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

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 ; )

Binodal [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

almost crossed polarizers distinguish orientational order vorticity direction P A

stretching of inhomogeneities growth of bands Shear flow vorticity direction Gapwidth 2.0 mm ~ 1 mm A

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

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

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

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, –

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

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, J. Chem Phys. 118, 2003, z y

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

unstable stable depends on the microstructural properties of the inhomogeneities concentration

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 ; Fischer P, Wheeler EK, Fuller GG, Shear-banding structure oriented in the vorticity direction observed for equimolar micellar solution, Rheol. Acta 2002 ; 41 ; Lin-Gibson S, Pathak JA, Grulke EA, Wang H, Hobbie EK, elastic flow instability in nanotube suspensions, Phys. Rev. Lett ; 92, Vermant J, Raynaud L, Mewis J, Ernst B, Fuller GG, Large-scale bundle ordering in sterically stabilized latices, J. Coll. Int. Sci ; 211 ; 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 ; Micellar worms Nanotube bundles Colloidal aggregates -Worms - Entanglements - Shear-induced phase

Kyongok Kang Pavlik Lettinga Wim Briels