Electromagnetohydrodynamic flows and mass transport in curved rectangular microchannels

doi:10.1007/s10483-020-2649-9

摘要/Abstract

摘要： 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.

关键词: electromagnetohydrodynamic (EMHD) flow, curved rectangular microchannel, mass transfer characteristic, effective diffusivity

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

中图分类号:

Yongbo LIU, Yongjun JIAN. Electromagnetohydrodynamic flows and mass transport in curved rectangular microchannels[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(9): 1431-1446.

参考文献

[1] STONE, H. A., STROOCK, A. D., and AJDARI, A. Engineering flows in small devices:microfluidics toward a lab-on-a-chip. Annual Review of Fluid Mechanics, 36(36), 381-411(2004)
[2] SARKAR, S. and GANGULY, S. Characterization of electromagnetohydrodynamic transport of power law fluids in microchannel. Journal of Non-Newtonian Fluid Mechanics, 250, 18-30(2017)
[3] KLEINSTREUER, C., JIE, L., and JUNEMO, K. Microfluidics of nano-drug delivery. International Journal of Heat and Mass Transfer, 51(23), 5590-5597(2008)
[4] KHAN, I. U., SERRA, C. A., ANTON, N., and VANDAMMEA, T. Microfluidics:a focus on improved cancer targeted drug delivery systems. Journal of Controlled Release, 172(3), 1065-1074(2013)
[5] MANSOURI, A., BHATTACHARJEE, S., and KOSTIUK, L. High-power electro kinetic energy conversion in a glass microchannel array. Lab on a Chip, 12(20), 4033-4036(2012)
[6] LIU, Y. Z., KIM, B. J., and SUNG, H. J. Two-fluid mixing in a microchannel. International Journal of Heat and Fluid Flow, 25(6), 986-995(2004)
[7] WEILIN, Q., MALA, G. M., and LI, D. Q. Pressure-driven water flows in trapezoidal silicon microchannels. International Journal of Heat and Mass Transfer, 43(3), 353-364(2000)
[8] CHANDA, S., SINHA, S., and DAS, S. Streaming potential and electroviscous effects in soft nanochannels:towards designing more efficient nanofluidic electrochemomechanical energy converters. Soft Matter, 10(38), 7558-7568(2014)
[9] DAS, S. and CHAKRABORTY, S. Analytical solutions for velocity, temperature and concentration distribution in electroosmotic microchannel flows of a non-Newtonian bio-fluid. Analytica Chimica Acta, 559(1), 15-24(2006)
[10] TSAO, H. K. Electroosmotic flow through an annulus. Journal of Colloid and Interface Science, 225(1), 247-250(2000)
[11] TAN, Z., QI, H. T., and JIANG, X. Y. Electroosmotic flow of Eyring fluid in slit microchannel with slip boundary condition. Applied Mathematics and Mechanics (English Edition), 35(6), 689-696(2014) https://doi.org/10.1007/s10483-014-1822-6
[12] WANG, C. Y., LIU, Y. H., and CHANG, C. C. Analytical solution of electro-osmotic flow in a semicircular microchannel. Physics of Fluids, 20(6), 063105(2008)
[13] DING, Z. D., JIAN, Y. J., and YANG, L. G. Time periodic electroosmotic flow of micropolar fluids through microparallel channel. Applied Mathematics and Mechanics (English Edition), 37(6), 769-786(2016) https://doi.org/10.1007/s10483-016-2081-6
[14] WANG, X., CHEN, B., and WU, J. A semianalytical solution of periodical electro-osmosis in a rectangular microchannel. Physics of Fluids, 19(12), 127101(2007)
[15] QI, C. and NG, C. O. Rotating electroosmotic flow of viscoplastic material between two parallel plates. Colloids and Surfaces A:Physicochemical and Engineering Aspects, 513, 355-366(2017)
[16] QI, C. and NG, C. O. Electroosmotic flow of a power-law fluid in a slit microchannel with gradually varying channel height and wall potential. European Journal of Mechanics-B/Fluids, 52, 160-168(2015)
[17] LEMOFF, A. V. and LEE, A. P. An AC magnetohydrodynamic micropump. Sensors and Actuators B:Chemical, 63(3), 178-185(2000)
[18] SHEIKHOLESLAMI, M. and BHATTI, M. M. Forced convection of nanofluid in presence of constant magnetic field considering shape effects of nanoparticles. International Journal of Heat and Mass Transfer, 111, 1039-1049(2017)
[19] DANIEL, Y. S., AZIZ, Z. A., ISMAIL, Z., and SALAH, F. Slip effects on electrical unsteady MHD natural convection flow of nanofluid over a permeable shrinking sheet with thermal radiation. Engineering Letters, 26(1), 107-116(2018)
[20] JANG, J. and LEE, S. S. Theoretical and experimental study of MHD (magnetohydrodynamic) micropump. Sensors and Actuators A:Physical, 80(1), 84-89(2000)
[21] CHAKRABORTY, S. and PAUL, D. Microchannel flow control through a combined electromagnetohydrodynamic transport. Journal of Physics D:Applied Physics, 39(24), 5364-5371(2006)
[22] DAS, S., MITRA, S. K., and CHAKRABORTY, S. Ring stains in the presence of electromagnetohydrodynamic interactions. Physical Review E, 86(5), 056317(2012)
[23] ESCANDON, J., SANTIAGO, F., BAUTISTA, O., and MENDEZ, F. Hydrodynamics and thermal analysis of a mixed electromagnetohydrodynamic-pressure driven flow for Phan-Thien-Tanner fluids in a microchannel. International Journal of Thermal Sciences, 86, 246-257(2014)
[24] WEIGL, B. H., BARDELL, R. L., and CABRERA, C. R. Lab-on-a-chip for drug development. Advanced Drug Delivery Reviews, 55(3), 349-377(2003)
[25] ARIS, R. On the dispersion of a solute in pulsating flow through a tube. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 259(1298), 370-376(1960)
[26] WATSON, E. J. Diffusion in oscillatory pipe flow. Journal of Fluid Mechanics, 133, 233-244(1983)
[27] JOSHI, C. H., KAMM, R. D., DRAZEN, J. M., and SLUTSKY, A. S. An experimental study of gas exchange in laminar oscillatory flow. Journal of Fluid Mechanics, 133, 245-254(2006)
[28] JAEGER, M. J. and KURZWEG, U. H. Determination of the longitudinal dispersion coefficient in flows subjected to high-frequency oscillations. Physics of Fluids, 26(6), 1380-1382(1983)
[29] MANOPOULOS, C. and TSANGARIS, S. Enhanced diffusion for oscillatory viscoelastic flow. Physica Scripta, 89(8), 085206(2014)
[30] ZHOU, Q. and NG, C. O. Electro-osmotic dispersion in a circular tube with slip-stick striped wall. Fluid Dynamics Research, 47(1), 015502(2014)
[31] NG, C. O. and CHEN, B. Dispersion in electro-osmotic flow through a slit channel with axial step changes of zeta potential. Journal of Fluids Engineering, 135(10), 101203(2013)
[32] NG, C. O. and ZHOU, Q. Dispersion due to electroosmotic flow in a circular microchannel with slowly varying wall potential and hydrodynamic slippage. Physics of Fluids, 24(11), 112002(2012)
[33] JIE, S., NG, C. O., and ADRIAN, W. K. Dispersion in oscillatory electro-osmotic flow through a parallel-plate channel with kinetic sportive exchange at walls. Journal of Hydrodynamics, 26(3), 363-373(2014)
[34] ARCOS, J. C., MÉNDEZ, F., BAUTISTA, E. G., and BAUTISTA, O. Dispersion coefficient in an electro-osmotic flow of a viscoelastic fluid through a microchannel with a slowly varying wall zeta potential. Journal of Fluid Mechanics, 839, 348-386(2018)
[35] HUANG, H. F. and LAI, C. L. Enhancement of mass transport and separation of species by oscillatory electroosmotic flows. Proceedings of the Royal Society A:Mathematical, Physical and Engineering Sciences, 462(2071), 2017-2038(2006)
[36] RAMON, G., AGNON, Y., and DOSORETZ, C. Solute dispersion in oscillating electro-osmotic flow with boundary mass exchange. Microfluidics and Nanofluidics, 10(1), 97-106(2011)
[37] RAMON, G. Z. Solute transport under oscillating electro-osmotic flow in a closed-ended cylindrical pore. Journal of Engineering Mathematics, 110(1), 195-205(2018)
[38] LI, H. C. and JIAN, Y. J. Dispersion for periodic electro-osmotic flow of Maxwell fluid through a microtube. International Journal of Heat Mass Transfer, 115, 703-713(2017)
[39] MEDINA, I., TOLEDO, M., MENDEZ, F., and BAUTISTA, O. Pulsatile electroosmotic flow in á microchannel with asymmetric wall zeta potentials and its effect on mass transport enhancement and mixing. Chemical Engineering Science, 184, 259-272(2018)
[40] MUÑOZ, J., ARCOS, J., BAUTISTA, O., and MÉNDEZ, F. Slippage effect on the dispersion coefficient of a passive solute in a pulsatile electro-osmotic flow in a microcapillary. Physical Review Fluids, 3, 084503(2018)
[41] TEODORO, C., BAUTISTA, O., and MÉNDEZ, F. Mass transport and separation of species in an oscillating electro-osmotic flow caused by distinct periodic electric fields. Physica Scripta, 94(11), 115012(2019)
[42] PERALTA, M., ARCOS, J., MENDEZ, F., and BAUTISTA, O. Mass transfer through á concentric-annulus microchannel driven by an oscillatory electroosmotic flow of a Maxwell fluid. Journal of Non-Newtonian Fluid Mechanics, 279, 104281(2020)
[43] ZHAO, J., ZHENG, L., ZHANG, X., and LIU, F. Convection heat and mass transfer of fractional MHD Maxwell fluid in a porous medium with Soret and Dufour effects. International Journal of Heat Mass Transfer, 103, 203-210(2016)
[44] SRINIVAS, S. and KOTHANDAPANI, M. The influence of heat and mass transfer on MHD peristaltic flow through a porous space with compliant walls. Applied Mathematics and Computation, 213(1), 197-208(2009)
[45] VARGAS, C., BAUTISTA, O., ARCOS, J., and MENDEZ, F. Hydrodynamic dispersion in a combined magnetohydrodynamic-electroosmotic-driven flow through a microchannel with slowly varying wall zeta potentials. Physics of Fluids, 29(9), 0922002(2017)
[46] ORTIZ-PEREZ, A. S., GARCIA-ANGEL, V., ACUNA-RAMIREZ, A., VARGAS-OSUNA, L., PEREZ-BARRERA, E. J., and CUEVAS, S. Magnetohydrodynamic flow with slippage in an annular duct for microfluidic applications. Microfluidics and Nanofluidics, 21(8), 138(2017)
[47] VALENZUELA-DELGADO, M., FLORES-FUENTES, W., RIVAS-LOPEZ, M., SERGIYENKO, O., LINDNER, L., HERNANDEZ-BALBUENA, D., and RODRIGUEZ-QUINONEZ, J. C. Electrolyte magnetohydrodynamic flow sensing in an open annular channel-a vision system for validation of the mathematical model. Sensors, 18(6), 1683(2018)
[48] NOROUZI, M., VAMERZANI, B. Z., DAVOODI, M., BIGLARI, N., and SHAHMARDAN, M. M. An exact analytical solution for creeping Dean flow of Bingham plastics through curved rectangular ducts. Rheologica Acta, 54(5), 391-402(2015)
[49] DEHARO, M. L., DELRIO, J. A., and WHITAKER, S. Flow of Maxwell fluids in porous media. Transport in Porous Media, 25(2), 167-192(1996)
[50] SAUER. T. Numerical Analysis, 2nd ed., Pearson Education Inc., New York, 399-401(2012)
[51] BANDOPADHYAY, A. and CHAKRABORTY, S. Giant augmentations in electro-hydro-dynamic energy conversion efficiencies of nanofluidic devices using viscoelastic fluids. Applied Physics Letters, 101(4), 043905(2012)
[52] LIU, Y. P., JIAN, Y. J., LIU, Q. S., and LI, F. Q. Alternating current magnetohydrodynamic electroosmotic flow of Maxwell fluids between two micro-parallel plates. Journal of Molecular Liquids, 211, 784-791(2015)
[53] RIVERO, M. and CUEVAS, S. Analysis of the slip condition in magnetohydrodynamic (MHD) micropumps. Sensors and Actuators B:Chemical, 166, 884-892(2012)
[54] ZHAO, G. P., JIAN, Y. J., CHANG, L., and BUREN, M. D. L. Magnetohydrodynamic flow of generalized Maxwell fluids in a rectangular micropump under an AC electric field. Journal of Magnetism and Magnetic Materials, 387, 111-117(2015)