Stability of Freely Falling Granular Streams

Ulrich, Stephan; Zippelius, Annette

doi:10.1103/PhysRevLett.109.166001

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Stability of Freely Falling Granular Streams

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Zippelius, Annette
Fellow Group Polymers, complex fluids and disordered systems, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Ulrich, S., & Zippelius, A. (2012). Stability of Freely Falling Granular Streams. Physical Review Letters, 109: 166001, pp. 166001-166006. doi:10.1103/PhysRevLett.109.166001.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-106B-E

Abstract

A freely falling stream of weakly cohesive granular particles is modeled and analyzed with the help of event driven simulations and continuum hydrodynamics. The former show a breakup of the stream into droplets, whose size is measured as a function of cohesive energy. Extensional flow is an exact solution of the one-dimensional Navier-Stokes equation, corresponding to a strain rate, decaying like t-1 from its initial value, γ˙0. Expanding around this basic state, we show that the flow is stable for short times, γ˙0t≪1, whereas for long times, γ˙0t≫1, perturbations of all wavelengths grow. The growth rate of a given wavelength depends on the instant of time when the fluctuation occurs, so that the observable patterns can vary considerably