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Effects of geometric modulation and surface potential heterogeneity on electrokinetic flow and solute transport in a microchannel

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Abstract

A numerical investigation is performed on the electroosmotic flow (EOF) in a surface-modulated microchannel to induce enhanced solute mixing. The channel wall is modulated by placing surface-mounted obstacles of trigonometric shape along which the surface potential is considered to be different from the surface potential of the homogeneous part of the wall. The characteristics of the electrokinetic flow are governed by the Laplace equation for the distribution of external electric potential; the Poisson equation for the distribution of induced electric potential; the Nernst–Planck equations for the distribution of ions; and the Navier–Stokes equations for fluid flow simultaneously. These nonlinear coupled set of governing equations are solved numerically by a control volume method over the staggered system. The influence of the geometric modulation of the surface, surface potential heterogeneity and the bulk ionic concentration on the EOF is analyzed. Vortical flow develops near a surface modulation, and it becomes stronger when the surface potential of the modulated region is in opposite sign to the surface potential of the homogeneous part of the channel walls. Vortical flow also depends on the Debye length when the Debye length is in the order of the channel height. Pressure drop along the channel length is higher for a ribbed wall channel compared to the grooved wall case. The pressure drop decreases with the increase in the amplitude for a grooved channel, but increases for a ribbed channel. The mixing index is quantified through the standard deviation of the solute distribution. Our results show that mixing index is higher for the ribbed channel compared to the grooved channel with heterogeneous surface potential. The increase in potential heterogeneity in the modulated region also increases the mixing index in both grooved and ribbed channels. However, the mixing performance, which is the ratio of the mixing index to pressure drop, reduces with the rise in the surface potential heterogeneity.

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References

  1. Stone, H.A., Stroock, A.D., Ajdari, A.: Engineering flows in a small devices: microfluidics toward a lab-on-a-chip. Annu. Rev. Fluid Mech. 36, 381–411 (2004)

    Article  MATH  Google Scholar 

  2. Chung, A.J., Kimb, D., Erickson, D.: Electrokinetic microfluidic devices for rapid, low power drug delivery in autonomous microsystems. Lab Chip 8, 330–338 (2008)

    Article  Google Scholar 

  3. Bayraktar, T., Pidugu, S.B.: Characterization of liquid flows in microfluidic systems. Int. J. Heat Mass Transf. 49, 815–824 (2006)

    Article  MATH  Google Scholar 

  4. Tian, F., Li, B., Kwok, D.Y.: Tradeoff between mixing and transport for electroosmotic flow in heterogeneous microchannels with nonuniform surface potentials. Langmuir 21, 1126–1131 (2005)

    Article  Google Scholar 

  5. Wu, H.-Y., Liu, C.-H.: A novel electrokinetic micromixer. Sensor Actuators A Phys. 118, 107–115 (2005)

    Google Scholar 

  6. Ewinga, M.M., Thompsona, J.M., McLarena, R.S., Purperob, V.M., Thomasb, K.J., Dobrowskic, P.A., DeGrootc, G.A., Romsosd, E.L., Stortsa, D.R.: Human DNA quantification and sample quality assessment: developmental validation of the PowerQuant1 system. Forensic Sci. Int. Genet. 23, 166–177 (2016)

    Article  Google Scholar 

  7. Srinivasan, V., Pamula, V.K., Fair, R.B.: An integrated digital microfluidic lab-on-a-chip for clinical diagnostics on human physiological fluids. Lab Chip 4, 310–315 (2004)

    Article  Google Scholar 

  8. Probstein, R.F.: Physicochemical Hydrodynamics: An Introduction, 2nd edn. Wiley Interscience, New York (1994)

    Book  Google Scholar 

  9. Conlisk, A.T., McFerran, J.: Mass transfer and flow in electrically charged micro-and nanochannels. Anal. Chem. 74, 2139–2150 (2002)

    Article  Google Scholar 

  10. Sadr, R., Yoda, M., Zheng, Z., Conlisk, A.T.: An experimental study of electro-osmotic flow in rectangular microchannels. J. Fluid Mech. 506, 357–367 (2004)

    Article  MATH  Google Scholar 

  11. Bhattacharyya, S., Zheng, M., Conlisk, A.T.: Electro-osmotic flow in two-dimensional charged micro- and nanochannels. J. Fluid Mech. 540, 247–267 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Park, H.M., Lee, J.S., Kim, T.W.: Comparison of the Nernst–Planck model and the Poisson–Boltzmann model for electroosmotic flows in microchannels. J. Colloid Interface Sci. 315, 731–739 (2007)

    Article  Google Scholar 

  13. Haywood, D.G., Harms, Z.D., Jacobson, S.C.: Electroosmotic flow in nanofluidic channels. Anal. Chem. 86, 11174–11180 (2014)

    Article  Google Scholar 

  14. Nguyen, N.-T., Wu, Z.: Micromixers—a review. J. Micromech. Microeng. 15, R1R16 (2005)

    Article  Google Scholar 

  15. Du, Y., Zhang, Z., Yim, C., Lin, M., Cao, X.: A simplified design of the staggered herringbone micromixer for practical applications. Biomicrofluidics 4, 024105–024113 (2010)

    Article  Google Scholar 

  16. Ajdari, A.: Electro-osmosis on inhomogeneously charged surfaces. Phys. Rev. Lett. 75, 755–758 (1995)

    Article  Google Scholar 

  17. Yariv, E.: Electro-osmotic flow near a surface charge discontinuity. J. Fluid Mech. 521, 181–189 (2004)

    Article  MATH  Google Scholar 

  18. Lin, T.-Y., Chen, C.-L.: Analysis of electroosmotic flow with periodic electric and pressure fields via the lattice Poisson–Boltzmann method. Appl. Math. Model. 37, 2816–2829 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  19. Tanga, G.H., Li, Z., Wang, J.K., He, Y.L., Tao, W.Q.: Electroosmotic flow and mixing in microchannels with the lattice Boltzmann method. J. Appl. Phys. 100, 094908–094918 (2006)

    Article  Google Scholar 

  20. Jain, M., Nandakumar, K.: Optimal patterning of heterogeneous surface charge for improved electrokinetic micromixing. Comput. Chem. Eng. 49, 18–24 (2013)

    Article  Google Scholar 

  21. Fang, Y., Ye, Y., Shen, R., Zhu, P., Guo, R., Hu, Y., Wu, L.: Mixing enhancement by simple periodic geometric features in microchannels. Chem. Eng. J. 187, 306–310 (2012)

    Article  Google Scholar 

  22. Xu, Z., Yang, Y., Vadillo, D., Ruan, X., Fu, X.: A mathematical model of mixing enhancement in microfluidic channel with a constriction under periodic electro-osmotic flow. Appl. Phys. Lett. 100, 041907–041912 (2012)

    Article  Google Scholar 

  23. Stroock, A.D., Weck, M., Chiu, D.T., Huck, W.T.S., Kenis, P.J.A., Ismagilov, R.F., Whitesides, G.M.: Patterning electro-osmotic flow with patterned surface charge. Phys. Rev. Lett. 84, 3314–3317 (2000)

    Article  Google Scholar 

  24. Krishnamoorthy, S., Feng, J., Henry, A.C., Locascio, L.E., Hickman, J.J., Sundaram, S.: Simulation and experimental characterization of electroosmotic flow in surface modified channels. Microfluid. Nanofluid. 2, 345–355 (2006)

    Article  Google Scholar 

  25. Lee, C.-Y., Lee, G.-B., Fu, L.-M., Lee, K.-H., Yang, R.-J.: Electrokinetically driven active micro-mixers utilizing zeta potential variation induced by field effect. J. Micromech. Microeng. 14, 1390–1398 (2004)

    Article  Google Scholar 

  26. Wu, H.-Y., Liu, C.-H.: A novel electrokinetic micromixer. Sens. Actuators A Phys. 118, 107–115 (2005)

    Google Scholar 

  27. Biddiss, E., Erickson, D., Li, D.: Heterogeneous surface charge enhanced micromixing for electrokinetic flows. Anal. Chem. 76, 3208–3213 (2004)

    Article  Google Scholar 

  28. Shu, Y.C., Chang, C.C., Chen, Y.S., Wang, C.Y.: Electro-osmotic flow in a wavy microchannel: coherence between the electric potential and the wall shape function. Phys. Fluids 22, 082001–082011 (2010)

    Article  Google Scholar 

  29. Hu, Y., Werner, C., Li, D.: Influence of the three-dimensional heterogeneous roughness on electrokinetic transport in microchannels. J. Colloid Interface Sci. 280, 527–536 (2004)

    Article  Google Scholar 

  30. Seo, H.-S., Kim, Y.-J.: A study on the mixing characteristics in a hybrid type microchannel with various obstacle configurations. Mater. Res. Bull. 47, 2948–2951 (2012)

    Article  Google Scholar 

  31. Cho, C.-C., Chen, C.-L., Chen, C.-K.: Mixing enhancement of electrokinetically-driven non-Newtonian fluids in microchannel with patterned blocks. Chem. Eng. J. 191, 132–140 (2012)

    Article  Google Scholar 

  32. Bhattacharyya, S., Bera, S.: Combined electroosmosis-pressure driven flow and mixing in a microchannel with surface heterogeneity. Appl. Math. Model. 39, 4337–4350 (2015)

    Article  MathSciNet  Google Scholar 

  33. Bhattacharyya, S., Bera, S.: Nonlinear electroosmosis pressure-driven flow in a wide microchannel with patchwise surface heterogeneity. J. Fluids Eng. Trans. ASME 135, 021303–0213015 (2013)

    Article  Google Scholar 

  34. Leonard, B.P.: Stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Eng. 19, 59–98 (1979)

    Article  MATH  Google Scholar 

  35. Fletcher, C.A.J.: Computational Techniques for Fluid Dynamics, Vol. I and II, Springer Ser. Comput. Phy. 2nd ed. Springer, Berlin, Heidelberg, New York (1991)

  36. Mirbozorgi, S.A., Niazmand, H., Renkrizbulut, M.: Electroosmotic flow in reservoir-connected flat microchannels with non-uniform zeta potential. J. Fluid Eng. Trans. ASME 128, 1133–1143 (2006)

    Article  Google Scholar 

  37. Fan, J., Ding, W., Zhang, J., He, Y., Tao, W.: A performance evaluation plot of enhanced heat transfer techniques oriented for energy-saving. Int. J. Heat Mass Transf. 52, 33–44 (2009)

    Article  MATH  Google Scholar 

  38. Charun, H.: Heat transfer and pressure drop in a vertical tube with a nodular turbulizer. Appl. Therm. Eng. 28, 1984–1994 (2008)

    Article  Google Scholar 

  39. Holvey, C.P., Roberge, D.M., Gottspone, M., Kockmann, N., Macchi, A.: Pressure drop and mixing in single phase microreactors: simplified designs of micromixers. Chem. Eng. Process Process Intensif. 50, 1069–1075 (2011)

    Article  Google Scholar 

  40. Jaafarzadeh, N., Ghanbari, F., Ahmadi, M.: Efficient degradation of 2,4- dichlorophenoxyacetic acid by peroxymonosulfate/magnetic copper ferrite nanoparticles/ozone: a novel combination of advanced oxidation processes. Chem. Eng. J. 320, 436–447 (2017)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Silchar, Silchar, 788010, India

    Subrata Bera

  2. Department of Mathematics, Indian Institute of Technology Khargapur, Kharagpur, 721302, India

    S. Bhattacharyya

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  1. Subrata Bera
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  2. S. Bhattacharyya
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Correspondence to S. Bhattacharyya.

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Communicated by S. Balachandar.

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Bera, S., Bhattacharyya, S. Effects of geometric modulation and surface potential heterogeneity on electrokinetic flow and solute transport in a microchannel. Theor. Comput. Fluid Dyn. 32, 201–214 (2018). https://doi.org/10.1007/s00162-017-0448-7

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  • DOI: https://doi.org/10.1007/s00162-017-0448-7

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