Universal stability curve for pattern formation in pulsed gas-solid fluidized beds of sandlike particles

A granular layer can form regular patterns, such as squares, stripes, and hexagons, when it is fluidized with a pulsating gas flow. These structures are reminiscent of the well-known patterns found in granular layers excited through vibration, but, contrarily to them, they have been hardly explored since they were first discovered. In this work, we investigate experimentally the conditions leading to pattern formation in pulsed fluidized beds and the dimensionless numbers governing the phenomenon. We show that the onset to the instability is universal for Geldart B (sandlike) particles and governed by the hydrodynamical parameters Gamma = u(a)/(u(t)(phi) over bar) and f/f(n), where u(a) and f are the amplitude and frequency of the gas velocity, respectively, ut is the terminal velocity of the particles, (phi) over bar is the average solids fraction, and f(n) is the natural frequency of the bed. These findings suggest that patterns emerge as a result of a parametric resonance between the kinematic waves originating from the oscillating gas flow and the bulk dynamics. Particle friction plays virtually no role in the onset to pattern formation, but it is fundamental for pattern selection and stabilization.