Dynamics of suspensions of rodlike polymers with hydrodynamic interactions.

摘要

Dynamics of suspensions of rigid rod-like polymers are studied by theoretical analysis and simulation considering hydrodynamic interactions. The motions of rigid rods in Newtonian suspending fluids are modeled using slender-body theory and and assumption of zero Reynolds number. Hydrodynamic interactions are included using the linearized force distribution along a rod axis. The orbits in trajectories of a pair of sedimenting rods and the concentration dependent trend of short-time diffusivities are simulated to validate the simulation method used in this study.;A kinetic theory is developed to investigate cross-stream migration of a rigid polymer undergoing rectilinear flow in the vicinity of a wall. Hydrodynamic interactions between the polymers and the boundary result in a cross-stream migration. In simple shear flow, polymers migrate away from the wall, creating a depletion layer in the vicinity of the wall which thickens as the flow strength increases relative to the Brownian force. In pressure-driven flow, an off-center maximum in the center-of-mass distribution occurs due to a competition between hydrodynamic interactions with the wall and the anisotropic diffusivity induced by the inhomogeneous flow field.;A rigid polymer within simple shear flow, parabolic flow, and oscillatory flow at high Peclet numbers (weak Brownian motion) is simulated to enable comparisons with the steady and transient distributions predicted by the theory and simulation. The simulation and theoretical results are in good agreement at sufficiently high shear rates, validating approximations made in the theory. The effect of the inhomogeneous distribution on the effective stress is also investigated.;A theoretical analysis on cross-stream migration of a rigid polymer in torsional flow is also investigated. Due to the curvature of radial shear flow, a rigid rod migrates towards the center axis. An analogy is made between flexible polymers migrating in torsional flows and the particle stress is also calculated for the purpose of determining the practical impact of the migration upon rheological measurement in parallel-plate geometries.