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Journal of Engineering Mathematics

, Volume 114, Issue 1, pp 177–196 | Cite as

Time-dependent analysis of electroosmotic fluid flow in a microchannel

  • V. K. Narla
  • Dharmendra TripathiEmail author
  • G. P. Raja Sekhar
Article
  • 131 Downloads

Abstract

The present work models electroosmotic induced fluid flow in a microfluidic device. For theoretical analysis, the geometry of this device is considered as an asymmetric, narrow, wavy channel with charged surface. It is assumed that the length of the channel is finite and the characteristic wavelength is very large compared to the half width of the channel. The flow is assumed to be governed by Navier–Stokes equations augmented with electric body force. A transient two-dimensional flow analysis is presented by employing lubrication theory. Debye–Hückel linearization is adopted to obtain a general solution of Poisson–Boltzmann equation. The flow rate, velocity profile, pressure distribution, and wall shear stress are analyzed as functions of various parameters involved like zeta-potential ratio, Debye–Hückel parameter, etc. It is noted that the fluctuations in pressure and shear stress increase with the increasing zeta-potential ratio when the Helmholtz–Smoluchowski velocity is positive. The streamline pattern and the particle trajectories are analyzed to understand the trapping phenomenon and the retrograde motion. It is observed that the electroosmosis phenomenon drastically modulates the fluid flow in microchannels. Although the asymmetric nature of the wavy channel does not support active particle transport, the applied electric field enhances the particle motion favoring optimal conditions. It is observed that the extreme asymmetry of the wall motility reduces the net flow rate. Further, it is noticed that the asymmetry reduces the amplitudes of the pressure. This model can help toward designing artificial organs based on microfluidic devices which can also be applicable to analyze lumenal flow inside arteries and flow inside intrauterine system, and to implant the embryo at the best location in the uterus for human-assisted reproduction.

Keywords

Electroosmosis Particle retrograde motion Peristalsis Trapping 

Mathematics Subject Classification

35Q35 74M25 76Z05 

Notes

Acknowledgements

The first author gratefully acknowledges the support by Centre for Theoretical Studies (CTS), Indian Institute of Technology Kharagpur, India under a visitors’ program.

References

  1. 1.
    Lin B (ed) (2014) Microfluidics: technologies and applications. Elsevier, AmsterdamGoogle Scholar
  2. 2.
    Tovar-Lopez FJ, Rosengarten G, Westein E, Khoshmanesh K, Jackson SP, Mitchell A, Nesbitt WS (2010) A microfluidics device to monitor platelet aggregation dynamics in response to strain rate micro-gradients in flowing blood. Lab Chip 10(3):291CrossRefGoogle Scholar
  3. 3.
    Esch MB, King TL, Shuler ML (2011) The role of body-on-a-chip devices in drug and toxicity studies. Ann Rev Biomed Eng 13:55CrossRefGoogle Scholar
  4. 4.
    Koh CG, Kang X, Xie Y, Fei Z, Guan J, Yu B, Lee LJ (2009) Delivery of polyethylenimine/DNA complexes assembled in a microfluidics device. Mol Pharm 6(5):1333CrossRefGoogle Scholar
  5. 5.
    Zhang W, Choi DS, Nguyen YH, Chang J, Qin L (2013) Studying cancer stem cell dynamics on PDMS surfaces for microfluidics device design. Sci Rep 6(5):2332CrossRefGoogle Scholar
  6. 6.
    Bhatia SN, Ingber DE (2014) Microfluidic organs-on-chips. Nat Biotechnol 32(8):760CrossRefGoogle Scholar
  7. 7.
    Huh D, Matthews BD, Mammoto A, Montoya-Zavala M, Hsin HY, Ingber DE (2010) Reconstituting organ-level lung functions on a chip. Science 328:1662CrossRefGoogle Scholar
  8. 8.
    Kim HJ, Huh D, Hamilton G, Ingber DE (2012) Human gut-on-a-chip inhabited by microbial flora that experiences intestinal peristalsis-like motions and flow. Lab Chip 12(12):2165CrossRefGoogle Scholar
  9. 9.
    Wei-Xuan L, Guang-Tie L, Wei Y, Qiong Z, Wei W, Xiao-Mian Z, Da-Yu L (2013) Artificial uterus on a microfluidic chip. Chin J Anal Chem 41(4):467CrossRefGoogle Scholar
  10. 10.
    Chakraborty S (2006) Augmentation of peristaltic microflows through electro-osmotic mechanisms. J Phys D Appl Phys 39(24):5356CrossRefGoogle Scholar
  11. 11.
    Cho CC, Chen CL (2013) Characteristics of transient electroosmotic flow in microchannels with complex-wavy surface and periodic time-varying electric field. J Fluids Eng 135(2):021301CrossRefGoogle Scholar
  12. 12.
    Ghosh U, Chakraborty S (2015) Electroosmosis of viscoelastic fluids over charge modulated surfaces in narrow confinements. Phys Fluids 27(6):062004CrossRefGoogle Scholar
  13. 13.
    Si D, Jian Y (2015) Electromagnetohydrodynamic (EMHD) micropump of Jeffrey fluids through two parallel microchannels with corrugated walls. J Phys D Appl Phys 48(8):085501CrossRefGoogle Scholar
  14. 14.
    Goswami P, Chakraborty J, Bandopadhyay A, Chakraborty S (2016) Electrokinetically modulated peristaltic transport of power-law fluids. Microvasc Res 103:41CrossRefGoogle Scholar
  15. 15.
    Baier T, Schönfeld F, Hardt S (2011) Analytical approximations to the flow field induced by electroosmosis during isotachophoretic transport through a channel. J Fluid Mech 682:101CrossRefzbMATHGoogle Scholar
  16. 16.
    Huang C, Hsu H, Lee E (2012) Electrophoretic motion of a charged porous sphere within micro- and nanochannels. Phys Chem Chem Phys 14(2):657CrossRefGoogle Scholar
  17. 17.
    Park SY, Russo CJ, Branton D, Stone HA (2006) Eddies in a bottleneck: an arbitrary Debye length theory for capillary electroosmosis. J Colloid Interface Sci 297(2):832CrossRefGoogle Scholar
  18. 18.
    Datta S, Ghosal S, Patankar NA (2004) Electroosmotic flow in a rectangular channel with variable wall zeta-potential: comparison of numerical simulation with asymptotic theory. Electrophoresis 27:611CrossRefGoogle Scholar
  19. 19.
    Bandopadhyay A, Tripathi D, Chakraborty S (2016) Electroosmosis-modulated peristaltic transport in microfluidic channels. Phys Fluids 28:052002CrossRefGoogle Scholar
  20. 20.
    Tripathi D, Bhushan S, Bég OA (2016) Transverse magnetic field driven modification in unsteady peristaltic transport with electrical double layer effects. Colloids Surf A Physicochem Eng Aspects 506:32CrossRefGoogle Scholar
  21. 21.
    Shit GC, Ranjit NK, Sinha A (2016) Electro-magnetohydrodynamic flow of biofluid induced by peristaltic wave: a non-Newtonian model. J Bionic Eng 13(3):436CrossRefGoogle Scholar
  22. 22.
    Martinez L, Bautista O, Escandon J, Mendez F (2016) Electroosmotic flow of a Phan–Thien–Tanner fluid in a wavy-wall microchannel. Colloids Surf A Physicochem Eng Aspects 498:7CrossRefGoogle Scholar
  23. 23.
    Sinha A, Mondal A, Shit GC, Kundu PK (2016) Effect of heat transfer on rotating electroosmotic flow through a micro-vessel: haemodynamical applications. Heat Mass Transfer 52(8):1549CrossRefGoogle Scholar
  24. 24.
    Tripathi D, Jhorar R, Bég OA, Kadir A (2017) Electro-magneto-hydrodynamic peristaltic pumping of couple stress biofluids through a complex wavy micro-channel. J Mol Liq 236:358CrossRefGoogle Scholar
  25. 25.
    Tripathi D, Sharma A, Bég OA (2017) Electrothermal transport of nanofluids via peristaltic pumping in a finite micro-channel: Effects of Joule heating and Helmholtz-Smoluchowski velocity. Int J Heat Mass Transf 111:138CrossRefGoogle Scholar
  26. 26.
    Tripathi D, Yadav A, Bég OA (2017) Electro-kinetically driven peristaltic transport of viscoelastic physiological fluids through a finite length capillary: mathematical modeling. Math Biosci 283:155MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Tripathi D, Yadav A, Bég OA (2017) Electro-osmotic flow of couple stress fluids in a micro-channel propagated by peristalsis. Eur Phys J Plus 132:1CrossRefGoogle Scholar
  28. 28.
    Bhatti MM, Zeeshan A, Ellahi R, Ijaz N (2017) Heat and mass transfer of two-phase flow with Electric double layer effects induced due to peristaltic propulsion in the presence of transverse magnetic field. J Mol Liq 230:237CrossRefGoogle Scholar
  29. 29.
    Eytan O, Elad D (1999) Analysis of intra-uterine fluid motion induced by uterine contractions. Bull Math Biol 61(2):221CrossRefzbMATHGoogle Scholar
  30. 30.
    Beebe DJ, Glasgow IK, Wheeler MB, Zeringue H (2001) Microfluidic embryo and/or oocyte handling device and methodGoogle Scholar
  31. 31.
    Raty S, Walters EM, Davis J, Zeringue H, Beebe DJ, Rodriguez-Zas SL, Wheeler MB (2004) Embryonic development in the mouse is enhanced via microchannel culture. Lab Chip 4(3):186CrossRefGoogle Scholar
  32. 32.
    Garfield RE, Carp H, Maner WL (2013) Uterine elecrical simulation system and methodGoogle Scholar
  33. 33.
    Karniadakis GE, Beskok A, Narayan A (2008) Microflows and nanoflows—fundamentals and simulation. New Age International Publisher, New DelhizbMATHGoogle Scholar
  34. 34.
    Kirby BJ, Hasselbrink EF (2004) Zeta potential of microfluidic substrates. II. Data for polymers. Electrophoresis 25:203CrossRefGoogle Scholar
  35. 35.
    Truskey GA, Yuan F, Katz DF (2004) Transport phenomena in biological systems. Pearson Prentice Hall, New JerseyGoogle Scholar
  36. 36.
    Aranda V, Cortez R, Fauci L (2011) Stokesian peristaltic pumping in a three-dimensional tube with a phase-shifted asymmetry. Phys Fluids 23:081901CrossRefzbMATHGoogle Scholar
  37. 37.
    Aranda V, Cortez R, Fauci L (2015) A model of Stokesian peristalsis and vesicle transport in a three-dimensional closed cavity. J Biomech 48:1631CrossRefGoogle Scholar
  38. 38.
    Boyarski S, Gottschalk C, Tanagho E, Zimskind P (1971) Urodynamics: hydrodynamics of the ureter and renal pelvis. Academic Press, New YorkGoogle Scholar
  39. 39.
    Li M, Brasseur JG (1993) Non steady peristaltic transport in finite length tubes. J Fluid Mech 248:129CrossRefzbMATHGoogle Scholar
  40. 40.
    Takabatake S, Ayukawa K, Mori A (1988) Peristaltic pumping in circular cylindrical tubes : a numerical study of fluid transport and its efficiency. J Fluid Mech 193:267CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • V. K. Narla
    • 1
  • Dharmendra Tripathi
    • 2
    Email author
  • G. P. Raja Sekhar
    • 3
  1. 1.Department of MathematicsGITAM School of TechnologyHyderabadIndia
  2. 2.Department of Sciences and HumanitiesNational Institute of TechnologySrinagarIndia
  3. 3.Department of MathematicsIndian Institute of TechnologyKharagpurIndia

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