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Spectral properties and universal behaviour of advecting–diffusing scalar fields in finite-length channels

Published online by Cambridge University Press:  10 October 2008

M. GIONA ,
S. CERBELLI  and
F. CRETA
M. GIONA
Affiliation:
Dipartimento di Ingegneria Chimica, Università di Roma “La Sapienza”, via Eudossiana 18, 00184Roma
S. CERBELLI
Affiliation:
Dipartimento di Ingegneria Chimica, Università di Roma “La Sapienza”, via Eudossiana 18, 00184Roma
F. CRETA
Affiliation:
Dipartimento di Meccanica ed Aeronautica, Università di Roma “La Sapienza”, via Eudossiana 18, 00184Roma
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Abstract

This paper analyses the relaxation towards the steady state of an advecting–diffusing field in a finite-length channel. The dominant eigenvalue, −-ΛF, of the advection–diffusion operator provides the slowest relaxation time scale for achieving steady state in open flow devices. We focus on parallel flows and analyse how ΛF depends on the velocity profile and the molecular diffusivity. As a result of the universal localization features of the eigenfunction associated with ΛF, we find that ΛF can be predicted analytically based on the local behaviour of the velocity profile near the stagnation points. Microfluidic applications of the theory are also addressed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 612 , 10 October 2008 , pp. 387 - 406
Copyright
Copyright © Cambridge University Press 2008

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