| The configuration of microstructure in complex fluids is important for understanding a wide range of mixing and separation processes. In this work, we considered the breakup of Newtonian drops under creeping flow conditions and analyzed drop dynamics in the disordered flows through fixed beds of randomly positioned fibers. We also studied the separation of DNA molecules during electrophoresis through two-dimensional obstacle arrays.; To understand drop dynamics in the Lagrangian-unsteady flow through dilute fiber beds, we coupled a boundary integral representation of drop shape evolution with separate descriptions of the flow far and near individual fibers within the porous medium. In each flow regime, we studied the mechanisms of breakup and estimated the critical conditions necessary for breakup. The experimental portion of this study involved a random bed of fixed fibers in which we captured images as drops were carried through the medium. Breakup was observed only after drops passed close to individual fibers, and the observed mechanisms agreed with our near-field simulations. We also compared the breakup probabilities from experiments with numerical predictions.; Using Brownian dynamics simulation, we studied the electrophoresis of double-stranded DNA molecules---modeled as beads linked by rigid rods---through two types of devices: dilute post arrays and geometric Brownian ratchets. In post arrays, the separation process requires the formation of hairpins that eventually unravel on a time scale dependent on molecular length. We found that these hairpin collisions are most frequent in random arrays at moderate electric field strengths, and by considering dispersion, we predicted that the separations achieved in dilute random arrays should be comparable to other techniques. We also showed that random arrangements, as opposed to ordered arrays, are essential for separation in strong electric fields. Our work on Brownian ratchets focused on the role of chain configurations, and we found that chain extension can be important for ratchet geometries that require operation in strong electric fields. Non-equilibrium configurations formed as a result of hairpin collisions and affected the separation by introducing trajectories dependent on chain length. |
