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Hydrodynamic Effects on Confined Polymers

We consider the statics and dynamics of a flexible polymer confined between parallel plates both in the presence and absence of hydrodynamic interactions. The hydrodynamic interactions are described at the level of the fluctuating, compressible Navier-Stokes equation. We consider two cases: (i) confinement for both the solvent and the polymer, and (ii) confinement for the polymer only (in a 3D solvent), which is experimentally feasible, for instance, by (optical) trapping. We find a continuous transition from 2D to 3D dynamic scaling as a function of decreasing degree of confinement within the de Gennes and the weak-confinement regimes. We demonstrate that, in the presence of hydrodynamics, the polymer's center-of-mass diffusion coefficient in the direction parallel to the walls scales differently as a function of the level of confinement in cases (i) and (ii). We also find that in the commonly used Langevin dynamics description, the polymer swells more parallel to the walls than in the presence of hydrodynamics, and the planar diffusion coefficient shows scaling behavior similar to case (ii) rather than case (i). In addition, we quantify the differences in the static structure factor of the polymer between cases (i) and (ii), and between case (i) and Langevin dynamics.