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Study of EDL effect on 3‐D developing flow in microchannel with Poisson–Boltzmann and Nernst–Planck models
Author(s) -
Ng E. Y. K.,
Tan S. T.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1965
Subject(s) - microchannel , mechanics , flow (mathematics) , nernst equation , boltzmann equation , momentum (technical analysis) , physics , thermodynamics , quantum mechanics , electrode , finance , economics
Microchannels have been suggested to be a very effective heat transfer device. However, the electrical double layer (EDL) effect in a microchannel is anticipated to be significant. In this paper, two EDL models coupled with Navier–Stokes equations were used to compute a 3‐D developing microchannel flow. The Poisson–Boltzmann model (PBM) has been proven to be a promising tool in studying the EDL effect for developed microchannel flow, with respect to its accuracy and efficiency. However, it was commended that the assumption of Boltzmann distribution in PBM, for electric ion concentration distribution in particular was questionable in the developing flow. Nernst–Planck model (NPM), with its two extra partial differential equations (PDEs) to predict the ion concentration distribution, was reported to be a more appropriate model for developing microchannel flow though increased RAM and CPU were needed as compared to the PBM. The governing equations for both models were discretized for developing rectangular microchannel flows in Cartesians co‐ordinate. An additional source term, related to the electric potential, resulting from the EDL effect was introduced in the conventional z ‐axis momentum equation as a body force, thereby modifying the flow characteristics. A finite‐volume scheme was used to solve the PDEs. The discrepancy in the results predicted by the two models was more dominant in the near‐wall region and not in the mainstream region. However, the performance of the microchannel was significantly affected by the EDL effect. An increase in Schmidt number will lead to decrease in friction coefficient. For the effect of aspect ratios (ARs), the discrepancy of f Re and Nu values for different ARs was obvious. Therefore, a 3‐D analysis was concluded to be important and necessary for investigating the EDL effect in microchannels. Copyright © 2006 John Wiley & Sons, Ltd.