Abstract
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 = ua/(utφ¯) and f/fn, where ua and f are the amplitude and frequency of the gas velocity, respectively, ut is the terminal velocity of the particles, φ¯ is the average solids fraction, and fn 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.
Highlights
Granular flows are well known for exhibiting rich and complex mesoscale dynamics due to the self-organization of the composing grains
We show that the threshold for pattern formation in shallow pulsed beds is universal for Geldart B particles [22] and determined by the hydrodynamical parameters = ua/(utφ) and f/fn, where ua and f are the amplitude and frequency of the gas velocity, respectively, ut is the terminal velocity of the particles, φis the average solids fraction, and fn is the natural frequency of the bed
The mechanism behind the instability leading to pattern formation in pulsed gas-fluidized and vertically vibrated granular layers is completely different as a result of the forces induced by the percolating gas phase
Summary
Granular flows are well known for exhibiting rich and complex mesoscale dynamics due to the self-organization of the composing grains. A phenomenon that has attracted great attention during the last two decades is the formation of standing wave patterns on the surface of vertically vibrated thin granular layers [2,3,4] These patterns can be obtained in vacuo to avoid heaping and typically manifest themselves as stripes, squares, or hexagons, strongly resembling the structures formed in vertically vibrated fluids, known as Faraday waves. Perhaps due to this analogy, vibrated granular patterns are often examined using the same control parameters as in the study of Faraday waves, i.e., the frequency f and dimensionless acceleration = 4π 2f 2D/g of the vibrating plate, where D is its displacement and g is the gravitational acceleration. These driving parameters represent a balance between the energy injected and energy dissipated in the layer [5], and they can be derived from the Navier-Stokes equations governing the liquid flow
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