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Unsteady convective–diffusive transport in semicircular microchannels with irreversible wall reaction

Published online by Cambridge University Press:  21 September 2022

Milad Azari Open the ORCID record for Milad Azari [Opens in a new window]  and
Arman Sadeghi Open the ORCID record for Arman Sadeghi [Opens in a new window]
Milad Azari
Affiliation:
Department of Mechanical Engineering, University of Kurdistan, Sanandaj 66177-15175, Iran
Arman Sadeghi*
Affiliation:
Department of Mechanical Engineering, University of Kurdistan, Sanandaj 66177-15175, Iran
*
†Email address for correspondence: [email protected]
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Abstract

The unsteady dispersion of a solute band by a steady pressure-driven flow in a semicircular microchannel is theoretically studied via the generalized dispersion model. Considering an irreversible first-order reaction at the curved wall while assuming a no-flux boundary condition at the flat wall, analytical solutions are obtained for the exchange, convection and dispersion coefficients as well as the dimensionless forms of solute concentration and mean solute concentration. The solutions are obtained assuming an initial solute band of arbitrary cross-sectional shape and axial distribution and the results are presented for both circular and semicircular shapes with the uniform distribution being a special case of the latter. Besides the general solutions, special solutions are also derived for uniform velocity and no-reaction cases. In the following, the influences of the initial concentration distribution and the Damköhler number, a measure of the reaction rate, on the transport coefficients and the concentration distribution are investigated in depth. It is demonstrated that the combination of the initial concentration distribution and the Damköhler number specifies the variations of the transport coefficients in the short term but the Damköhler number is the only parameter dominating the long-term values: the exchange and convection coefficients are increasing functions of the Damköhler number whereas the opposite is true for the dispersion coefficient. Moreover, we show that, provided the solute injection is appropriately positioned and shaped, liquid-phase transportation with little dispersion is possible in typical microchannels utilizing semicircular geometry.

JFM classification

Mass Transport: Dispersion Micro-/Nano-fluid dynamics: Microfluidics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 949 , 25 October 2022 , A1
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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