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Nonlinear dynamics of a shear banding interface

Suzanne M. Fielding·Peter D. Olmsted
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Abstract

We study numerically the nonlinear dynamics of a shear banding interface in two dimensional planar shear flow, within the non-local Johnson Segalman model. Consistent with a recent linear stability analysis, we find that an initially flat interface is unstable with respect to small undulations for sufficiently small ratio of the interfacial width $\ell$ to cell length $L_x$. The instability saturates in finite amplitude interfacial fluctuations. For decreasing $\ell/L_x$ these undergo a non equilibrium transition from simple travelling interfacial waves with constant average wall stress, to periodically rippling waves with a periodic stress response. When multiple shear bands are present we find erratic interfacial dynamics and a stress response suggesting low dimensional chaos.

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Suzanne M. Fielding, Peter D. Olmsted. 2005-11-09. Nonlinear dynamics of a shear banding interface. https://doi.org/10.1103/physrevlett.96.104502

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