The stirring of passive scalar (tracer) in simple laminar flows that give rise to nonintegrable particle motion is investigated in five independent chapters. The first chapter provides a general introduction to this phenomenon of "chaotic advection" and a brief review of its historical development.;In the second chapter a model flow driven by a potential flow source and sink is analyzed using standard dynamical systems diagnostics such as Poincare sections and Lyapunov exponents. In addition numerical experiments are performed to study the stirring of "blobs" of tracer. This flow possesses zero circulation about any contour. Despite the absence of vorticity it is shown that the flow stirs efficiently.;A strategy to mechanically separate tracers with different molecular diffusivities is developed in Chapter 3. This strategy, which combines the reversibility of Stokes flow with the irreversibility of diffusion, is based on a scaling argument that equates the "striation thickness" of an advected cloud of tracer with a characteristic diffusion length. This scaling is verified by numerical simulations over a large range of parameter values.;In the fourth chapter the stirring characteristics of a model flow through a "twisted pipe" are examined. A one-dimensional mapping of the pipe boundary onto itself provides insight into the onset of chaotic particle motion. The parameter regime that leads to efficient stirring in the transverse direction is determined by a set of numerical experiments. The coupling between this transverse chaos and the longitudinal distribution of particles is illustrated. Implications for heat and mass transfer in engineering and physiological flows are commented upon.;In the final chapter the axial dispersion of tracer by the model flow described in Chapter 4 is studied. It is found that chaotic particle trajectories augment molecular diffusion and lead to a smaller effective diffusivity than obtained for comparable integrable flows. However, in the limit of infinite Peclet number, this effective diffusivity is singular. The divergence of the effective diffusivity is due to long-time velocity correlations near the pipe wall owing to the no-slip condition. Thus this flow fails to provide a deterministic counterpart to classical Taylor dispersion in straight tubes.
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