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On the origin of the vorticity-banding instability 5 cm 2 cm constant shear rate throughout the system multi-valued flow curve isotropic and nematic branch different concentrations shear-induced viscous phase not clear what the origin of the banding instability is

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low high rolling flow within the bands normal stresses along the gradient direction normal streses generated within the interface of a gradient-banded flow ( S. Fielding, Phys. Rev. E 2007 ; 76 ; 016311 )

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Binodal 0.00.20.40.60.81.0 0 1 2 [s ]. nem Vorticity banding Spinodals Tumbling wagging Critical point concentration 1 fd virus : L = 880 nm D = 6.7 nm P = 2200 nm ( P. Lettinga ) 0 1

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almost crossed polarizers distinguish orientational order vorticity direction P A

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12 3 4 5 6 7 8 1 2 3 4 5 6 7 8 stretching of inhomogeneities growth of bands Shear flow vorticity direction Gapwidth 2.0 mm ~ 1 mm A

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band width growth rate 23 % : 35 % : heterogeneous vorticity banding interconnected disconnected

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spinodal decomposition : nucleation and growth : ( with Didi Derks, Arnout Imhof and Alfons van Blaaderen )

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tracking of a seed particle ( counter-rotating couette cell ) with Bernard Pouligny (Bordeaux)

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increasing shear rate elastic instability for polymers : non-uniform deformation equidistant velocity lines Weissenberg or rod-climbing effect K. Kang, P. Lettinga, Z. Dogic, J.K.G. Dhont Phys. Rev. E 74, 2006, 026307-1 – 026307-12

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New viscous phases can be induced by the flow (under controlled shear-rate conditions ) stress shear rate new phase homogeneous inhomogeneous personal communication with John Melrose

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Stability analysis : discreteness of inhomogeneities along the flow direction is of minor importance : mass density gradient component of the body force z-dependence with the typical distance between inhomogeneities Brownian contributions +rod-rod interactions +flow-structure coupling linear bi-linear linear probability density for the position and orientation of a rod x y z J.K.G. Dhont and W.J. Briels J. Chem Phys. 117, 2002, 3992-3999 J. Chem Phys. 118, 2003, 1466-1478 z y

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small large renormalized base flow probability linear contributions bi-linear contributions rod-rod interactions

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unstable stable depends on the microstructural properties of the inhomogeneities 0.0 0.20.40.6 concentration

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Wilkins GMH, Olmsted PD, Vorticity banding during the lamellar-to-onion transition in a lyotropic surfactant solution in shear flow, Eur. Phys. J. E 2006 ; 21 ; 133-143. Fischer P, Wheeler EK, Fuller GG, Shear-banding structure oriented in the vorticity direction observed for equimolar micellar solution, Rheol. Acta 2002 ; 41 ; 35-44. Lin-Gibson S, Pathak JA, Grulke EA, Wang H, Hobbie EK, elastic flow instability in nanotube suspensions, Phys. Rev. Lett. 2004 ; 92, 048302-1 - 048302-4. Vermant J, Raynaud L, Mewis J, Ernst B, Fuller GG, Large-scale bundle ordering in sterically stabilized latices, J. Coll. Int. Sci. 1999 ; 211 ; 221-229. Bonn D, Meunier J, Greffier O, Al-Kahwaji A, Kellay H, Bistability in non-Newtonian flow : rheology and lyotropic liquid crystals, Phys. Rev. E 1998 ; 58 ; 2115-2118. Micellar worms Nanotube bundles Colloidal aggregates -Worms - Entanglements - Shear-induced phase

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Kyongok Kang Pavlik Lettinga Wim Briels

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