Meandering instability of air flow in a granular bed

Meandering instability of air flow in a granular bed

10 Pages · 2016 · 1.09 MB · English

fluid-solid duality. Yuki Yoshimura, Yui Yagisawa & Ko Okumura. Meandering instability is familiar to everyone through river meandering or small rivulets of a linear-instability analysis of a continuum equation that takes into account the fluid-solid duality, i.e., .. to gasoline and biomass gasif

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1 Meandering instability of air flow in a granular bed: selfsimilarity and fluidsolid duality Yuki Yoshimura , Yui Yagisaw a & Ko Okumura Meandering instability is familiar to everyone through river meandering or small rivulets of rain flowing down a windshield However, its physical understanding is still premature, although it could inspire researchers in various fields, such as nonlinear science, fluid mechanics and geophysics, to resolve their longstanding problems Here, we perform a smallscale experiment in which air flow is created in a thin granular bed to successfully find a meandering regime, together with other remarkable fluidized regimes, such as a turbulent regime We discover that phase diagrams of the flow regimes for different types of grains can be universally presented as functions of the flow rate and the granularbed thickness when the two quantities are properly renormalized We further reveal that the meandering shapes are selfsimilar as was shown for meandering rivers The experimental findings are explained by theory, with elucidating the physics The theory is based on force balance, a minimumdissipation principle, and a linearinstability analysis of a continuum equation that takes into account the fluidsolid duality, ie, the existence of fluidized and solidified regions of grains along the meandering path The present results provide fruitful links to related issues in various fields, including fluidized bed reactors in industry Fluid flows in a medium often display spectacular instabilities; there are various examples of this in cosmological 1, geophysical 2, biological 3, and physical systems 4 Among such phenomena, meandering instability is familiar to everyone in the form of small rivulets of rain flowing down a windshield or, in a more largescale form, in river meandering In particular, for a meandering fluid interacting with a solid surface, the physics has been relatively well understood The meandering of a liquid jet flowing down an inclined plate and some variations of this have actively been studied 5–7 (for largerscale experiments, see ref 8 and references therein) For such a meandering, the physical mechanism has been elucidated in terms of force balance, linear stability 9–11 and flowrate fluctuation 12 On the contrary, for a meandering fluid interacting with a surrounding “complex fluid,” the mechanism of the instability has yet to be clarified This latter case includes the meandering of rivers, which is ubiquitous and is even found on Mars 13, and has been studied in geography 8,14, biology 15–17 , hydrodynamics 18–20 , and physics, from various viewpoints such as pattern formation 20,21 , random walks 22,23 , and statistical models 24,25 For example, more than a halfcentury ago, shapes of meandering rivers were shown to be scale invariant or selfsimilar, ie, the cur vature, amplitude, and wavelength of the shape all scale with the width, using the data obtained by field studies 26, which has yet to be understood More recently, a systematic dependence of the sinuosity of meandering rivers on the Froude number has been shown, which is interpreted through results obtained by a simple numerical model 27 Here, we perform a smallscale experiment in which an air flow is created in a granular bed as follows: the flow of a lighter fluid is surrounded by a heavier “complex fluid,” which is similar to river meandering As a result, we find that the flow can be destabilized to show meandering shapes The meandering regime can be universally demonstrated as a function of the normalized flow rate and normalized granularbed thickness In addition, the meandering flow shape is found to be scale invariant or selfsimilar, as was shown for river meandering These experimental findings can be explained by the proposed physical principles ResultsExperiment Setup The main setup consists of a transparent acrylic cell and a gasflow controller (see Fig 1(a)) The inside thickness D, width

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