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# Project B.3: Shear-driven instabilities of colloidal disks and disk-rod mixtures

The goal of this project is to investigate the collective behavior of suspensions of disklike colloids and mixtures of particles of different shape under shear. Focal questions concern the nature of the oscillatory states with respect to the mixture’s components, the occurrence of shear banding or other spontaneous spatial inhomogeneities, and the related rheological behavior (stress-strain relation). Another new question arising only in mixtures is the impact of a demixing transition of the underlying equilibrium systems. So far, colloidal mixtures have rather been investigated in equilibrium. As a starting point of our investigations we need to construct expressions for the equilibrium free energy functional capable of describing the thermodynamic phase behavior of the system. To this end, we will use techniques from classical density functional theory, where microscopic features such as shape, electrostatic interactions etc. enter via the excess functional. The resulting functional will then be used as an input into a mesoscopic equation of motion for the relevant order parameters. For a two-component mixture, these are the tensors Q_{α}(with α = 1, 2) of the mixture components, and the concentration field. By expanding the tensorial equations into an appropriate basis set one obtains an 11-dimensional coupled system of partial differential equations. These equation will be analyzed by standard Runge-Kutta algorithms, as well as by a numerical bifurcation analysis based on continuation techniques such as MATCONT.**Project leaders: Prof. Dr. S. Klapp, Prof. Dr. H. Engel**