Abstract
In this study, we performed experimental studies on the formation of stripe patterns in a granular mixture under horizontal vibration. The granular mixture was prepared by mixing brass and glass beads of 1 mm in diameter in the ratio of 1:2 by volume and immersing them in a liquid. The mixture becomes separated into glass-only and brass-only bands of random sizes. The number of bands is an increasing function of \(\Gamma \times \sqrt {\operatorname{Re} } \) only (Γ: acceleration relative to gravity; Re: Reynolds number based on the particle diameter). As the mechanism of stripe formation, the formation of clusters in the mixture due to local fluctuations and strong hydrodynamic interactions between particles is proposed. The initial-condition dependency also supports the cluster formation mechanism rather than the Kelvin-Helmholtz-like hydrodynamic instability.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. M. Neddermann, Statics and kinematics of granular materials (Cambridge University Press, Cambridge, 1992).
J. T. Jenkins and D. K. Yoon, Phys. Rev. Lett. 88, 194301 (2002).
P. M. Reis, T. Sykes and T. Mullin, Phys. Rev. E 74, 051306 (2006).
A. Rosato, K. J. Strandburg, F. Prinz and R. H. Swendsen, Phys. Rev. Lett. 58, 1038 (1987).
N. Burtally, P. J. King, M. R. Swift and M. Leaper, Granular Matter 5, 57 (2003).
M. E. Möbius, B. E. Lauderdale, S. R. Nagel and H. M. Jaeger, Nature 414, 270 (2001).
N. Burtally, P. J. King and M. R. Swift, Science 295, 1877 (2002).
P. Biswas, P. Sanchez, M. R. Swift and P. J. King, Phys. Rev. E 68, 050301 (2003)
M. C. Leaper, A. J. Smith, M. r. Swift, P. J. King, H. E. Webster, N. J. Miles and S. W. Kingman, Granular Matter 7, 57 (2005).
C. Zeilstra, M. A. van der Hoef and J. A. M. Kuipers, Phys. Rev. E 77, 031309 (2008).
P. Sanchez, M. R. Swift and P. J. King, Phys. Rev. Lett. 93, 184302 (2004).
S. Chandrasekhar, Hydrodynamic and hydromagnetic stability (Oxford University Press, Oxford, 1961, Reprinted by Dover Pub., New York, 1981).
P. Drazin and W. H. Reid, Hydrodynamic Stability, 2nd ed. (Cambridge University Press, Cambridge, 2004).
S. Kim and S. Karrila, Microhydrodynamics (Butterworth-Heinemann, Boston, 1991).
D. J. Goldfarb, B. J. Glasser and T. Shinbrot, Nature 415, 302 (2002).
M. P. Ciamarra, A. Conoglio and M. Nicodemi, Phys. Rev. Lett. 94, 188001 (2005).
A. A. Zick and G. M. Homsy, J. Fluid Mech. 115, 13 (1982).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jung, J., Kim, C. Scaling law and mechanism for the formation of stripe patterns in a binary mixture of granular materials under horizontal vibration. Journal of the Korean Physical Society 63, 1937–1943 (2013). https://doi.org/10.3938/jkps.63.1937
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3938/jkps.63.1937