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The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis

Bysakh, S and Chattopadhyay, K and Ling, H and Wu, JD and Dong, C and Wang, YQ and Duan, XF and Kuo, KH (2004) The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis. In: Journal of Materials Research, 19 (3). pp. 759-767.

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The tendency of granular materials in rapid shear ow to form non-uniform structures is well documented in the literature. Through a linear stability analysis of the solution of continuum equations for rapid shear flow of a uniform granular material, performed by Savage (1992) and others subsequently, it has been shown that an infinite plane shearing motion may be unstable in the Lyapunov sense, provided the mean volume fraction of particles is above a critical value. This instability leads to the formation of alternating layers of high and low particle concentrations oriented parallel to the plane of shear. Computer simulations, on the other hand, reveal that non-uniform structures are possible even when the mean volume fraction of particles is small. In the present study, we have examined the structure of fully developed layered solutions, by making use of numerical continuation techniques and bifurcation theory. It is shown that the continuum equations do predict the existence of layered solutions of high amplitude even when the uniform state is linearly stable. An analysis of the effect of bounding walls on the bifurcation structure reveals that the nature of the wall boundary conditions plays a pivotal role in selecting that branch of non-uniform solutions which emerges as the primary branch. This demonstrates unequivocally that the results on the stability of bounded shear flow of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.

Item Type: Journal Article
Publication: Journal of Materials Research
Publisher: Cambridge University Press
Additional Information: Copyright of this article belongs to Cambridge University Press.
Keywords: Amorphous;Electron energy loss spectroscopy (EELS);Ablation
Department/Centre: Division of Mechanical Sciences > Materials Engineering (formerly Metallurgy)
Date Deposited: 17 Aug 2011 06:57
Last Modified: 17 Aug 2011 06:57
URI: http://eprints.iisc.ac.in/id/eprint/40012

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