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The goal of this project is to investigate the dynamics of complex fluids in confined geometries (e.g., pores and thin films), under conditions where the smallest dimension of the system is comparable to the lengthscale l that characterizes the fluid microstructure. Fluid flow in a slit of width d~l can be described as a continuum in the longitudinal direction, but a microscopic approach is required for the transverse direction. My aim is to develop appropriate descriptions that incorporate the interaction of the structural lengthscale l with the scale d set by the size of the pore. The dynamics of complex fluids in confined geometries is important for many applications, such as microfluidic devices that involve flows of suspensions (e.g., protein solutions) in micron-size channels. The interaction between the intrinsic lengthscale of the fluid and the geometrical lengthscale of the device gives rise to a number of interesting and poorly understood phenomena, including wall-slip effects, size segregation, and dynamically-driven order-disorder transitions. The primary focus of these studies is on the dynamics of colloidal suspensions confined between rigid walls or fluid interfaces. Recently, there have been a number of experiments that reveal interesting behavior in these systems, such as fluctuations between ordered and disordered regions in quasi-two-dimensional suspensions. The proposed investigations are also relevant to our research on highly-asymmetric bidisperse colloidal mixtures, where important equilibrium and nonequilibrium effects result from the confinement of small nonadsorbing particles in the narrow gaps separating the larger particles. An immediate goal of this project is to develop Brownian-dynamics simulations for a colloidal suspension confined between two parallel walls. Previous attempts to perform such simulations were hindered by the lack of accurate methods for evaluating the hydrodynamic interactions between colloidal particles and the walls. In a recent paper we have proposed an efficient image representation for the flow field reflected from the walls, which will make such calculations possible.
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