Theoretical Study Of Hydrodynamic Ratchet And Entropic Stochastic Resonance In Confined System

With the development of nanotechnology and life science, more and more research systems were focused on mesoscopic scale(Generally, the range of mesoscopic is10nm～1μm). Recently, the understanding of the characteristics and the exploration of the physical laws for mesoscopic complex systems have become a frontier domain of scientific research. Generally, the dynamic of mesoscopic complex systems(such as cell, nanopores, etc.) will be affected by space limitations, which make its features notably different from macroscopic ones and produce some peculiar effects on the system’s reaction and diffusion behavior. For example, fluctuation usually plays a very constructive role in the transport of particles under space limitations, amplifies the response of the system to external signal through resonance behavior. On the other hand, in complex fluids, confined spaces change the nonequilibrium features of complex systems through hydrodynamic interaction. So they will affect the mobility and transport of the system in fluids. In this dissertation, we take polymer as an example, mainly focused on how fluctuation and hydrodynamic interactions affect the dynamic behavior of the polymer in confined system. Main research includes several parts:●Entropic stochastic resonanceIn the last three years, stochastic resonance (SR)-like phenomenon has gained extensive research attention due to its significant practical applications. While the system is scaled down to mesoscopic level and confined to move in a constrained space, the uneven boundaries usually have the effect of entropic barriers, leading to entropic stochastic resonance(ESR). Previously, research on ESR primarily focused on Brownian particles, the gravity in the vertical direction is crucial for the occurrence of ESR in order to feel the entropic barrier. In this dissertation, we has investigated ESR of a flexible polymer chain in constrained dumb-bell-shape, found that even if the gravity is ignored, the system can also feel the effect of the entropic barrier through the different number of allowed configurations, resulting in ESR. In other words, In our system, the gravity is not essential for the occurrence of ESR, but the elastic coupling between polymer beads is crucial for ESR. Because the chain length, channel width may affect the height of the entropic barrier, we further investigate how these factors influence ESR. We found that the occurrence of ESR is robust to the change of chain length, while the bottleneck width lies in a proper range.(This works has been published in J. Chem. Phys)●Hydrodynamic ratchetThe so-called ratchet effect, leads microparticles’directed motion through the breaking of the thermal equilibrium or the breaking of the spatial inversion symmetry. From the discovery of ratchet, people re-discover and recognize its basic principles in different fields, and widely use in biology, chemistry and other fields. So far, previous research on ratchet mainly focused on Brownian particle subject to Brownian ratchet. We proposed a new kind of ratchet-hydrodynamic ratchet. We mainly study the dynamic of the semi-flexible polymer in a narrow channel. We found that the ratchet can be observed in our system and depends on the model parameters. We found that the Poiseuille flow induced by space limitations is the basic condition of hydrodynamic ratchet effect. Since the velocity distribution of Poiseuille flow is parabola, when the polymer lies in different position, the polymer is dragged differently by the flow. Thus, we introduce a feedback control for the lateral position of the polymer, resulting in its directed motion. We further consider ratchet under different conditions. Channel is essential for oscillating Poiseuille flow. We found that the velocity initially increases with the transverse force, but then starts to decrease. There is an optimal ratchet effect by introducing an appropriate control. In contrast to this, the dependence of the propagation velocity on the oscillation amplitude is monotonous. Note that propagation is absent when the oscillation amplitude is zero. This means that thermal is not sufficient for the considered ratchet effect and externally induced alternating fluid flows are essential. Besides, there is a strong dependence of the propagation velocity on the oscillation frequency. The ratchet effect gets progressively weaker as the oscillation frequency is increased.(This works has been published in Europhys. Lett.)●The effect of hydrodynamic interaction on Entropic stochastic resonanceIn our first project, the effect of the fluid is described by fluctuation and friction force. In this part, we mainly focused on how the long-ranged hydrodynamic interaction affect entropic stochastic resonance of the polymer. We found that hydrodynamic interaction enhanced the entropic stochastic resonance of the system under the same condition(To be preparing).