Stability of Freely Falling Granular Streams

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, (gamma)over dot(0). Expanding around this basic state, we show that the flow is stable for short times, (gamma)over dot(0)t << 1, whereas for long times, (gamma)over dot(0)t >> 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.