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Mass transport in electrokinetic microflows with the wall reaction affecting the hydrodynamics

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Abstract

The mass transport in electrokinetically actuated microchannel flow is interesting when the wall reactions influence the wall potential, thereby affecting the hydrodynamics. This is the first work where the electro-osmotic flow is impacted by the chemical reactions. Since the wall potential is non-uniform, we have compared the results of the classical Poisson–Boltzmann equations with the generalized Poisson–Nernst–Planck model and investigated the applicability within the range of the operating conditions of the problem. The results provide fundamental understanding of the velocity profile within the channel and the wall concentration, which is significantly different from the classical species transport. The wall concentration is dependent on the electrokinetic parameters rather than the Reynolds and Peclet number solely. For constant volumetric flow rate, the resultant electro-osmotic velocity profile is not parabolic and exhibits higher convection close to the wall, leading to reduced solute polarization. The overall mass transport rate can be enhanced by more than two times with respect to non-electrical phenomena. The results will be useful in understanding the physics and provide operational know-how of electrokinetic-based applications related to capillary electrophoresis, electrochromatrogaphy and (bio-)chemical sensing.

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References

  1. Li, D.: Electrokinetics in Microfluidics, vol. 2. Elsevier, Amsterdam (2004)

    Google Scholar 

  2. Dejam, M.: Dispersion in non-newtonian fluid flows in a conduit with porous walls. Chem. Eng. Sci. 189, 296–310 (2018)

    Google Scholar 

  3. Dejam, M., Hassanzadeh, H., Chen, Z.: A reduced-order model for chemical species transport in a tube with a constant wall concentration. Can. J. Chem. Eng. 96(1), 307–316 (2018)

    Google Scholar 

  4. Rathore, A., Guttman, A.: Electrokinetic Phenomena: Principles and Applications in Analytical Chemistry and Microchip Technology. CRC Press, Boca Raton (2003)

    Google Scholar 

  5. Tallarek, U., Pačes, M., Rapp, E.: Perfusive flow and intraparticle distribution of a neutral analyte in capillary electrochromatography. Electrophoresis 24(24), 4241–4253 (2003)

    Google Scholar 

  6. Li, Y., Xiang, R., Wilkins, J.A., Horváth, C.: Capillary electrochromatography of peptides and proteins. Electrophoresis 25(14), 2242–2256 (2004)

    Google Scholar 

  7. Hu, G., Gao, Y., Li, D.: Modeling micropatterned antigen-antibody binding kinetics in a microfluidic chip. Biosens. Bioelectron. 22(7), 1403–1409 (2007)

    Google Scholar 

  8. Lee, M.Y., Srinivasan, A., Ku, B., Dordick, J.S.: Multienzyme catalysis in microfluidic biochips. Biotechnol. Bioeng. 83(1), 20–28 (2003)

    Google Scholar 

  9. Zaytseva, N.V., Montagna, R.A., Baeumner, A.J.: Microfluidic biosensor for the serotype-specific detection of dengue virus rna. Anal. Chem. 77(23), 7520–7527 (2005)

    Google Scholar 

  10. Bazant, M.Z., Squires, T.M.: Induced-charge electrokinetic phenomena: theory and microfluidic applications. Phys. Rev. Lett. 92(6), 066101 (2004)

    Google Scholar 

  11. Dejam, M., Hassanzadeh, H., Chen, Z.: Shear dispersion in combined pressure-driven and electro-osmotic flows in a capillary tube with a porous wall. AIChE J. 61(11), 3981–3995 (2015)

    Google Scholar 

  12. Dejam, M., Hassanzadeh, H., Chen, Z.: Shear dispersion in combined pressure-driven and electro-osmotic flows in a channel with porous walls. Chem. Eng. Sci. 137, 205–215 (2015)

    Google Scholar 

  13. Dejam, M.: Derivation of dispersion coefficient in an electro-osmotic flow of a viscoelastic fluid through a porous-walled microchannel. Chem. Eng. Sci. 204, 298–309 (2019)

    Google Scholar 

  14. Kou, Z., Dejam, M.: Dispersion due to combined pressure-driven and electro-osmotic flows in a channel surrounded by a permeable porous medium. Phys. Fluids 31(5), 056603 (2019)

    Google Scholar 

  15. Cao, J., Sun, T., Grattan, K.T.: Gold nanorod-based localized surface plasmon resonance biosensors: A review. Sens. Actuators B: Chem. 195, 332–351 (2014)

    Google Scholar 

  16. Wittenberg, N.J., Wootla, B., Jordan, L.R., Denic, A., Warrington, A.E., Oh, S.H., Rodriguez, M.: Applications of spr for the characterization of molecules important in the pathogenesis and treatment of neurodegenerative diseases. Expert Rev. Neurother. 14(4), 449–463 (2014)

    Google Scholar 

  17. Tamayo, J., Kosaka, P.M., Ruz, J.J., San Paulo, Á., Calleja, M.: Biosensors based on nanomechanical systems. Chem. Soc. Rev. 42(3), 1287–1311 (2013)

    Google Scholar 

  18. Bhattacharya, S., Jang, J., Yang, L., Akin, D., Bashir, R.: Biomems and nanotechnology-based approaches for rapid detection of biological entities. J. Rapid Methods Autom. Microbiol. 15(1), 1–32 (2007)

    Google Scholar 

  19. Boisen, A., Dohn, S., Keller, S.S., Schmid, S., Tenje, M.: Cantilever-like micromechanical sensors. Rep. Prog. Phys. 74(3), 036101 (2011)

    Google Scholar 

  20. Ryu, G., Huang, J., Hofmann, O., Walshe, C.A., Sze, J.Y., McClean, G.D., Mosley, A., Rattle, S.J., deMello, J.C., deMello, A.J., et al.: Highly sensitive fluorescence detection system for microfluidic lab-on-a-chip. Lab Chip 11(9), 1664–1670 (2011)

    Google Scholar 

  21. Barbosa, A.I., Gehlot, P., Sidapra, K., Edwards, A.D., Reis, N.M.: Portable smartphone quantitation of prostate specific antigen (psa) in a fluoropolymer microfluidic device. Biosens. Bioelectron. 70, 5–14 (2015)

    Google Scholar 

  22. Qi, J., Zeng, J., Zhao, F., Lin, S.H., Raja, B., Strych, U., Willson, R.C., Shih, W.C.: Label-free, in situ sers monitoring of individual dna hybridization in microfluidics. Nanoscale 6(15), 8521–8526 (2014)

    Google Scholar 

  23. Javanmard, M., Davis, R.: A microfluidic platform for electrical detection of dna hybridization. Sens. Actuators B: Chem. 154(1), 22–27 (2011)

    Google Scholar 

  24. Ghosal, S.: The effect of wall interactions in capillary-zone electrophoresis. J. Fluid Mech. 491, 285–300 (2003)

    MATH  Google Scholar 

  25. Prakash, S., Yeom, J.: Nanofluidics and Microfluidics: Systems and Applications. William Andrew, Norwich (2014)

    Google Scholar 

  26. Gervais, T., Jensen, K.F.: Mass transport and surface reactions in microfluidic systems. Chem. Eng. Sci. 61(4), 1102–1121 (2006)

    Google Scholar 

  27. Jomeh, S., Hoorfar, M.: Numerical modeling of mass transport in microfluidic biomolecule-capturing devices equipped with reactive surfaces. Chem. Eng. J. 165(2), 668–677 (2010)

    Google Scholar 

  28. Sharma, H., Vasu, N., De, S.: Mass transfer during catalytic reaction in electroosmotically driven flow in a channel microreactor. Heat Mass Transf. 47(5), 541–550 (2011)

    Google Scholar 

  29. Sadeghi, A., Amini, Y., Saidi, M.H., Chakraborty, S.: Numerical modeling of surface reaction kinetics in electrokinetically actuated microfluidic devices. Anal. Chim. Acta 838, 64–75 (2014)

    Google Scholar 

  30. Herr, A., Molho, J., Santiago, J., Mungal, M., Kenny, T., Garguilo, M.: Electroosmotic capillary flow with nonuniform zeta potential. Anal. Chem. 72(5), 1053–1057 (2000)

    Google Scholar 

  31. Dejam, M.: Hydrodynamic dispersion due to a variety of flow velocity profiles in a porous-walled microfluidic channel. Int. J. Heat Mass Transf. 136, 87–98 (2019)

    Google Scholar 

  32. Sadeghi, M., Saidi, M.H., Moosavi, A., Sadeghi, A.: Unsteady solute dispersion by electrokinetic flow in a polyelectrolyte layer-grafted rectangular microchannel with wall absorption. J. Fluid Mech. 887, A13-1-48 (2020)

  33. Ghosal, S.: Lubrication theory for electro-osmotic flow in a microfluidic channel of slowly varying cross-section and wall charge. J Fluid Mech. 459, 103–128 (2002)

    MATH  Google Scholar 

  34. Zholkovskij, E.K., Masliyah, J.H., Yaroshchuk, A.E.: Broadening of neutral analyte band in electroosmotic flow through slit channel with different zeta potentials of the walls. Microfluid. Nanofluid. 15(1), 35–47 (2013)

    Google Scholar 

  35. Ng, C.O., Zhou, Q.: Dispersion due to electroosmotic flow in a circular microchannel with slowly varying wall potential and hydrodynamic slippage. Phys. Fluids 24(11), 112002 (2012)

    Google Scholar 

  36. Vargas, C., Arcos, J., Bautista, O., Méndez, F.: Hydrodynamic dispersion in a combined magnetohydrodynamic-electroosmotic-driven flow through a microchannel with slowly varying wall zeta potentials. Phys. Fluids 29(9), 092002 (2017)

    Google Scholar 

  37. Park, H., Lee, J., Kim, T.: Comparison of the Nernst–Planck model and the Poisson–Boltzmann model for electroosmotic flows in microchannels. J. Colloid Interface Sci. 315(2), 731–739 (2007)

    Google Scholar 

  38. Ng, E., Tan, S.: Study of edl effect on 3-d developing flow in microchannel with poisson-boltzmann and nernst-planck models. Int. J. Numer. Methods Eng. 71(7), 818–836 (2007)

    MATH  Google Scholar 

  39. Wang, M., Chen, S.: On applicability of Poisson–Boltzmann equation for micro-and nanoscale electroosmotic flows. Commun. Comput. Phys. 3(5), 1087–1099 (2008)

    Google Scholar 

  40. Park, H., Choi, Y.: Electroosmotic flow driven by oscillating zeta potentials: comparison of the poisson-boltzmann model, the debye-hückel model and the nernst-planck model. Int. J. Heat Mass Transf. 52(19–20), 4279–4295 (2009)

    MATH  Google Scholar 

  41. Masliyah, J.H., Bhattacharjee, S.: Electrokinetic and Colloid Transport Phenomena. John Wiley & Sons, New Jersey (2006)

    Google Scholar 

  42. Yang, R.J., Fu, L.M., Lin, Y.C.: Electroosmotic flow in microchannels. J. Colloid Interface Sci. 239(1), 98–105 (2001)

    Google Scholar 

  43. Højgaard, C., Kofoed, C., Espersen, R., Johansson, K.E., Villa, M., Willemoes, M., Lindorff-Larsen, K., Teilum, K., Winther, J.R.: A soluble, folded protein without charged amino acid residues. Biochemistry 55(28), 3949–3956 (2016)

    Google Scholar 

  44. Glatzel, S., Laschewsky, A., Lutz, J.F.: Well-defined uncharged polymers with a sharp ucst in water and in physiological milieu. Macromolecules 44(2), 413–415 (2011)

    Google Scholar 

  45. Probstein, R.F.: Physicochemical Hydrodynamics: An Introduction. John Wiley & Sons, New Jersey (2005)

    Google Scholar 

  46. Kuo, J.S., Chiu, D.T.: Controlling mass transport in microfluidic devices. Ann. Rev. Anal. Chem. 4, 275–296 (2011)

    Google Scholar 

  47. Gaikwad, H.S., Baghel, P., Sarma, R., Mondal, P.K.: Transport of neutral solutes in a viscoelastic solvent through a porous microchannel. Phys. Fluids 31(2), 022006 (2019)

    Google Scholar 

  48. Sadeghi, A., Amini, Y., Saidi, M.H., Yavari, H.: Shear-rate-dependent rheology effects on mass transport and surface reactions in biomicrofluidic devices. AIChE J. 61(6), 1912–1924 (2015)

    Google Scholar 

  49. Mondal, S., De, S.: Effects of non-newtonian power law rheology on mass transport of a neutral solute for electro-osmotic flow in a porous microtube. Biomicrofluidics 7(4), 044113 (2013)

    Google Scholar 

  50. Peterman, M.C.: Hand-held microfluidic testing device. US Patent 8,702,976 (2014)

  51. Cussler, E.: Diffusion: Mass Transfer in Fluid Systems. Cambridge Series in Chemical Engineering. Cambridge University Press (2009). https://books.google.co.uk/books?id=dq6LdJyN8ScC

  52. Fogler, H.S.: Essentials of Chemical Reaction Engineering: Essenti Chemica Reactio Engi. Pearson Education, London (2010)

    Google Scholar 

  53. Song, H., Chen, D.L., Ismagilov, R.F.: Reactions in droplets in microfluidic channels. Angew. Chem. Int. Edition 45(44), 7336–7356 (2006)

    Google Scholar 

  54. Ismagilov, R.F., Tice, J.D., Gerdts, C.J., Zheng, B.: Method for conducting reactions involving biological molecules in plugs in a microfluidic system (2012). US Patent 8,329,407

  55. Pompano, R.R., Li, H.W., Ismagilov, R.F.: Rate of mixing controls rate and outcome of autocatalytic processes: theory and microfluidic experiments with chemical reactions and blood coagulation. Biophys. J. 95(3), 1531–1543 (2008)

    Google Scholar 

  56. Ducry, L., Roberge, D.M.: Controlled autocatalytic nitration of phenol in a microreactor. Angew. Chem. Int. Edition 44(48), 7972–7975 (2005)

    Google Scholar 

  57. Xuan, J., Wang, H., Leung, D.Y., Leung, M.K., Xu, H., Zhang, L., Shen, Y.: Theoretical graetz-damköhler modeling of an air-breathing microfluidic fuel cell. J Power Sources 231, 1–5 (2013)

    Google Scholar 

  58. Pryor, R.W.: Multiphysics Modeling Using COMSOL: A First Principles Approach. Jones & Bartlett Publishers, Burlington (2009)

    Google Scholar 

  59. Siegel, C.: Review of computational heat and mass transfer modeling in polymer-electrolyte-membrane (PEM) fuel cells. Energy 33(9), 1331–1352 (2008)

    Google Scholar 

  60. Cai, L., White, R.E.: Mathematical modeling of a lithium ion battery with thermal effects in COMSOL Inc. Multiphysics (MP) software. J Power Sources 196(14), 5985–5989 (2011)

    Google Scholar 

  61. Van Schijndel, A.W.M.: Integrated modeling of dynamic heat, air and moisture processes in buildings and systems using Simulink and COMSOL. Building Simul. 2(2), 143–155 (2009)

    Google Scholar 

  62. Hu, H.H., Patankar, N.A., Zhu, M.Y.: Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian technique. J. Comput. Phys. 169(2), 427–462 (2001)

    MathSciNet  MATH  Google Scholar 

  63. Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics. Oxford University Press, Oxford (2014)

    MATH  Google Scholar 

  64. Saad, Y., Schultz, M.H.: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7(3), 856–869 (1986)

    MathSciNet  MATH  Google Scholar 

  65. Saad, Y.: A flexible inner-outer preconditioned GMRES algorithm. SIAM J. Sci. Comput. 14(2), 461–469 (1993)

    MathSciNet  MATH  Google Scholar 

  66. Barrett, R., Berry, M.W., Chan, T.F., Demmel, J., Donato, J., Dongarra, J., Eijkhout, V., Pozo, R., Romine, C., Van der Vorst, H.: Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. SIAM (1994)

  67. Eisenstat, S.C., Walker, H.F.: Choosing the forcing terms in an inexact Newton method. SIAM J. Sci. Comput. 17(1), 16–32 (1996)

    MathSciNet  MATH  Google Scholar 

  68. Wang, M., Kang, Q.: Modeling electrokinetic flows in microchannels using coupled lattice boltzmann methods. J. Comput. Phys. 229(3), 728–744 (2010)

    MathSciNet  MATH  Google Scholar 

  69. Horiuchi, K., Dutta, P., Ivory, C.F.: Electroosmosis with step changes in zeta potential in microchannels. AIChE J. 53(10), 2521–2533 (2007)

    Google Scholar 

  70. Mondal, S., De, S.: Mass transport in a porous microchannel for non-newtonian fluid with electrokinetic effects. Electrophoresis 34(5), 668–673 (2013)

    Google Scholar 

  71. Dydek, E.V., Zaltzman, B., Rubinstein, I., Deng, D., Mani, A., Bazant, M.Z.: Overlimiting current in a microchannel. Phys. Rev. Lett. 107(11), 118301 (2011)

    Google Scholar 

  72. Mouheb, N.A., Malsch, D., Montillet, A., Solliec, C., Henkel, T.: Numerical and experimental investigations of mixing in t-shaped and cross-shaped micromixers. Chem. Eng. Sci. 68(1), 278–289 (2012)

    Google Scholar 

  73. Lyu, W., Yu, M., Qu, H., Yu, Z., Du, W., Shen, F.: Slip-driven microfluidic devices for nucleic acid analysis. Biomicrofluidics 13(4), 041502 (2019)

    Google Scholar 

  74. Lee, W., Amini, H., Stone, H.A., Di Carlo, D.: Dynamic self-assembly and control of microfluidic particle crystals. Proc. Natl. Acad. Sci. 107(52), 22413–22418 (2010)

    Google Scholar 

  75. Wang, J.: Cargo-towing synthetic nanomachines: towards active transport in microchip devices. Lab Chip 12(11), 1944–1950 (2012)

    Google Scholar 

  76. Nagai, M., Hirano, T., Shibata, T.: Phototactic algae-driven unidirectional transport of submillimeter-sized cargo in a microchannel. Micromachines 10(2), 130 (2019)

    Google Scholar 

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Acknowledgements

One of the authors (Sourav Mondal) would like to acknowledge the student members of the ECMI Modelling Week 2017, organized by Lappeenranta University of Technology, Finland—Wajid Ali (University of Koblenz), Ana Galhoz (Technical University of Lisbon), Fedor Garbuzov (Peter the Great St. Petersburg Polytechnic University), Gaston Holmen (Lund University), Victoria Pereira (University of Oxford) and Gulzhan Zhassulanbaikyzy (University of Grenoble Alpes) who has worked a part of this problem during the modelling week. Sourav Mondal would like to acknowledge the graduate students of the InFoMM CDT of the Mathematical Institute, Oxford University—Federico Danieli, Alissa Kamilova, Raquel Gonzalez, Kristian Kiradjiev, Clint Wong and Attila Kovacs, for working on this topic as a case study problem. Sourav Mondal would also like to acknowledge Yilu Wang of Oxford University, for working on this problem during the summer break.

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  1. Department of Chemical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

    Sourav Mondal & Sirshendu De

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  1. Sourav Mondal
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Mondal, S., De, S. Mass transport in electrokinetic microflows with the wall reaction affecting the hydrodynamics. Theor. Comput. Fluid Dyn. 35, 39–60 (2021). https://doi.org/10.1007/s00162-020-00549-5

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