Transient electroosmotic flow of general Maxwell fluids through a slit microchannel

  • Yongjun Jian
  • Jie Su
  • Long Chang
  • Quansheng Liu
  • Guowei He
Article

Abstract

Using Laplace transform method, semi-analytical solutions are presented for transient electroosmotic flow of Maxwell fluids between micro-parallel plates. The solution involves solving the linearized Poisson–Boltzmann equation, together with the Cauchy momentum equation and the Maxwell constitutive equation considering the depletion effect produced by the interaction between macro-molecules of the Maxwell fluids and the channel surface. The overall flow is divided into depletion layer and bulk flow outside of depletion layer. In addition, the Maxwell stress is incorporated to describe the boundary condition at the interface. The velocity expressions of these two layers were obtained respectively. By numerical computations of inverse Laplace transform, the influences of viscosity ratio μ, density ratio ρ, dielectric constant ratio \({\varepsilon}\) of layer II to layer I, relaxation time \({{\bar{\lambda}}_1}\), interface charge density jump Q, and interface zeta potential difference \({\Delta {\bar{\psi}}}\) on transient velocity amplitude are presented.

Mathematics Subject Classification (2000)

76A05 76D05 76W05 

Keywords

Electric double layer (EDL) Unsteady electroosmotic flow (EOF) Maxwell fluids Micro-parallel plates Laplace transform 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Yongjun Jian
    • 1
  • Jie Su
    • 1
  • Long Chang
    • 1
    • 2
  • Quansheng Liu
    • 1
  • Guowei He
    • 3
  1. 1.School of Mathematical ScienceInner Mongolia UniversityHohhotChina
  2. 2.School of Mathematics and StatisticsInner Mongolia University of Finance and EconomicsHohhotChina
  3. 3.The State Key Laboratory of Nonlinear Mechanics (LNM)Institute of Mechanics, Chinese Academy of SciencesBeijingChina

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