Skip to main content
SpringerLink
Log in

Electroosmotic flows in an electric double layer overlapped channel with rectangle-waved surface roughness

  • Research Paper
  • Published:
Microfluidics and Nanofluidics Aims and scope Submit manuscript

Abstract

To further understand the wall-roughness effect, the present study has performed numerical simulations, by employing the Poisson–Nernst–Planck model, on the two-dimensional electroosmotic flow in a plane channel with dielectric walls of rectangle-waved surface roughness where the two electric double layers (EDLs) are overlapped. Results show that the steady electroosmotic flow and ionic-species transport depend significantly on the shape of the surface roughness such as the amplitude and periodic length of wall wave, but their characteristics are basically different from those in the case where the EDLs are not overlapped at all (Kang and Suh in Microfluid Nanofluid, doi:10.1007/s10404-008-0321-5, 2008). It is found that the fluid flows over the waved wall (or wall roughness) with involving a separation or recirculation of flow in the cavity, which resembles much the traditional pressure-driven flow. In addition, the flow characteristics are determined chiefly by the level of the electric-charge density in the bulk region above the waved wall. As a result, with increasing wall-wave amplitude (0.01 ≤ h/H ≤ 0.2), the flow rate increases due to the enhanced amount of electric charges released from the enlarged wet surface at low amplitudes and then decreases due to the reduced flow-passage area at high amplitudes above a certain critical value. With increasing periodic length (0.2 ≤ L/H ≤ 1.2), on the other hand, the flow rate decreases in a hyperbolic fashion due to the reduced amount of electric charges.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Abbreviations

C p , C m :

nondimensional concentrations

C 0 :

molar ionic concentration in the bulk region (mol/m3)

D p , D m , D :

ionic diffusion coefficients (m2/s)

E i :

nondimensional total electric field

E 0 :

mean external streamwise electric field (V/m)

F :

Faraday constant (=96,485.338,3 C/mol)

F e,i :

nondimensional total electric force

F e,ϕ,i :

nondimensional force due to the external electric field

F e,ψ,i :

nondimensional force due to the induced electric field

H :

channel half-width (m)

h :

nondimensional amplitude of wall wave

L :

nondimensional periodic length of wall wave

P :

nondimensional mean pressure

Pe :

Peclet number (=U eo H/D)

p :

nondimensional pressure

Q :

nondimensional flow rate

Q * :

real flow rate (m3/s)

R :

gas constant (=8.314 J/Kmol)

Sc :

Schmidt number (=ν/D)

T :

absolute temperature (K)

t :

nondimensional time

U eo :

electroosmotic velocity [=ɛζ0 E 0/ρν, m/s]

u i :

nondimensional velocity

x i :

nondimensional Cartesian coordinates

z p , z m , z :

ionic valences

β:

nondimensional parameter (=PeΩ)

ɛ:

fluid permittivity (C/Vm)

ζ0 :

reference zeta potential (V)

ζ *0 :

nondimensional reference zeta potential (=−zFζ0/RT)

κ:

nondimensional EDL thickness (=λ/H)

Λ:

aspect ratio of the cavity (=4h/L)

λ:

EDL thickness [=(ɛRT/2F 2 z 2 C 0)1/2, m]

ν:

fluid kinematic viscosity (m2/s)

ρ:

fluid density (kg/m3)

ρ e :

nondimensional volumetric electric-charge density

σ0 :

surface electric-charge density (C/m2)

Φ:

nondimensional total electric potential

ϕ:

nondimensional external electric potential

ψ:

nondimensional induced electric potential

Ω:

nondimensional parameter (=ζ0/E 0 H)

cr:

critical

i, j :

coordinate indices (1, 2)

m :

anions

n :

wall-normal direction

p :

cations

t :

wall-tangential direction

References

  • Chakraborty S (2007a) Towards a generalized representation of surface effects on pressure-driven liquid flow in microchannels. Appl Phys Lett 90:034108

    Article  Google Scholar 

  • Chakraborty S (2007b) Order parameter modeling of fluid dynamics in narrow confinements subjected to hydrophobic interactions. Phys Rev Lett 99:094504

    Article  Google Scholar 

  • Chakraborty S (2008) Generalization of interfacial electrohydrodynamics in the presence of hydrophobic interactions in narrow fluidic confinements. Phys Rev Lett 100:097801

    Article  Google Scholar 

  • Chakraborty S, Anand KD (2008) Implications of hydrophobic interactions and consequent apparent slip phenomenon on the entrance region transport of liquids through microchannels. Phys Fluids 20:043602

    Article  Google Scholar 

  • Chakraborty S, Padhy S (2008) Induced pressure gradients due to entrance and exit effects in electroosmotically driven flows through nanopores within the continuum regime. J Phys D Appl Phys 41:065502

    Article  Google Scholar 

  • Chakraborty S, Srivastava AK (2007) Generalized model for time periodic electroosmotic flows with overlapping electrical double layers. Langmuir 23:12421–12428

    Article  Google Scholar 

  • Fu L-M, Lin J-Y, Yang R-J (2003) Analysis of electroosmotic flow with step change in zeta potential. J Colloid Interface Sci 258:266–275

    Article  Google Scholar 

  • Hlushkou D, Kandhai D, Tallarek U (2004) Coupled lattice-Boltzmann and finite-difference simulation of electroosmosis in microfluidic channels. Int J Numer Meth Fluids 46:507–532

    Article  MATH  Google Scholar 

  • Hu Y, Werner C, Li D (2003) Electrokinetic transport through rough microchannels. Anal Chem 75:5747–5758

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Hu Y, Xuan X, Werner C, Li D (2007) Electroosmotic flow in microchannels with prismatic elements. Microfluid Nanofluid 3:151–160

    Article  Google Scholar 

  • Huang K-D, Yang R-J (2007) Electrokinetic behavior of overlapped electric double layers in nanofluidic channels. Nanotechnology 18:115701

    Article  Google Scholar 

  • Kang S, Suh YK (2006) Unsteady electroosmotic channel flows with the nonoverlapped and overlapped electric double layers. J Mech Sci Technol 20:2250–2264

    Article  Google Scholar 

  • Kang S, Suh YK (2008) Numerical analysis on electroosmotic flows in a microchannel with rectangle-waved surface roughness using the Poisson–Nernst–Planck model. Microfluid Nanofluid. doi:10.1007/s10404-008-0321-5

  • Keh HJ, Tseng HC (2001) Transient electrokinetic flow in fine capillaries. J Colloid Interface Sci 242:450–459

    Article  Google Scholar 

  • Kim D, Darve E (2006) Molecular dynamics simulation of electro-osmotic flows in rough wall nanochannels. Phys Rev E 73:051203

    Article  Google Scholar 

  • Kwak HS, Hasselbrink Jr EF (2005) Timescales for relaxation to Boltzmann equilibrium in nanopores. J Colloid Interface Sci 284:753–758

    Article  Google Scholar 

  • Li D (2004) Electrokinetics in microfluidics. Elsevier, London

    Google Scholar 

  • Lin JY, Fu LM, Yang RJ (2002) Numerical simulation of electrokinetic focusing in microfluidic chips. J Micromech Microeng 12:955–961

    Article  Google Scholar 

  • 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 297:832–839

    Article  Google Scholar 

  • Park HM, Lee JS, Kim TW (2007) Comparison of the Nernst–Planck model and the Poisson–Boltzmann model for electroosmotic flows in microchannels. J Colloid Interface Sci 315:731–739

    Article  Google Scholar 

  • Patankar NA, Hu HH (1998) Numerical simulation of electroosmotic flow. Anal Chem 70:1870–1881

    Article  Google Scholar 

  • Qiao R (2007) Effects of molecular level surface roughness on electroosmotic flow. Microfluid Nanofluid 3:33–38

    Article  MathSciNet  Google Scholar 

  • Qu W, Li D (2000) A model for overlapped EDL fields. J Colloid Interface Sci 224:397–407

    Article  Google Scholar 

  • Stroock AD, Dertinger SKW, Ajdari A, Mezić I, Stone HA, Whitesides GM (2002) Chaotic mixer for microchannels. Science 295:647–651

    Article  Google Scholar 

  • Talapatra S, Chakraborty S (2008) Double layer overlap in AC electroosmosis. Eur J Mech B Fluid 27:297–308

    Article  MATH  Google Scholar 

  • van der Heyden FHJ, Stein D, Dekker C (2005) Streaming currents in a single nanofluidic channel. Phys Rev Lett 95:116104

    Article  Google Scholar 

  • Wang M, Wang J, Chen S (2007) Roughness and cavitations effects on electro-osmotic flows in rough microchannels using the lattice Poisson–Boltzmann methods. J Comput Phys 226:836–851

    Article  MATH  Google Scholar 

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

    Google Scholar 

  • Yang R-J, Fu L-M, Hwang C-C (2001) Electroosmotic entry flow in a microchannel. J Colloid Interface Sci 244:173–179

    Article  Google Scholar 

Download references

Acknowledgments

This work has been supported by the Korea Science and Engineering Foundation (KOSEF) through the National Research Laboratory Program funded by the Ministry of Education, Science and Technology (No. 2005-1091).

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Dong-A University, 840, Hadan2-dong, Saha-gu, Pusan, 604-714, Republic of Korea

    Sangmo Kang & Yong Kweon Suh

Authors
  1. Sangmo Kang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yong Kweon Suh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sangmo Kang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kang, S., Suh, Y.K. Electroosmotic flows in an electric double layer overlapped channel with rectangle-waved surface roughness. Microfluid Nanofluid 7, 337–352 (2009). https://doi.org/10.1007/s10404-008-0384-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10404-008-0384-3

Keywords

Search

Navigation