Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2004-11-23
Physics
Condensed Matter
Soft Condensed Matter
11 pages and 6 figures; Proceedings of the Symposium on Trends in Applications of Mathematics to Mechanics, 22-28 August, 2004
Scientific paper
A numerical bifurcation analysis is carried out to understand the role of gravity on the shear-band formation in rapid granular Couette flow. At {\it low} shear rates, there is a unique solution with a {\it plug} near the bottom wall and a {\it shear-layer} near the top-wall; this solution mirrors typical shearbanding-type profiles in earth-bound shear-cell experiments. Interestingly, a {\it stable} plug near the top-wall is also a solution of these equations at {\it high} shear rates; there is a multitude of other plugged states, with the plugs being located in an ordered fashion within the Couette gap. The origin of such shearbanding solutions is tied to the spontaneous symmetry-breaking {\it shearbanding} instabilities of the gravity-free uniform shear flow, leading to both subcritical and supercritical pitchfork bifurcations. In the language of singularity theory, we have established that this bifurcation problem admits {\it universal unfolding} of pitchfork bifurcations.
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