We investigate the dynamic and static properties of polymeric suspensions via a numerical simulation method. This method couples Newtonian mechanics of solid phase suspended particles with a fluctuating lattice-Boltzmann fluid. This results in the solution of the Navier-Stokes equation, including thermal fluctuations and hydrodynamic interactions for the solid particles. The coupling can be achieved either through boundary conditions for a finite sized particle or through a Stokes-like frictional coupling for point particles. The frictional coupling procedure is a very efficient approach due to the use of point particles which take up much smaller volumes. This in turn results in simulations of far fewer lattice nodes, while retaining essential hydrodynamic features for dynamics of polymers. This approach has enabled us to simulate polymer chains with more than 1000 segments, including hydrodynamic interactions. This discretization is nearly an order of magnitude higher than what is feasible using traditional Brownian dynamics methods.; The fluctuating lattice-Boltzmann method is presented for both colloidal and polymeric suspensions. A verification of the fluctuations for the case of colloidal finite sized particles is presented as a test case. However, the main theme of this thesis is the simulations of dilute polymer solutions.; The hydrodynamic interactions play an important role in these systems and the effect of these interactions is the focus of this study. In unbounded geometries, the effects lead to important differences in the scaling of the polymer properties, such as the radius of gyration and diffusion coefficient, with the linear length of the polymer. In bounded geometries the hydrodynamic interactions can result in a transverse migration. In unidirectional shearing flow or external fields, this leads to a nonuniform concentration of the polymer across the lateral axis. In both cases although the underlying phenomenon is the hydrodynamic interactions, the motion created by these two driving forces are distinctly different.; The magnitude and direction of the migration can be manipulated using a combination of hydrodynamic and external fields. The migration observed in this study also affects macroscopic transport properties of the polymer, such as dispersion and segregation velocities, due to changes in the center of mass distribution. The migration under all flow conditions depends on the dimensionless ratio between the channel size and the polymer size. Therefore, separation of polymers based on chain length is possible as long as the shear rate across the channel varies. Our results for combined flows, when compared with recent experiments, also indicate that hydrodynamic interactions, usually neglected in the electric field driven motion of polymers, may only be partially screened.
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