Time periodic electroosmotic flow of micropolar fluids through microparallel channel

doi:10.1007/s10483-016-2081-6

Abstract

Abstract:

The time periodic electroosmotic flow of an incompressible micropolar fluid between two infinitely extended microparallel plates is studied. The analytical solutions of the velocity and microrotation are derived under the Debye-H¨uckel approximation. The effects of the related dimensionless parameters, e.g., the micropolar parameter, the frequency, the electrokinetic width, and the wall zeta potential ratio of the upper plate to the lower plate, on the electroosmotic velocity and microrotation are investigated. The results show that the amplitudes of the velocity and the volume flow rate will drop to zero when the micropolar parameter increases from 0 to 1. The effects of the electrokinetic width and the frequency on the velocity of the micropolar fluid are similar to those of the Newtonian fluid. However, the dependence of the microrotation on the related parameters mentioned above is complex. In order to describe these effects clearly, the dimensionless microrotation strength and the penetration depth of the microrotation are defined, which are used to explain the variation of the microrotation. In addition, the effects of various parameters on the dimensionless stress tensor at the walls are studied.

Key words: micropolar fluid, electroosmotic flow, microrotation strength, penetration depth

2010 MSC Number:

Zhaodong DING, Yongjun JIAN, Liangui YANG. Time periodic electroosmotic flow of micropolar fluids through microparallel channel. Applied Mathematics and Mechanics (English Edition), 2016, 37(6): 769-786.

TrendMD

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: https://www.amm.shu.edu.cn/EN/10.1007/s10483-016-2081-6

https://www.amm.shu.edu.cn/EN/Y2016/V37/I6/769

[1] Karniadakis, G., Beskok, A., and Aluru, N. Microflows and Nanoflows: Fundamentals and Simulation, Springer, New York (2005)
[2] Laser, D. J. and Santiago, J. G. A review of micropumps. Journal of Micromechanics and Microengineering, 14, R35-R64 (2004)
[3] 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, 381-411 (2004)
[4] Abhari, F., Jaafar, H., and Yunus, N. A. M. A comprehensive study of micropumps technologies. International Journal of Electrochemical Science, 7, 9765-9780 (2012)
[5] Burgreen, D. and Nakache, F. R. Electrokinetic flow in ultrafine capillary slits. Journal of Physical Chemistry, 68, 1084-1091 (1964)
[6] Xie, Z. and Jian, Y. Rotating electroosmotic flow of power-law fluids at high zeta potential. Colloids and Surfaces, A: Physicochemical and Engineering Aspects, 461, 231-239 (2014)
[7] Jian, Y. J., Su, J., Chang, L., Liu, Q. S., and He, G. H. Transient electroosmotic flow of general Maxwell fluids through a slit microchannel. Zeitschrift für Angewandte Mathematik und Physik, 65, 435-447 (2014)
[8] Jang, J. and Lee, S. S. Theoretical and experimental study ofMHD micropump. Sensors Actuators, A: Physical, 80, 84-89 (2000)
[9] Pamme, N. Magnetism and microfluidics. Lab on a Chip, 6, 24-38 (2006)
[10] Buren, M., Jian, Y., and Chang, L. Electromagnetohydrodynamic flow through a microparallel channel with corrugated walls. Journal of Physics, D: Applied Physics, 47, 425501 (2014)
[11] Buren, M. and Jian, Y. Electromagnetohydrodynamic (EMHD) flow between two transversely wavy microparallel plates. Electrophoresis, 36, 1539-1548 (2015)
[12] Dutta, P. and Beskok, A. Analytical solution of time periodic electroosmotic flows: analogies to Stokes' second problem. Analytical Chemistry, 73, 5097-5102 (2001)
[13] Keh, H. J. and Tseng, H. C. Transient electrokinetic flow in fine capillaries. Journal of Colloid and Interface Science, 242, 450-495 (2001)
[14] Kang, Y., Yang, C., and Huang, X. Dynamic aspects of electroosmotic flow in a cylindrical microcapillary. International Journal of Engineering Science, 40, 2203-2221 (2002)
[15] Wang, X. M., Chen, B., and Wu, J. K. A semianalytical solution of periodical electro-osmosis in a rectangular microchannel. Physics of Fluids, 19, 127101 (2007)
[16] Chakraborty, S. and Ray, S. Mass flow-rate control through time periodic electro-osmotic flows in circular microchannels. Physics of Fluids, 20, 083602 (2008)
[17] Chakraborty, S. and Srivastava, A. K. A generalized model for time periodic electroosmotic flows with overlapping electrical double layers. Langmuir, 23, 12421 (2007)
[18] Jian, Y., Yang, L., and Liu, Q. Time periodic electro-osmotic flow through a microannulus. Physics of Fluids, 22, 042001 (2010)
[19] Jian, Y., Liu, Q., and Yang, L. AC electroosmotic flow of generalized Maxwell fluids in a rectangular microchannel. Journal of Non-Newtonian Fluid Mechanics, 166, 1304-1314 (2011)
[20] Liu, Q., Jian, Y., and Yang, L. Time periodic electroosmotic flow of the generalized Maxwell fluids between two micro-parallel plates. Journal of Non-Newtonian Fluid Mechanics, 166, 478- 486 (2011)
[21] Liu, Q., Jian, Y., and Yang, L. Alternating current electroosmotic flow of the Jeffreys fluids through a slit microchannel. Physics of Fluids, 23, 102001 (2011)
[22] Bhattacharyya, A., Masliyah, J. H., and Yang, J. Oscillating laminar electrokinetic flow in infinitely extended circular microchannels. Journal of Colloid and Interface Science, 261, 12-20 (2003)
[23] Chang, C. C. and Wang, C. Y. Starting electroosmotic flow in an annulus and in a rectangular channel. Electrophoresis, 29, 2970-2979 (2008)
[24] Islam, N. and Wu, J. Microfluidic transport by AC electroosmosis. Journal of Physics: Conference Series, 34, 356-361 (2006)
[25] Erickson, D. and Li, D. Analysis of alternating current electroosmotic flows in a rectangular microchannel. Langmuir, 19, 5421-5430 (2003)
[26] Yang, J., Bhattacharyya, A., Masliyah, J. H., and Kwok, D. Y. Oscillating laminar electrokinetic flow in infinitely extended rectangular microchannels. Journal of Colloid and Interface Science, 261, 21-31 (2003)
[27] Marcos, Yang, C., Ooi, K. T., Wong, T. N., and Masliyah, J. H. Frequency-dependent laminar electroosmotic flow in a closed-end rectangular microchannel. Journal of Colloid and Interface Science, 275, 679-698 (2004)
[28] Minor, M., van der Linde, A. J., van Leeuwen, H. P., and Lyklema, J. Dynamic aspects of electrophoresis and electroosmosis: a new fast method for measuring particle mobilities. Journal of Colloid and Interface Science, 189, 370-375 (1997)
[29] Oddy, M. H., Santiago, J. G., and Mikkelsen, J. C. Electrokinetic instability micromixing. Analytical Chemistry, 73, 5822-5832 (2001)
[30] Das, S. and Chakraborty, S. Transverse electrodes for improved DNA hybridization in microchannels. AIChE Journal, 53, 1086-1099 (2007)
[31] Das, S., Subramanian, K., and Chakraborty, S. Analytical investigations on the effects of substrate kinetics on macromolecular transport and hybridization through microfluidic channels. Colloids and Surfaces, B: Biointerfaces, 58, 203-217 (2007)
[32] Eringen, A. C. Simple microfluids. International Journal of Engineering Science, 2, 205-217 (1964)
[33] Eringen, A. C. Theory of micropolar fluids. Journal of Applied Mathematics and Mechanics, 16, 1-18 (1965)
[34] Eringen, A. C. Microcontinuum Field Theories, II: Fluent Media, Springer, New York (2001)
[35] Hayakawa, H. Slow viscous flows in micropolar fluids. Physical Review E, 61, 5477-5492 (2000)
[36] Papautsky, I., Brazzle, J., Ameel, T., and Frazier, A. B. Laminar fluid behavior in microchannels using micropolar fluid theory. Sensors and Actuators, A: Physical, 73, 101-108 (1999)
[37] Magyari, E., Pop, I., and Valkó, P. P. Stokes' first problem for micropolar fluids. Fluid Dynamics Research, 42, 025503 (2010)
[38] Ariman, T., Turk, M. A., and Sylvester, N. D. Microcontinuum fluid mechanics—a review. International Journal of Engineering Science, 11, 905-930 (1973)
[39] Ariman, T., Turk, M. A., and Sylvester, N. D. Application of microcontinum fluid mechanics. International Journal of Engineering Science, 12, 273-293 (1974)
[40] Stokes, V. K. Theories of Fluids with Microstructures, Springer, New York (1984)
[41] Lukaszewicz, G. Micropolar Fluids: Theory and Application, Birkhäuser, Basel (1999)
[42] Siddiqui, A. A. and Lakhtakia, A. Steady electroosmotic flow of a micropolar fluid in a microchannel. Proceedings of the Royal Society, A: Mathematical, Physical and Engineering Sciences, 465, 501-522 (2009)
[43] Siddiqui, A. A. and Lakhtakia, A. Debye-Hückel solution for steady electro-osmotic flow of micropolar fluid in cylindrical microcapillary. Applied Mathematics and Mechanics (English Edition), 34(11), 1305-1326 (2013) DOI 10.1007/s10483-013-1747-6
[44] Siddiqui, A. A. and Lakhtakia, A. Non-steady electro-osmotic flow of a micropolar fluid in a microchannel. Journal of Physics, A: Mathematical and Theoretical, 42, 355501 (2009)
[45] Misra, J. C., Chandra, S., Shit, G. C., and Kundu, P. K. Electroosmotic oscillatory flow of micropolar fluid in microchannels: application to dynamics of blood flow in microfluidic devices. Applied Mathematics and Mechanics (English Edition), 35(6), 749-766 (2014) DOI 10.1007/s10483-014-1827-6
[46] Hunter, J. Zeta Potential in Colloid Science, Academic Press, New York (1981)
[47] Ahmadi, G. Self-similar solution of imcompressible micropolar boundary layer flow over a semiinfinite plate. International Journal of Engineering Science, 14, 639-646 (1976)
[48] Rees, D. A. S. and Bassom, A. P. The Blasius boundary-layer flow of a micropolar fluid. International Journal of Engineering Science, 34, 113-124 (1996)
[49] Green, N. G., Ramos, A., Gonzalez, A., Morgan, H., and Castellanos, A. Fluid flow induced by nonuniform AC electric fields in electrolytes on microelectrodes, I: experimental measurements. Physical Review E, 61, 4011-4018 (2000)

Time periodic electroosmotic flow of micropolar fluids through microparallel channel

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	D. BANERJEE, S. PATI, P. BISWAS. Analytical study of pulsatile mixed electroosmotic and shear-driven flow in a microchannel with a slip-dependent zeta potential [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(6): 1007-1022.
[2]	T. SIVA, S. JANGILI, B. KUMBHAKAR. Heat transfer analysis of MHD and electroosmotic flow of non-Newtonian fluid in a rotating microfluidic channel: an exact solution [J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(7): 1047-1062.
[3]	M. G. REDDY, S. A. SHEHZAD. Molybdenum disulfide and magnesium oxide nanoparticle performance on micropolar Cattaneo-Christov heat flux model [J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(4): 541-552.
[4]	S. A. SHEHZAD, T. MUSHTAQ, Z. ABBAS, A. RAUF, S. U. KHAN, I. TLILI. Dynamics of bioconvection flow of micropolar nanoparticles with Cattaneo-Christov expressions [J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(9): 1333-1344.
[5]	Yongbo LIU, Yongjun JIAN. Rotating electroosmotic flows in soft parallel plate microchannels [J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(7): 1017-1028.
[6]	A. RAUF, S. A. SHEHZAD, Z. ABBAS, T. HAYAT. Unsteady three-dimensional MHD flow of the micropolar fluid over an oscillatory disk with Cattaneo-Christov double diffusion [J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(10): 1471-1486.
[7]	P. K. YADAV, S. JAISWAL, B. D. SHARMA. Mathematical model of micropolar fluid in two-phase immiscible fluid flow through porous channel [J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(7): 993-1006.
[8]	M. PERALTA, O. BAUTISTA, F. MÉNDEZ, E. BAUTISTA. Pulsatile electroosmotic flow of a Maxwell fluid in a parallel flat plate microchannel with asymmetric zeta potentials [J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(5): 667-684.
[9]	M. A. A. MAHMOUD;S. E. WAHEED. Melting heat transfer effects on stagnation point flow of micropolar fluid saturated in porous medium with internal heat generation (absorption) [J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(8): 979-992.
[10]	Zhen TAN;Hai-tao QI;Xiao-yun JIANG. Electroosmotic flow of Eyring fluid in slit microchannel with slip boundary condition [J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(6): 689-696.
[11]	I. A. HASSANIEN;H. M. EL-HAWARY;M. A. A. MAHMOUD;R. G. ABDEL-RAHMAN;A. S. Thermal radiation effect on flow and heat transfer of unsteady MHD micropolar fluid over vertical heated nonisothermal stretching surface using [J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(6): 703-720.
[12]	A. A. SIDDIQUI; A. LAKHTAKIA. Debye-Hückel solution for steady electro-osmotic flow of micropolar fluid in cylindrical microcapillary [J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(11): 1305-1326.
[13]	M. A. A. MAHMOUD;S. E. WAHEED. Variable fluid properties and thermal radiation effects on flow and heat transfer in micropolar fluid film past moving permeable infinite flat plate with slip velocity [J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(5): 663-678.
[14]	T. HAYAT;M. HUSSAIN;A. A. HENDI;S. NADEEM. MHD stagnation point flow towards heated shrinking surface subjected to heat generation/absorption [J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(5): 631-648.
[15]	M. ASHRAF;A.R.WEHGAL. MHD flow and heat transfer of micropolar fluid between two porous disks [J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(1): 51-64.