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The theoretical description of the threshold and near-threshold behavior of electrohydrodynamic convection in nematic liquid crystals in the (low-frequency) conduction regime is reconsidered. We present essentially the full three-dimensional linear stability analysis of the basic state and a major part of the weakly-nonlinear theory of the convective state. Boundary conditions at the upper and lower plates as well as the time dependence are treated rigorously but the flexoelectric effect is neglected. Related transitions like the periodic splay-twist instability, which is relevant in polymer materials with positive dielectric anisotropy, are also considered. We give criteria for finding the oblique-roll state and for the competition between different instabilities. Comparison with experiments is made wherever possible. Good qualitative and sometimes quantitative agreement is found

The migration of a suspended vesicle in an unbounded Poiseuille flow is investigated numerically in the low Reynolds number limit. We consider the situation without viscosity contrast between the interior of the vesicle and the exterior. Using the boundary integral method we solve the corresponding hydrodynamic flow equations and track explicitly the vesicle dynamics in two dimensions. We find that the interplay between the nonlinear character of the Poiseuille flow and the vesicle deformation causes a cross-streamline migration of vesicles towards the center of the Poiseuille flow. This is in a marked contrast with a result [L.G. Leal, Ann. Rev. Fluid Mech. 12, 435 (1980)] according to which the droplet moves away from the center (provided there is no viscosity contrast between the internal and the external fluids). The migration velocity is found to increase with the local capillary number (defined by the time scale of the vesicle relaxation towards its equilibrium shape times the local shear rate), but reaches a plateau above a certain value of the capillary number. This plateau value increases with the curvature of the parabolic flow profile. We present scaling laws for the migration velocity.

The flow orientation of anisotropic particles through narrow channels is of importance in many fields, ranging from the spinning and molding of fibers to the flow of cells and proteins through thin capillaries. It is commonly assumed that anisotropic particles align parallel to the flow direction. When flowing through narrowed channel sections, one expects the increased flow rate to improve the parallel alignment. Here, we show by microfocus synchrotron X-ray scattering and polarized optical microscopy that anisotropic colloidal particles align perpendicular to the flow direction after passing a narrow channel section. We find this to be a general behavior of anisotropic colloids, which is also observed for disk-like particles. This perpendicular particle alignment is stable, extending downstream throughout the remaining part of the channel. We show by microparticle image velocimetry that the particle reorientation in the expansion zone after a narrow channel section occurs in a region with considerable extensional flow. This extensional flow is promoted by shear thinning, a typical property of complex fluids. Our discovery has important consequences when considering the flow orientation of polymers, micelles, fibers, proteins, or cells through narrow channels, pipes, or capillary sections. An immediate consequence for the production of fibers is the necessity for realignment by extension in the flow direction. For fibrous proteins, reorientation and stable plug flow are likely mechanisms for protein coagulation.block copolymers | microfluidics | small-angle X-ray scattering T he flow orientation of anisotropic particles in narrow channels is relevant in many fields, ranging from the spinning and molding of fibers to the flow of cells or proteins through thin capillaries (1-4). It is commonly assumed that anisotropic particles align parallel to the flow direction (5). When flowing through thin channel sections, one expects the increased flow rate to improve the alignment. We investigated the alignment of anisotropic colloids (i.e., cylindrical micelles) flowing through thin sections of microchannels using synchrotron microfocus small-angle X-ray diffraction and polarized optical microscopy. Surprisingly, we find that anisotropic colloids orient perpendicular to the flow direction after passing through narrow channel sections. The perpendicular alignment is surprisingly stable, extending throughout the remaining part downstream of the channel. Ongoing experimental studies indicate that this observation holds for other anisotropic cylindrical or disk-like colloids as well. We show by microparticle image velocimetry and finite element fluid dynamics simulations that the perpendicular flow orientation is induced by perpendicular extensional flow in the expansion zone after the narrow section. Only close to the channel walls does shear flow dominate, leading to parallel flow orientation of anisotropic particles.In situ investigations of the flow orientation of colloids in solution under very well-defined flow conditi...

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