle diameter.