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Unsteady electroosmosis in a microchannel with Poisson–Boltzmann charge distribution
Author(s) -
Chang Chien C.,
Kuo ChihYu,
Wang ChangYi
Publication year - 2011
Publication title -
electrophoresis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.666
H-Index - 158
eISSN - 1522-2683
pISSN - 0173-0835
DOI - 10.1002/elps.201100181
Subject(s) - electrokinetic phenomena , microchannel , electro osmosis , mechanics , poisson's equation , poisson–boltzmann equation , amplitude , physics , thermodynamics , chemistry , electrophoresis , ion , optics , chromatography , quantum mechanics
The present study is concerned with unsteady electroosmotic flow (EOF) in a microchannel with the electric charge distribution described by the Poisson–Boltzmann (PB) equation. The nonlinear PB equation is solved by a systematic perturbation with respect to the parameter λ which measures the strength of the wall zeta potential relative to the thermal potential. In the small λ limits (λ≪1), we recover the linearized PB equation – the Debye–Hückel approximation. The solutions obtained by using only three terms in the perturbation series are shown to be accurate with errors <1% for λ up to 2. The accurate solution to the PB equation is then used to solve the electrokinetic fluid transport equation for two types of unsteady flow: transient flow driven by a suddenly applied voltage and oscillatory flow driven by a time‐harmonic voltage. The solution for the transient flow has important implications on EOF as an effective means for transporting electrolytes in microchannels with various electrokinetic widths. On the other hand, the solution for the oscillatory flow is shown to have important physical implications on EOF in mixing electrolytes in terms of the amplitude and phase of the resulting time‐harmonic EOF rate, which depends on the applied frequency and the electrokinetic width of the microchannel as well as on the parameter λ.