期刊
JOURNAL OF FLUID MECHANICS
卷 949, 期 -, 页码 -出版社
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2022.717
关键词
dispersion; Navier-Stokes equations; microfluidics
资金
- Alexander von Humboldt Foundation
The paper theoretically studies the unsteady dispersion of a solute band in a semicircular microchannel under a steady pressure-driven flow. Analytical solutions are obtained for the exchange, convection, and dispersion coefficients as well as the solute concentration and mean solute concentration. The study investigates the influences of the initial concentration distribution and the reaction rate on the transport coefficients.
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 Damkohler 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 Damkohler number specifies the variations of the transport coefficients in the short term but the DamkOhler number is the only parameter dominating the long-term values: the exchange and convection coefficients are increasing functions of the Damkohler 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.
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