Meandering instability of air flow in a granular bed: self-similarity and fluid-solid duality.

Yuki Yoshimura,Yui Yagisawa,Ko Okumura

doi:10.1038/srep38457

Yuki Yoshimura, Yui Yagisawa + Show 1 more

Open Access

https://doi.org/10.1038/srep38457

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Journal: Scientific Reports	Publication Date: Dec 1, 2016
Citations: 8	License type: CC BY 4.0

Affiliation: Ochanomizu University

Abstract

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 long-standing problems. Here, we perform a small-scale 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 granular-bed thickness when the two quantities are properly renormalized. We further reveal that the meandering shapes are self-similar 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 minimum-dissipation principle, and a linear-instability analysis of a continuum equation that takes into account the fluid-solid duality, i.e., 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.

Highlights

Meandering instability is familiar to everyone through river meandering or small rivulets of rain flowing down a windshield
We perform a small-scale 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
We show that an air flow in a thin granular bed can be destabilized to show meandering shape

Summary

Results

There exists a minimum wavelength in the present theory; the condition λ > w should be satisfied, that is, the wavelength of the fastest-growing mode is practically given by λ w This is because the present theory is valid only when the width of the path is smaller than any other length scales characterizing the shape of the path; the flow is here treated as a (curved) “line”. This implies that the value of K1 is almost the same for the glass and alumina beads despite the large difference in the particle-level stiffness This may be because the interaction between the air flow and “granular solid” is weak in the sense that it is not related to the deformation associated with the Hertz contact[32] but rather to the gravity acting on granular materials (note that the term is proportional to ρGg)

Discussion

Conclusion

Methods