Abstract
We computationally determine the force on single spherical intruder particles in sheared granular flows as a function of particle size, particle density, shear rate, overburden pressure, and gravitational acceleration. The force scales similarly to, but deviates from, the buoyancy force predicted by Archimedes' principle. The deviation depends only on the intruder to bed particle size ratio, but not the density ratio or flow conditions. We propose a simple force model that successfully predicts whether intruders rise or sink, knowing only the size and density ratios, for a variety of flow configurations in physical experiments.
Highlights
Intruder particles in fluidized or flowing granular beds tend to segregate due to their size or density difference with the bed particles [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
Since we focus on the flow far from rigid boundaries, this geometry can be viewed as a representative volume where the segregation force may be associated with a controlled, locally uniform shear rate and vertical normal stress
The scaling law we propose for the segregation force has a simple, buoyancy-like form, which is not unfamiliar given that Archimedes’ principle with corrections has been applied to creeping granular fluids [35], vibrofluidized granular gases [7,8], and yielding granular solids [32]
Summary
The buoyancy force on an intruder follows Archimedes’ principle [8], explaining the phase transition between normal and reverse Brazil nut effects [5] In contrast to this clear picture, the force driving segregation in dense granular flows remains elusive. We solve the puzzle by providing a general scaling law that allows shear-induced segregation to be viewed as a result of the imbalance between the gravitational force and a size-corrected buoyancy force. This is achieved by exploring a wide range of size and density ratios under controlled pressure and shear rate in a constant-shear-rate system. The scaling law is confirmed in chute flow simulations where shear rate gradients are small and validated by previous canonical surface flow experiments [9]
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