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Updated: Jun 12, 2026

Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique
Published on: June 12, 2015
Perturbation analysis of mixing and dispersion regimes in the low and intermediate Péclet number region
1Dipartimento di Ingegneria Chimica, Sapienza Università di Roma, via Eudossiana 18, 00184 Roma, Italy. max@giona.ing.uniroma1.it
Abstract:
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).
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