| In this work, we study the dynamics of polyelectrolytes in microchannel and nanochannel flows under externally applied pressure and electric fields using both theoretical and computational approaches. Hydrodynamic interactions, acting directly within the chain and indirectly, mediated by the confinement, play a crucial role in polymer transport and migration. Emphasis is placed on properly resolving them in terms of point-force solutions to the Stokes equation.;First, we analyze the transport and separation of biomolecules (polyelectrolytes and DNA in particular) under electrokinetic flows in microscale geometries of critical dimensions on the order of the characteristic size of the molecules, i.e. radius of gyration for chains. The governing systems of field equations are discretized by finite differences on boundary-fitted overlapping grids, while the polymer is coarse-grained into a bead-spring model that follows Langevin dynamics. The objective of the work is a mesoscale-level treatment of hydrodynamic interactions in nanopores and entropic traps. We report on electrophoretic mobilities, trapping times and translocation times and quantify the chain transition from free flowing behavior to trapping behavior in terms of the electric field strength.;Second, we extend the kinetic theory of dilute polymer solutions under external pressure and electric fields∼cite{kek10} to a) include finite chain extensibility and b) properly account for wall-induced hydrodynamic interactions due to charged polymers in an electrolyte. Focusing on cross-stream migration due to individual and combined effects of these fields, we conclude that the thickness of the depletion layer is overpredicted by the Hookean spring model and scales quadratically with the Peclet number, similar to the dependence on Weissenberg number reported in shear flows. We show the variation of molecular stretch and normal stresses across the channel and derive migration tensors for the Green's function of Stokes flow in a Debye-Hückel electrolyte.;Next we examine DNA electrophoresis under pressure-driven flow in a microchannel using Brownian Dynamics. In addition to hydrodynamic interactions due to non-electric forces, we also include electrically-induced hydrodynamic interactions, which arise due to velocity disturbances generated by localized bead charges and their counter-ion clouds. All modeled bulk interactions are supplemented with the appropriate wall corrections, thus providing a uniformly valid solution for small Debye lengths. We analyze cross-stream migration patterns in light of competition among different types of hydrodynamic interactions and show the Peclet number dependence of electrophoretic mobility and radius-of-gyration tensor in moderate flows.;Finally, we develop a semi-analytical form of the Stokes flow Green's function in a rectangular channel using a combination of Fourier transform, eigenfunction expansions and a rapidly convergent representation of the Green's function for a potential flow. The solution may serve as a basis for further analytical study of flow disturbances and their hydrodynamic interaction with the confining walls, with potential use e.g. in the hydrodynamics of swimming microorganisms. |
