Study of Slip Effect on Electro-osmotic Micromixer Performance Based on Entropy Index

Document Type : Research Article

Authors

1 Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

2 Department of Mechanical Engineering, Razi University, Kermanshah, Iran

Abstract

In this article electrokinetic mixing through heterogeneous microchannels has been studied and
the effects of slip coefficient, zeta-potential, Debye-Huckel parameter and Reynolds number on mixing efficiency
have been investigated. The microchannels have homogenous surface properties except for zeta-potential. In order to
study the electro-osmotic mixing, the Navier-Stokes, Nernst–Planck, electric potential and concentration equations
have been solved numerically. In order to evaluate the mixing efficiency, entropy of concentration has been used as a
quantitative index. The results show that the behavior of electro-osmotic micromixers is highly depended to amount
and distribution of wall zeta-potential. Furthermore, mixing efficiency increases with reduction of slip coefficient and
Debye-Huckel and Reynolds number parameters in most cases. It is seen that slip coefficient can decrease or increase
mixing efficiency dependent on the Reynolds number. Furthermore the accuracy of Helmholtz-Smoluchowski
approximate model is also investigated and it is found that in high wall zeta-potential cases or low values of Debye-
Huckel parameter, results of this model have significant error compared to Nernst-Planck model. It is also found that
the mixing performance increases when as the charge pattern of micromixer is more asymmetric so that the certain
mixing value can be obtained in shorter length which is importance in micromixers design.

Keywords

Main Subjects


[1] L.M. Fu, R.J. Yang, G.B. Lee, H.H. Liu, Electrokinetic injection techniques in microfluidic chips, Analytical chemistry, 74(19) (2002) 5084-5091.
[2] V.E. Papadopoulos, I.N. Kefala, G. Kaprou, G. Kokkoris, D. Moschou, G. Papadakis, E. Gizeli, A. Tserepi, A passive micromixer for enzymatic digestion of DNA, Microelectronic Engineering, 124 (2014) 42-46.
[3] A. Ahmadian Yazdi, A. Sadeghi, M.H. Saidi, Electrokinetic mixing at high zeta potentials: Ionic size effects on cross stream diffusion, Journal of Colloid and Interface Science, 442 (2015) 8-14.
[4] A. Alizadeh, L. Zhang, M. Wang, Mixing enhancement of low-Reynolds electro-osmotic flows in microchannels with temperature-patterned walls, Journal of Colloid and Interface Science, 431 (2014) 50-63.
[5] S. Ebrahimi, A. Hasanzadeh-Barforoushi, A. Nejat, F.Kowsary, Numerical study of mixing and heat transfer in mixed electroosmotic/pressure driven flow through T-shaped microchannels, International Journal of Heat and Mass Transfer, 75 (2014) 565-580.
[6] R. Peng, D. Li, Effects of ionic concentration gradient on electroosmotic flow mixing in a microchannel, Journal of Colloid and Interface Science, 440 (2015) 126-132.
[7] S. Bera, S. Bhattacharyya, On mixed electroosmoticpressure driven flow and mass transport in microchannels,International Journal of Engineering Science, 62 (2013)165-176.
[8] A.K. Nayak, Analysis of mixing for electroosmotic flow in micro/nano channels with heterogeneous surface potential, International Journal of Heat and Mass Transfer, 75 (2014) 135-144.
[9] Y.Y. Liang, G.A. Fimbres Weihs, D.E. Wiley,Approximation for modelling electro-osmotic mixing in the boundary layer of membrane systems, Journal of Membrane Science, 450 (2014) 18-27.
[10] C.O. Ng, C. Qi, Electroosmotic flow of a power-law fluid in a non-uniform microchannel, Journal of Non-Newtonian Fluid Mechanics, 208–209 (2014) 118-125.
[11] J. Jamaati, H. Niazmand, M. Renlsizbulut, Investigation of electrokinetic mixing in 3D non-homogenous microchannels, Journal Of Computational And Applied Research In Mechanical Engineering, 3(1) (2013) 41-52.
[12] J. Jamaati, A.R. Farahinia, H. Niazmand, Mixing Investigation In Combined Electroosmotic/Pressuredriven Micromixers With Heterogeneous Wall Charges,Modares Mechanical Engineering, 15(7) (2015) 297-306.
[13] S. Bhattacharyya, S. Bera, Nonlinear Electroosmosis Pressure-Driven Flow in a Wide Microchannel With Patchwise Surface Heterogeneity, Journal of Fluids Engineering, 135(2) (2013) 021303.
[14] S. Bhattacharyya, S. Bera, Combined electroosmosispressure driven flow and mixing in a microchannel with surface heterogeneity, Applied Mathematical Modelling,39 (15) (2015) 4337-4350.
[15] J. Jamaati, A.R. Farahinia, H. Niazmand, Numerical Investigate of Electroosmotic Flow in Heterogeneous Microchannels, Modares Mechanical Engineering, 15(3)(2015) 260-270.
[16] J. Jamaati, A.R. Farahinia, H. Niazmand, Investigation of Mixing in Electroosmotic Micromixers using Nernst-Planck Equations, Modares Mechanical Engineering,15(4) (2015) 203-213.
[17] J.T. Cheng, N. Giordano, Fluid flow through nanometerscale channels, Physical Review E - Statistical, Nonlinear,and Soft Matter Physics, 65 (3) (2002) 0312061-0312065.
[18] J.K. Holt, H.G. Park, Y. Wang, M. Stadermann, A.B.Artyukhin, C.P. Grigoropoulos, A. Noy, O. Bakajin,Fast mass transport through sub-2-nanometer carbon nanotubes, Science, 312 (5776) (2006) 1034-1037.
[19] M. Majumder, N. Chopra, R. Andrews, B.J. Hinds,Nanoscale hydrodynamics: Enhanced flow in carbon nanotubes, Nature, 438 (7064) (2005) 44.
[20] D.C. Tretheway, C.D. Meinhart, A generating mechanism for apparent fluid slip in hydrophobic microchannels, Physics of Fluids, 16 (5) (2004) 1509-1515.
[21] Y. Zhu, S. Granick, Rate-dependent slip of Newtonian liquid at smooth surfaces, Physical Review Letters, 87 (9)(2001) 961051-961054.
[22] C. Neto, D.R. Evans, E. Bonaccurso, H.J. Butt, V.S.J.Craig, Boundary slip in Newtonian liquids: A review of experimental studies, Reports on Progress in Physics, 68(12) (2005) 2859-2897.
[23] J.W.G. Tyrrell, P. Attard, Images of nanobubbles on hydrophobic surfaces and their interactions, Physical Review Letters, 87 (17) (2001) 1761041-1761044.
[24] L. Joly, C. Ybert, E. Trizac, L. Bocquet, Liquid friction on charged surfaces: From hydrodynamic slippage to electrokinetics, Journal of Chemical Physics, 125 (20)(2006) 204716
[25] Y. Ren, D. Stein, Slip-enhanced electrokinetic energy conversion in nanofluidic channels, Nanotechnology, 19(19) (2008) 195707.
[26] C.I. Bouzigues, P. Tabeling, L. Bocquet, Nanofluidics in the debye layer at hydrophilic and hydrophobic surfaces,Physical Review Letters, 101 (11) (2008) 114503.
[27] S. Chakraborty, Generalization of interfacial electrohydrodynamics in the presence of hydrophobic interactions in narrow fluidic confinements, Physical Review Letters, 100 (9) (2008) 097801.
[28] J. Yang, D.Y. Kwok, Effect of liquid slip in electrokinetic parallel-plate microchannel flow, Journal of Colloid and Interface Science, 260 (1) (2003) 225-233.
[29] H.M. Park, Y.J. Choi, A method for simultaneous estimation of inhomogeneous zeta potential and slip coefficient in icrochannels, Analytical Chimica. Acta.,616 (2) (2008) 160-169.
[30] H.M. Park, T.W. Kim, Simultaneous estimation of zeta potential and slip coefficient in hydrophobic microchannels, Analytical Chimica. Acta., 593 (2) (2007)171-177.
[31] A. Alam, A. Afzal, K.Y. Kim, Mixing performance of a planar micromixer with circular obstructions in a curved microchannel, Chemical Engineering Research and Design, 92 (3) (2014) 423-434.
[32] N. Solehati, J. Bae, A.P. Sasmito, Numerical investigation of mixing performance in microchannel T-junction with wavy structure, Computers & Fluids, 96(2014) 10-19.
[33] M.M. Afsari, Joule heating effects in electroosmotic flow through microchannel, Birjand University, Birjand,2012.
[34] P. Fodor, B. Vyhnalek, M. Kaufman, Entropic Evaluation of Dean Flow Micromixer, in: Proceeding of COMSOLConference, Boston, 2013.
[35] F.M. Mastrangelo, F. Pennella, F. Consolo, M. Rasponi, A. Redaelli, F.M. Montevecchi, U. Morbiducci,Micromixing and Microchannel Design: Vortex Shape and Entropy, in: 2nd Micro and Nano Flows Conference,West London, 2009.
[36] G. Zongyu, J.J. Chen, An analysis of the entropy of mixing for granular materials, Powder Technology, 266(2014) 90-95.
[37] M. Wang, J. Wang, S. Chen, N. Pan, Electrokinetic pumping effects of charged porous media in microchannels using the lattice Poisson-Boltzmann method, J. Colloid Interface Sci., 304(1) (2006) 246-253.
[38] J.H. Masliyah, Electrokinetik transport phenomena,Alberta Oil Sands Technology and Research Authority,Canada, 1994.
[39] E.B. Cummings, S.K. Griffiths, R.H. Nilson, P.H. Paul,Conditions for similitude between the fluid velocity and electric field in electroosmotic flow, Analytical chemistry, 72(11) (2000) 2526-2532.
[40] J.G. Santiago, Electroosmotic Flows in Microchannels with Finite Inertial and Pressure Forces, Analytical chemistry, 73(10) (2001) 2353-2365.
[41] C.E. Shannon, A mathematical theory of communication,Bell Syst. Technol. J., 27 (1948) 379-423, 623-656.
[42] W. Weaver, C.E. Shannon, The Mathematical Theory of Communication, University of Illinois Press, United State of America, 1963.
[43] R.J. Hunter, Zeta Potential in Colloid Science, Academic Press, United State of America, 1981.
[44] S.A. Mirbozorgi, H. Niazmand, M. Renksizbulut,Electro-Osmotic Flow in Reservoir-Connected Flat Microchannels With Non-Uniform Zeta Potential, Journal of Fluids Engineering, 128(6) (2006) 1133-1143.