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


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.


Electroosmosis Particle retrograde motion Peristalsis Trapping 

Mathematics Subject Classification

35Q35 74M25 76Z05 



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


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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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