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A minimal model for chaotic shear banding in shear-thickening fluids

A minimal model for chaotic shear banding in shear-thickening fluids. Ashod Aradian & Mike Cates The University of Edinburgh & Centre de Recherche Paul Pascal @ CNRS (Bordeaux). . New long-term behaviours in complex fluids. Couette.

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A minimal model for chaotic shear banding in shear-thickening fluids

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  1. A minimal model for chaotic shear banding in shear-thickening fluids Ashod Aradian & Mike Cates The University of Edinburgh & Centre de Recherche Paul Pascal @ CNRS (Bordeaux)

  2. New long-term behaviours in complex fluids Couette  Long-term behaviour under steady shear may NOT be steady-state  Fluid may reach a more complex dynamical state (oscillations, rheochaos,…)  New class of instabilities of structural origin (Reynolds number Re = 0)

  3. ordered disordered Oscillations • Polymer solutions • Surfactants PS in DOP CPyCl/NaSal Multilamellar vesicles (onions) Shear rate (s-1) (s-1) time (s) time (s) (Hilliou & Vlassopoulos, 2002) (Herle et al., 2005) (Wunenburger et al., 2001) • Dense colloids(Laun, 1994) ) Oscillations are •SLOW • STRUCTURAL • associated to SHEAR BANDS

  4. Erratic responses: rheochaos • Wormlike micelles (Bandyopadhyay et al., 2000) • Onions (Salmon et al., 2002) • Colloids (Lootens et al., 2003)

  5. A minimal model for shear-thickening fluids • Two central physical ingredients: I. Tendency to form (vorticity) shear bands II. Slow build-up / breakdown of some shear-induced structure (SIS) ) “structural” variable with slow dynamics ) typical lifetime :with

  6. stable unstable stable Model equations 1.Rheological eq. shear rate relaxation inhomogeneous flows (shear bands) 2.Structural eq. • Flow curves • Long-term curve (steady state) : • Short-term curves : with fixed ) INSTABILITY!

  7. O T C C stable stable Imposed torque Non-equilibrium phase diagram Oscillating Travelling Chaotic

  8. time space `Flip-flopping’ bands

  9. Zig-zagging interface time space

  10. time space Complex periodic

  11. time space Travelling bands

  12. Rheochaos time space

  13. More rheochaos… time space

  14. Chaos in the low-dimensional reduction of the model • Fourier: • 2 stress modes • 2 memory modes • Chaos persists • Phase diagram is robust • Dynamical attractor Route to chaos = Period doubling stable stable

  15. OPEN ISSUES • Wall slip dynamics? (Manneville et al) • Micro-banding? (Callaghan et al) • Mechanism: Unsteady bands via bulk instability vs ‘steady’ bands driven by interfacial instability • Routes to chaos: Does period doubling / intermittency scenario /... tell us much about mechanism / constitutive properties? NB: superb data on intermittency now available e.g. Sood group (Bangalore) • Theorists dilemma: Resolved spatiotemporal studies of coarse-grained (dJS-level) models vs ‘realistic’ (reptation-reaction, MCT, etc) constitutive equations with unresolved modes

  16. type II intermittency R. Ganapathy and A.J. Sood, Phys Rev Lett 2006

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