Particle jamming during the discharge of fluid-driven granular flow

Abstract

When a stream of granular material attempts to flow through a small opening, the particles may spontaneously form a strong arch-like arrangement of particles capable of supporting the weight of the overhead particles. This arching of particles, referred to as a "jam" stops all particle flow and must be removed if flow is to resume. This work presents observations of particle "jamming" where fluid is the driving medium for the granular flow. I use two experimental systems - an open-channel flume, and a bench-scale flowloop - and a series of computer simulations jamming to study this random event. In the experimental systems I focus on three pieces of jamming: 1) jamming with a dilute stream of particles, 2) the transition of a dilute to dense flow of particles (i.e., when particle accumulation or "backlogging" occurs), and 3) jamming with a dense flow of backlogged particles. In backlogged particles I see the instantaneous per-particle jamming probability, 1 - p, scales as ln(1- p) [proportional to] R[superscript 2] - 1, where R is the ratio of the opening diameter, d[subscript o], to the particle diameter, d[subscript p]. I also observe that 1 - p is only constant after the particle backlog is sufficiently deep, and relate this depth to the number of particles that have discharged. Knowing how a system acts after backlog information, I focus on when particle backlogs form by modeling particle discharge rates, [N with a dot above it]. I model discharge rates with free-fall arch theory and experimentally observe [N with a dot above it] [approximately equal to] 3[Phi][subscript C][beta][superscript 2]v[subscript f](R -1)[superscript 2]/2d[subscript p], where [Phi][subscript C] [approximately equal to] 0.585 is the outlet concentration, [beta] is the ratio of the pipe diameter, d[subscript pipe] to opening diameter, and v[subscript f] is the fluid velocity. The main finding is that particles appear to match the fluid velocity at the orifice exit. The final experimental findings were measurements of the instantaneous per-second jamming rate, r(t). I generalize the time-to-jam distribution in terms of a dynamic jamming rate, and find the characteristic time, t[subscript c] = d[subscript p]/v[subscript f] eliminates fluid velocity effects. This corresponds to a dimensionless jamming rate [sigma](T) = r(t)t[subscript c]. I also measure [sigma] as a function of the particle volume fraction, [Phi], in pre-backlogged systems. Lastly, I look at the origin of jammed configurations through the use of DEM simulations. I hypothesize that an infinitely long (periodic) slit will have per-particle jamming probability, 1 - p, that scales with ln(1 - p) [proportional to] L where L is the length of the explicitly simulated system. I extend this theory to simple openings (circles, squares, and triangles) and develop a "universal" approximation for small openings where I observe ln(1 - p) [proportional to] A[subscript o](1 - R[subscript L][superscript -2])/d[subscript p][superscript 2], where A[subscript o] is the total area of the opening, and R[subscript L] is the characteristic length of the opening, L[subscript c], divided by the particle diameter, where L[subscript c] [right arrow] d[subscript p] when the restriction shape circumscribes exactly 1 particle. I show this fit gives good approximation to 16 openings of different sizes, and geometries.