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Induced mixing electrokinetics in a charged corrugated nano-channel: towards a controlled ionic transport

  • A. Banerjee
  • A. K. Nayak
  • A. Haque
  • B. Weigand
Research Paper
  • 87 Downloads

Abstract

To perform a fluid analysis for electroosmotic flows in micro- and nano-channels, it is necessary to mix various fluid contents in micro- and nano-scales. It is observed that fluids in electroosmotic flow exhibits Reynolds number effect as the flow exerts very weak inertial force and it requires long channel for mixing of different layers and species through diffusion process. Hence, if the desired length scale of mixing is large, an enormous time is needed for the molecules to be thoroughly mixed by diffusion. The theory of dynamic equations on time scale is used to study the stability of these systems. It is found that such a system may exhibits an unstable nature for overlapping electric double layer field with fluctuating velocities and stability is preserved for zero linear growth coefficient. To obtain an improved understanding of mixing performance, a numerical study is performed with the variation of channel height when more than one ionic species with channels patterned with heterogeneity is considered. The wall heterogeneity may be created by placing some blocks of unequal size (with or without charged) close to the channel wall or some external potential patches. The analytical results for the transport characteristics of electroosmotic flow obtained are compared with the direct numerical simulation of the Navier–Stokes equation, Nernst–Plank equation, and Poisson equation, simultaneously. It is shown that heterogeneous potential could generate complex flow structures and the increment of species layers at different levels of the channel cross section from inlet to outlet significantly improve the mixing rate.

Keywords

Patterned heterogeneity Analytical solution Diffusion dominated mixing Stability analysis 

Notes

References

  1. Arcos JC, Mendez F, Bautista EG, Bautista O (2018) Dispersion coefficient in an electro-osmotic flow of a viscoelastic fuid through a microchannel with a slowly varying wall zeta potential. J Fluid Mech 839:348–386MathSciNetCrossRefGoogle Scholar
  2. Bhattacharyya S, Bera S (2015) Combined electroosmosis-pressure driven flow and mixing in a micro channel with surface heterogenity. Appl Math Model 39(15):4337–4350MathSciNetCrossRefGoogle Scholar
  3. Bhattacharyya S, Nayak AK (2008) Time periodic electro-osmotic transport in a charged micro/nano-channel. Colloids Surf A Physicochem Eng Aspects 325:152–159CrossRefGoogle Scholar
  4. Bhattacharyya S, Nayak AK (2010) Combined effect of surface roughness and heterogeneity of wall potential on electroosmosis in microfluidic/nanofuidic channels. J Fluids Eng 132:041103–11CrossRefGoogle Scholar
  5. Bhattachryya S, Zheng Z, Conlisk AT (2005) Electro-osmotic flow in two-dimensional charged micro- and nanochannels. J Fluid Mech 540:247–267MathSciNetCrossRefGoogle Scholar
  6. Brody JP, Yager P, Goldstein RE, Austin RH (1996) Biotechnology at low Reynolds number. Biophys J 71:3430–3441CrossRefGoogle Scholar
  7. Campo AD, Greiner C, Alvarez I, Arzt E (2007) Patterned surfaces with pillars with controlled 3D tip geometry mimicking bioattachment devices. Adv Mater 19:1973–1977CrossRefGoogle Scholar
  8. Capretto L, Cheng W, Hill M, Zhang X (2011) Micromixing within microfluidic devices. Top Curr Chem 304:27–68CrossRefGoogle Scholar
  9. Carneiro-da-Cunha MG, Cerqueira MA, Souza BWS, Teixeira JA, Vicente AA (2011) Influence of concentration, ionic strength and pH on zeta potential and mean hydrodynamic diameter of edible polysaccharide solutions envisaged for multinanolayered films production. Carbohydr Polym 85:522–528CrossRefGoogle Scholar
  10. Chang CC, Wang CY (2009) Electro-osmotic flow in a sector microchannel. Phys Fluids 21:042002CrossRefGoogle Scholar
  11. Chang CC, Yang RJ (2007) Electrokinetic mixing in microfluidic systems. Microfluid Nanofluid 3:501–525CrossRefGoogle Scholar
  12. Chen L, Conlisk AT (2009) Effect of nonuniform surface potential on elctroosmotic flow at large applied electric field strength. Biomed Microdev 11:173–181CrossRefGoogle Scholar
  13. Cheng LJ, Guo LJ (2009) Ionic current rectification, breakdown, and switching in heterogeneous oxide nanofluidic devices. ACS Nano 3(3):575–584MathSciNetCrossRefGoogle Scholar
  14. Conlisk AT, McFerran J, Zheng Z, Hansford D (2002) Mass transfer and flow in electrically charged micro- and nano-channels. Anal Chem 74:2139–2150CrossRefGoogle Scholar
  15. Datta S, Ghosal S, Patankar NA (2006) Electroosmotic flow in a rectangular channel with variable wall zeta-potential: comparison of numerical simulation with asymptotic theory. Electrophoresis 27:611–619CrossRefGoogle Scholar
  16. Duan C, Wang W, Xie Q (2013) Review article: fabrication of nanofluidic devices. Biomicrofluidics 7:026501CrossRefGoogle Scholar
  17. Erickson D, Li D (2002) Influence of surface heterogeneity on electrokinetically driven microfluidic mixing. Langmuir 18:1883–1892CrossRefGoogle Scholar
  18. Fu LM, Lin JY, Yang RJ (2003) Analysis of electroosmtoic flow with step change in zeta potential. J Colloid Interface Sci 258:266–275CrossRefGoogle Scholar
  19. Fuest M, Boone C, Rangharajan KK, Conlisk AT, Prakash S (2015) A three-state nanofluidic field effect switch. Nano Lett 15:2365–2371CrossRefGoogle Scholar
  20. Hsu JP, Kuo YC, Tseng S (1997) Dynamic interactions of two electrical double layers. J Colloid Interface Sci 195:388–394CrossRefGoogle Scholar
  21. Hu JS, Chao CYH (2007) Numerical study of electroosmotic (EO) flow inmicrofabricated EO pump with overlapped electrical double layer (EDL). Int J Refrig 30:290–298CrossRefGoogle Scholar
  22. Jain M, Nandakumar K (2013) Optimal patterning of heterogeneous surface charge for improved electrokinetic micromixing. Comput Chem Eng 49:18–24CrossRefGoogle Scholar
  23. Jain M, Yeung A, Nandakumar K (2009) Efficient micromixing using induced-charge electroosmosis. J Micro Electr Mech Syst 18(2):376–384CrossRefGoogle Scholar
  24. Jeon W, Shin CB (2009) Design and simulation of passive mixing in microfluidic systems with geometric variations. Chem Eng J 152(2–3):575–582CrossRefGoogle Scholar
  25. Kang S, Suh YK (2009) Electroosmotic flows in an electric double layer overlapped channel with rectangle-waved surface roughness. Microfluid Nanofluid 7:337–352CrossRefGoogle Scholar
  26. Karnik R, Castelino K, Duan CH, Majumdar A (2006) Diffusion-limited patterning of molecules in nanofluidic channels. Nano Lett 6(8):1735–1740CrossRefGoogle Scholar
  27. Koga Y, Kuriyama R, Sato Y, Hishida K, Miki N (2013) Effects of micormachining process on electroosmotic flow mobility of glass surfaces. Micromachines 4:67–79CrossRefGoogle Scholar
  28. Kumar V, Paraschivoiu M, Nigam KDP (2011) Single-phase fluid flow and mixing in microchannels. Chem Eng Sci 66(7):1329–1373CrossRefGoogle Scholar
  29. Lee CY, Lee GB, Lin JL, Huang FC, Liao CS (2005) Integrated microfluidic systems for cell lysis, mixing/pumping and DNA amplification. J Micromech Microeng 15:1215–1223CrossRefGoogle Scholar
  30. Lei Y, Wang W, Wu W, Li Z (2010) Nanofluidic diode in a suspended nanoparticle crystal. Appl Phys Lett 96(26):263102CrossRefGoogle Scholar
  31. Lim CY, Lam YC, Yang C (2010) Mixing enhancement in microfluidic channel with a constriction under periodic electro-osmotic flow. Biomicrofluidics 4:014101CrossRefGoogle Scholar
  32. Lin CH, Tsai CH, Fu LM (2005) A rapid three-dimensional vortex micromixer utilizing self rotation effects under low Reynolds number conditions. J Micromech Microeng 15:935–943CrossRefGoogle Scholar
  33. Liu Y, Yang D (2010) Effect of wall roughness on electroosmotic flow in microchannels. Adv Tribiol 3:1087–1099Google Scholar
  34. Luo WJ (2006) Transient electro-osmotic flow induced by AC electric field in micro-channel with patchwise surface heterogeneities. J Colloid Interface Sci 295:551–561CrossRefGoogle Scholar
  35. Mansur EA, Ye M, Wang Y, Dai Y (2008) A state of the art review of mixing in microfluidic mixtutres. Chin J Chem Eng 16(4):503–516CrossRefGoogle Scholar
  36. Masilamani K, Ganguly S, Feichtinger C, Bartuschat D, Rude U (2015) Effects of surface roughness and electrokinetic heterogeneity on electroosmotic flow in microchannel. Fluid Dyn Res 47:035505MathSciNetCrossRefGoogle Scholar
  37. Matteucci M, Christiansen TL, Tanzi S, stergaard PF, Larsen ST, Taboryski R (2013) Fabrication and characterization of injection molded multi level nano and microfluidic systems. Microelectron Eng 111:294–298CrossRefGoogle Scholar
  38. Meisel I, Ehrhard P (2006) Electrically excited (electroosmotic) flow in micro channels for mixing applications. Eur J Mech B Fluids 25:491–504MathSciNetCrossRefGoogle Scholar
  39. Nayak AK (2013) An analysis of steady/unsteady electroosmotic flows through charged cylindrical nano channel. Theor Comp Fluid Dyn 24:3006–3017Google Scholar
  40. Nayak AK (2014) Analysis of mixing for electroosmotic flow in micro/nano channels with heterogeneous surface potential. Int J Heat Mass Transf 75:135–144CrossRefGoogle Scholar
  41. Pacheco JR (2008) Mixing enhancement in electroosmotic flows via modulation of electric fields. Phys Fluids 20:093603CrossRefGoogle Scholar
  42. Peng R, Li D (2015) Effects of ionic concentration gradient on electroosmotic flow mixing in a microchannel. J Colloid Interface Sci 440:126–132CrossRefGoogle Scholar
  43. Prakash S, Conlisk AT (2016) Field effect nanofluidics. Lab Chip 16:3855CrossRefGoogle Scholar
  44. Prakash S, Zambrano HA, Fuest M, Boone C, Rosenthal-Kim E, Vasquez N, Conlisk AT (2015) Electrokinetic transport in silica nanochannels with asymmetric surface charge. Microfluid Nanofluid 19:1455–1464CrossRefGoogle Scholar
  45. Probstien RF (1999) Physiochemical hydrodynamics. Butterworth Publishers, BostonGoogle Scholar
  46. Ramirez S, Conlisk AT (2006) Formation of vortices near abrupt nano-channel height changes in electro-osmotic flow of aqueous solutions. Biomed Microdevices 8:325–330CrossRefGoogle Scholar
  47. Ramsey JM, Jacobsen SC, Knapp MR (1995) Microfabricated chemical measurement system. Nat Med 1:1093–1095CrossRefGoogle Scholar
  48. Sadr R, Yoda M, Zheng Z, Conlisk AT (2004) An experimental study of electroosmotic flow in rectangular microchannels. J Fluid Mech 506:357–367CrossRefGoogle Scholar
  49. Siddiqui AA, Lakhtakia A (2009) Steady electro-osmotic flow of a micropolar fluid in a microchannnel. Proc R Soc A 465:501–522CrossRefGoogle Scholar
  50. Singh KP, Guo C (2017) Current-voltage characteristics influenced by the nanochannel diameter and surface charge density in a fluidic field-effect-transistor. Phys Chem Chem Phys 19:15701CrossRefGoogle Scholar
  51. Tian F, Li B, Kwok DY (2005) Tradeoff between mixing and transport for electroosmotic flow in heterogeneous microchannels with nonuniform surface potentials. Langmuir 21:1126–1131CrossRefGoogle Scholar
  52. Wang PM, Wang J, Chen S (2008) On applicability of Poisson–Boltzmann equation in micro- and nanoscale electroosmotic flows. Commun Comput Phys 3:1087–1099Google Scholar
  53. Wu ZM, Zhao ZJ, Yang JX, Liu LP, Yang XL (2005) Frequency-modulation-type MI sensor with nanocrystalline ribbon core. Sens Actuators A Phys 121:430–433CrossRefGoogle Scholar
  54. Xia Q, Zhong S (2013) Liquid mixing enhanced by pulse width modulation in a Y-shaped jet configuration. Fluid Dyn Res 45:025504CrossRefGoogle Scholar
  55. Xie F, Wang Y, Wang W, Li Z, Yossifon G, Chang H-C (2010) Preparation of rhombus-shaped micro/nanofluidic channels with dimensions ranging from hundred nanometers to several micrometers. J Nanosci Nanotechnol 10(11):7277–7281CrossRefGoogle Scholar
  56. Xu Y (2018) Nanofluidics: a new arena for materials science. Adv Mater 30:1702419CrossRefGoogle Scholar
  57. Xu Z, Yang Y, Vadillo D, Ruan X, Fu X (2012) A mathematical model of mixing enhancement in microfluidic channel with a constriction under periodic electro-osmotic flow. Appl Phys Lett 100:0141907CrossRefGoogle Scholar
  58. Zheng Z, Hansford D, Conlisk AT (2003) Effect of multivalent ions on electroosmotic flow in micro- and nanochannels. Electrophoresis 24:3006–3017CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia
  2. 2.Institut für Thermodynamik der Luft- und RaumfahrtStuttgartGermany

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