Numerical Investigation of Traveling Wave Electroosmotic Flows in A Microchannel

ABSTRACT

In this paper, a coordinate transformation method (CTM) is employed to numerically solve the Poisson–Nernst–Planck (PNP) equation and Navier–Stokes (NS) equations for studying the traveling-wave electroosmotic flow (TWEF) in a two-dimensional microchannel. Numerical solutions indicate that the numerical solutions of TWEF with and without the coordinate transformation are in good agreement, while CTM effectively improves stability and convergence rate of the numerical solution, and saves computational cost. It is found that the averaged flow velocity of TWEF in a micro-channel strongly depends on frequency of the electric field. Flow rate achieves a maximum around the charge frequency of the electric double layer. The approximate solutions of TWEF with slip boundary conditions are also presented for comparison. It is shown that the NS solution with slip boundary conditions agree well with those of complete PNP-NS equations in the cases of small ratios of Electric double layer(EDL) thickness to channel depth(*λD*/*H*). The NS solution with slip boundary conditions over-estimates the electroosmotic flow velocity as this ratio(*λD*/*H*) is large.

In this paper, a coordinate transformation method (CTM) is employed to numerically solve the Poisson–Nernst–Planck (PNP) equation and Navier–Stokes (NS) equations for studying the traveling-wave electroosmotic flow (TWEF) in a two-dimensional microchannel. Numerical solutions indicate that the numerical solutions of TWEF with and without the coordinate transformation are in good agreement, while CTM effectively improves stability and convergence rate of the numerical solution, and saves computational cost. It is found that the averaged flow velocity of TWEF in a micro-channel strongly depends on frequency of the electric field. Flow rate achieves a maximum around the charge frequency of the electric double layer. The approximate solutions of TWEF with slip boundary conditions are also presented for comparison. It is shown that the NS solution with slip boundary conditions agree well with those of complete PNP-NS equations in the cases of small ratios of Electric double layer(EDL) thickness to channel depth(

Cite this paper

B. Chen, J. Wu and H. Chen, "Numerical Investigation of Traveling Wave Electroosmotic Flows in A Microchannel,"*Journal of Biomaterials and Nanobiotechnology*, Vol. 3 No. 2, 2012, pp. 280-285. doi: 10.4236/jbnb.2012.322034.

B. Chen, J. Wu and H. Chen, "Numerical Investigation of Traveling Wave Electroosmotic Flows in A Microchannel,"

References

[1] D. Li, “Electrokinetics in Microfluidics: Interfaces Science and Technology,” 1st Edition, Academic Press, New York, 2004.

[2] M. S. Yoon, B. J. Kim and H. J. Sung, “Pumping and Mixing in a Microchannel Using AC Asymmetric Electrode Arrays,” International Journal of Heat and Fluid Flow, Vol. 29, 2008, pp. 269-280. doi:10.1016/j.ijheatfluidflow.2007.10.002

[3] J. Lyklema, “Fundamentals of Interface and Colloid Science,” 1st Edition, Academic Press, New York, 1995.

[4] R. J. Hunter, “Zeta Potential in Colloid Science,” 1st Edition, Academic Press, New York, 1981.

[5] Y. Zhen and L. G. Anthony, “Electrokinetic Transport and Separations in Fluidic Nanochannels,” Electrophoresis, Vol. 28, No. 4, 2007, pp. 595-610. doi:10.1002/elps.200600612

[6] J. M. Edwards and M. N. Hamblin, “Thin Film Electroosmotic Pumps for Biomicrofluidic Applications,” Biomicrofluidics, Vol. 1, No. 1, 2007, Article ID 014101.

[7] A. L. Margaret and C. J. Stephen, “Electrokinetic Fluid Control in Two-Dimensional Planar Microfluidic Devices,” Analytical Chemistry, Vol. 79, No. 19, 2007, pp. 7485-7491. doi:10.1021/ac071003y

[8] G. E. Karniadakis and A. Beskok, “Micro Flows: Fundamentals and Simulation,” Springer-Verlag, New York, 2002.

[9] D. B. Pengra, S. L. Li and P. Wong, “Determination of Rock Properties by Low Frequency AC Electrokinetics,” Journal of Geo-physical Research, Vol. 104, No. B12, 1999, pp. 29485-29508. doi:10.1029/1999JB900277

[10] H. K. Yang, H. Y. Jiang, et al., “AC electrokinetic Pumping on Symmetric Electrode Arrays,” Microfluid and Nanofluid, Vol. 7, 2009, pp. 767-772.

[11] A. Ramos, A. Gonzalez, A. Castellanos, et al., “Pumping of Liquids with AC Voltages Applied to Asymmetric Pairs of Microelectrodes,” Physical Review E, Vol. 67, No. 5, 2003, Article ID 056302. doi:10.1103/PhysRevE.67.056302

[12] M. Pribyl, K. Adamiak, et al., “Numerical Models for AC Electro-Osmotic Micropumps,” IEEE Industry Applications Society Annual Meeting, Edmonton, 5-9 October 2008, pp. 1870-1877.

[13] A. Ramos, H. Morgan, N. G. Green, et al., “Pumping of Liquids with Traveling-Wave Electroosmosis,” Journal of Applied Physics, Vol. 97, No. 8, 2005, Article ID 084906. doi:10.1063/1.1873034

[14] A. Ramos, A. Gonzalez, P. Garcia-Sanchez, et al., “A Linear Analysis of the Effect of Faradaic Currents on Traveling-Wave Electroosmosis,” Journal of Colloid and Interface Science, Vol. 309, No. 2, 2007, pp. 323-331. doi:10.1016/j.jcis.2007.01.076

[15] A. Gonzalez, A. Ramos and A. Castellanos, “Pumping of Electrolytes Using Traveling-Wave Electro-Osmosis: A Weakly Nonlinear Analysis,” Microfluid and Nanofluid, Vol. 5, 2008, pp. 507-515. doi:10.1007/s10404-008-0261-0

[16] P. Garcia-Sanchez and A. Ramos, “The Effect of Electrode Height on the Performance of Traveling-Wave Electroosmotic Micropumps,” Microfluid and Nanofluid, Vol. 5, 2008, pp. 307-312. doi:10.1007/s10404-007-0247-3

[17] M. Z. Bazant and T. M. Squires, “Induced-Charge Electrokinetic Phenomena: Theory and Microfluidic Applications,” Physical Review Letters, Vol. 92, No. 6, 2004, Article ID 066101. doi:10.1103/PhysRevLett.92.066101

[18] Y. Zhang, J. k. Wu and B. Chen, “A Coordinate Transformation Method for Numerical Solutions of the Electric Double Layer and Electroosmotic ?ows in a Microchannel,” International Journal for Numerical Methods in Fluids, Vol. 68, No. 6, 2012, pp. 671-685. doi:10.1002/fld.2527

[19] J. Hrdlicka, P. Cervenka, M. Pribyl and D. Snita, “Mathematical Modeling of AC Electroosmosis in Microfluidic and Nanofluidic Chips Using Equilibrium and Non-Equilibrium Approaches,” Journal of Applied Electrochemistry, Vol. 40, No. 5, 2010, pp. 967-980. doi:10.1007/s10800-009-9966-3

[1] D. Li, “Electrokinetics in Microfluidics: Interfaces Science and Technology,” 1st Edition, Academic Press, New York, 2004.

[2] M. S. Yoon, B. J. Kim and H. J. Sung, “Pumping and Mixing in a Microchannel Using AC Asymmetric Electrode Arrays,” International Journal of Heat and Fluid Flow, Vol. 29, 2008, pp. 269-280. doi:10.1016/j.ijheatfluidflow.2007.10.002

[3] J. Lyklema, “Fundamentals of Interface and Colloid Science,” 1st Edition, Academic Press, New York, 1995.

[4] R. J. Hunter, “Zeta Potential in Colloid Science,” 1st Edition, Academic Press, New York, 1981.

[5] Y. Zhen and L. G. Anthony, “Electrokinetic Transport and Separations in Fluidic Nanochannels,” Electrophoresis, Vol. 28, No. 4, 2007, pp. 595-610. doi:10.1002/elps.200600612

[6] J. M. Edwards and M. N. Hamblin, “Thin Film Electroosmotic Pumps for Biomicrofluidic Applications,” Biomicrofluidics, Vol. 1, No. 1, 2007, Article ID 014101.

[7] A. L. Margaret and C. J. Stephen, “Electrokinetic Fluid Control in Two-Dimensional Planar Microfluidic Devices,” Analytical Chemistry, Vol. 79, No. 19, 2007, pp. 7485-7491. doi:10.1021/ac071003y

[8] G. E. Karniadakis and A. Beskok, “Micro Flows: Fundamentals and Simulation,” Springer-Verlag, New York, 2002.

[9] D. B. Pengra, S. L. Li and P. Wong, “Determination of Rock Properties by Low Frequency AC Electrokinetics,” Journal of Geo-physical Research, Vol. 104, No. B12, 1999, pp. 29485-29508. doi:10.1029/1999JB900277

[10] H. K. Yang, H. Y. Jiang, et al., “AC electrokinetic Pumping on Symmetric Electrode Arrays,” Microfluid and Nanofluid, Vol. 7, 2009, pp. 767-772.

[11] A. Ramos, A. Gonzalez, A. Castellanos, et al., “Pumping of Liquids with AC Voltages Applied to Asymmetric Pairs of Microelectrodes,” Physical Review E, Vol. 67, No. 5, 2003, Article ID 056302. doi:10.1103/PhysRevE.67.056302

[12] M. Pribyl, K. Adamiak, et al., “Numerical Models for AC Electro-Osmotic Micropumps,” IEEE Industry Applications Society Annual Meeting, Edmonton, 5-9 October 2008, pp. 1870-1877.

[13] A. Ramos, H. Morgan, N. G. Green, et al., “Pumping of Liquids with Traveling-Wave Electroosmosis,” Journal of Applied Physics, Vol. 97, No. 8, 2005, Article ID 084906. doi:10.1063/1.1873034

[14] A. Ramos, A. Gonzalez, P. Garcia-Sanchez, et al., “A Linear Analysis of the Effect of Faradaic Currents on Traveling-Wave Electroosmosis,” Journal of Colloid and Interface Science, Vol. 309, No. 2, 2007, pp. 323-331. doi:10.1016/j.jcis.2007.01.076

[15] A. Gonzalez, A. Ramos and A. Castellanos, “Pumping of Electrolytes Using Traveling-Wave Electro-Osmosis: A Weakly Nonlinear Analysis,” Microfluid and Nanofluid, Vol. 5, 2008, pp. 507-515. doi:10.1007/s10404-008-0261-0

[16] P. Garcia-Sanchez and A. Ramos, “The Effect of Electrode Height on the Performance of Traveling-Wave Electroosmotic Micropumps,” Microfluid and Nanofluid, Vol. 5, 2008, pp. 307-312. doi:10.1007/s10404-007-0247-3

[17] M. Z. Bazant and T. M. Squires, “Induced-Charge Electrokinetic Phenomena: Theory and Microfluidic Applications,” Physical Review Letters, Vol. 92, No. 6, 2004, Article ID 066101. doi:10.1103/PhysRevLett.92.066101

[18] Y. Zhang, J. k. Wu and B. Chen, “A Coordinate Transformation Method for Numerical Solutions of the Electric Double Layer and Electroosmotic ?ows in a Microchannel,” International Journal for Numerical Methods in Fluids, Vol. 68, No. 6, 2012, pp. 671-685. doi:10.1002/fld.2527

[19] J. Hrdlicka, P. Cervenka, M. Pribyl and D. Snita, “Mathematical Modeling of AC Electroosmosis in Microfluidic and Nanofluidic Chips Using Equilibrium and Non-Equilibrium Approaches,” Journal of Applied Electrochemistry, Vol. 40, No. 5, 2010, pp. 967-980. doi:10.1007/s10800-009-9966-3