Nonlinear Fluctuation Effects in Dilute Polymer Solutions Under Periodic Flow.

This thesis studies dilute solutions subjected to finite amplitude periodic velocity gradient fields of characteristic strength Omega, frequency omega and vanishing time average. On time scales large compared to the flow period, fluctuations in particle position are equilibrium-like but with an effective diffusivity matrix, D(lambda) equiv E(lambda)D where D is the no-flow diagonal diffusion matrix and ~ D depends non-linearly on lambda equiv Omega/omega. We show that trD >= trD; physically, this implies that the growth with time of the mean square size of a diffusing cloud of particles is always increased by flows of this class. This enhancement arises from the interaction of the flow with microscopic fluctuations and is an example of Taylor dispersion. When 1/Omega, 1/omega become comparable to the longest internal particle relaxation time the behavior changes since internal modes are excited. As an example, we consider a dilute polymer solution in a simplified "Rouse dynamics" treatment. Relative to the centre of gravity the motion of a monomer decomposes into an "infinite" deterministic part, arising from the periodic stretching of the chain, plus fluctuations whose long time form is characterized by the same effective diffusivity D that governs the motion of the centre of gravity. The mean squared size of the chain is increased, relative to equilibrium, by the same factor trE/3 as the diffusivity. Correlation functions amenable to measurement in dynamical scattering experiments are calculated; these provide direct measurement of the non-linear D.