Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2005-10-13
Published in Phys. Rev. E vol. 73, article 041508 (2006)
Physics
Condensed Matter
Soft Condensed Matter
Revised version (in particular, new section III.E. and Appendix A)
Scientific paper
10.1103/PhysRevE.73.041508
We present a minimal model for spatiotemporal oscillation and rheochaos in shear-thickening complex fluids at zero Reynolds number. In the model, a tendency towards inhomogeneous flows in the form of shear bands combines with a slow structural dynamics, modelled by delayed stress relaxation. Using Fourier-space numerics, we study the nonequilibrium `phase diagram' of the fluid as a function of a steady mean (spatially averaged) stress, and of the relaxation time for structural relaxation. We find several distinct regions of periodic behavior (oscillating bands, travelling bands, and more complex oscillations) and also regions of spatiotemporal rheochaos. A low-dimensional truncation of the model retains the important physical features of the full model (including rheochaos) despite the suppression of sharply defined interfaces between shear bands. Our model maps onto the FitzHugh-Nagumo model for neural network dynamics, with an unusual form of long-range coupling.
Aradian Achod
Cates Michael E.
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