Perturbation analysis of mixing and dispersion regimes in the low and intermediate Péclet number region

The object of this paper is to show that a variety of dispersion and mixing phenomena induced by laminar convection and diffusion can be approached by perturbation analysis of the spectrum associated with the corresponding advection-diffusion operator. As a case study for dispersion, we consider the classical Taylor-Aris problem, whereas a prototypical model of Sturm-Liouville generalized eigenvalue problem is considered for describing mixing in open or closed bounded flows. For both cases, we show how a simplified (low-order) perturbative approach defines quantitatively the range of different mixing regimes and the associated time scales. Furthermore, we show how a complete higher-order approach cannot improve significantly the simplified low-order analysis due to the lack of analyticity of the eigenvalue branches. The perturbation analysis is also extended to models of physically realizable mixing systems (lid-driven cavity flow). © 2010 The American Physical Society.