Electromagnetohydrodynamic flows and mass transport in curved rectangular microchannels
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APPLIED MATHEMATICS AND MECHANICS (ENGLISH EDITION) https://doi.org/10.1007/s10483-020-2649-9
Electromagnetohydrodynamic flows and mass transport in curved rectangular microchannels∗ Yongbo LIU,
Yongjun JIAN†
School of Mathematical Science, Inner Mongolia University, Hohhot 010021, China (Received Feb. 3, 2020 / Revised Jun. 3, 2020)
Abstract Curved microchannels are often encountered in lab-on-chip systems because the effective axial channel lengths of such channels are often larger than those of straight microchannels for a given per unit chip length. In this paper, the effective diffusivity of a neutral solute in an oscillating electromagnetohydrodynamic (EMHD) flow through a curved rectangular microchannel is investigated theoretically. The flow is assumed as a creeping flow due to the extremely low Reynolds number in such microflow systems. Through the theoretical analysis, we find that the effective diffusivity primarily depends on five dimensionless parameters, i.e., the curvature ratio of the curved channel, the Schmidt number, the tidal displacement, the angular Reynolds number, and the dimensionless electric field strength parameter. Based on the obtained results, we can precisely control the mass transfer characteristics of the EMHD flow in a curved rectangular microchannel by appropriately altering the corresponding parameter values. Key words electromagnetohydrodynamic (EMHD) flow, curved rectangular microchannel, mass transfer characteristic, effective diffusivity Chinese Library Classification O357.1 2010 Mathematics Subject Classification
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76W99, 74A60, 76A05
Introduction
Recently, many scholars have been interested in studying the transport phenomena in microchannels because of its various applications in chemistry[1–2] , medicine[3–4] , energy conversion[5], and mixing[6] . The fluid flow in microchannels can be driven by the pressure gradient[7–8] , the electroosmosis force[9–16] , and the Lorentz force[17–23] . Among these flows, the flow driven by the Lorentz force has the advantage of a larger flow rate. The Lorentz force is generated by the interaction of the externally applied orthogonal electric field and the magnetic field[17] . When a solute band is injected into a fluid flow, it is broaden by the hydrodynamic dispersion (HD) on account of the combined effects of nonuniformity in the fluid velocity and molecular ∗ Citation: LIU, Y. B. and JIAN, Y. J. Electromagnetohydrodynamic flows and mass transport in curved rectangular microchannels. Applied Mathematics and Mechanics (English Edition) (2020) https://doi.org/10.1007/s10483-020-2649-9 † Corresponding author, E-mail: [email protected] Project supported by the National Natural Science Foundation of China (No. 11772162) and the Natural Science Foundation of Inner Mongolia Autonomous Region of China (No. 2016MS0106) ©Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2020
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Yongbo LIU and Yongjun JIAN
diffusion. As a result, the solute dispersion is enhanced. This behavior may play an important role in the mass transfer character
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