Abstract:
This thesis explores the transport of particles and fluids through soft micro- and nanochannels with spatiotemporally undulating walls, a problem that sits at the intersection of biological transport and the design of next-generation nanofluidic devices. To study these systems, the work combines analytical perturbation theory for low-Reynolds-number flows with computational Langevin dynamics, capturing how thermal fluctuations, wall interactions, and external driving forces work together to shape transport. The research is presented in three parts. First, we investigate an entropic flashing ratchet model, demonstrating that asymmetric surface fluctuations alone can drive directed particle transport. Our results identify optimal conditions for this phenomenon, showing it is maximally efficient for 10 nm particles in a water-like medium at room temperature. Second, we analyze the competition between pressure-driven bulk flow and surface-driven boundary flow in a soft nanochannel. We develop a perturbation analysis that delineates these two regimes and derive a dimensionless parameter that quantifies the flow crossover, a result critical for applications in particle filtration and trapping. In the final part, we develop a hydrodynamic ratchet model. Here, we demonstrate that carefully designed wall undulations can generate an asymmetric flow field capable of rectifying Brownian motion, resulting in a steady net particle drift. This mechanism provides a promising route for achieving controlled transport through purely hydrodynamic means. We derive the structure of fluid flow in this microchannel and the Boundary modes sustaining this fluid flow structure. Since surface-driven flow becomes stronger near the channel boundary, the presence of surface undulations is crucial when studying fluid or particle transport in a channel. This mechanism provides a promising route for achieving controlled transport through purely hydrodynamic means. Overall, the thesis advances our theoretical understanding of particle transport in soft, confined environments and offers a quantitative framework that could guide the development of new nanofluidic pumps and separation devices.
