Dynamics of flowing polymer solutions under confinement

This thesis focuses on the dynamics and transport of flowing polymer solutions near surfaces or confined to small geometries. Combining the theoretical analysis and simulation approaches, we explore the dynamics of dilute polymer solutions under three types of confinements: single-wall confinement, slit and grooved channel.; Starting from the single-wall confinement, we develop a kinetic theory based on a dumbbell model of the dissolved polymer chains. It is shown that hydrodynamic interactions between the chains and the wall lead to migration away from the wall in shear flow. The depletion layer thickness is determined by the normal stresses that develop in flow and can be much larger than the size of the polymer molecule. Numerical and similarity solutions show that the developing concentration profile generally displays a maximum at an intermediate distance from the wall. Using single-reflection approximation, the kinetic theory for single-wall confinement is extended to slit geometry.; Our Brownian Dynamics (BD) simulations results confirm that the kinetic theory captures the correct far-field (relative to the walls) behavior. Once a finite-size dipole is used, the theory improves its near-wall predictions. In the regime 2h ∼ L > R g, the results are significantly affected by the level of discretization of the polymer chain, because the spatial distribution of the forces exerted by the chain on the fluid acts on the scale of the channel geometry.; Finally, we consider the chain center-of-mass distribution in a dilute linear polymer solution during flow in a channel with grooves running perpendicular to the flow direction. A simulation method which couples a bead-spring chain model of the polymer molecule to a Lattice-Boltzmann fluid is implemented. We observe that in flow, polymer chains leave the groove, leading to lower concentration there than in the bulk. Furthermore, a band of increased concentration formes near the wall containing the grooves. The degree of depletion of chains from the groove increases significantly with increasing Weissenberg number. Our results show that the chain connectivity and the complex flow field are the primary reasons for these observations.