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Electroosmosis with step changes in zeta potential in microchannels
Author(s) -
Horiuchi Keisuke,
Dutta Prashanta,
Ivory Cornelius F.
Publication year - 2007
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.11275
Subject(s) - microchannel , biharmonic equation , mechanics , stream function , laplace transform , laplace's equation , flow (mathematics) , heaviside step function , constant (computer programming) , potential flow , classical mechanics , mathematical analysis , physics , mathematics , partial differential equation , boundary value problem , vorticity , vortex , computer science , programming language
This article presents an analytical solution for two‐dimensional fluid flow in a rectangular microchannel in the vicinity of a step change in the zeta (ζ) potential. The stream function is determined from the creeping flow approximation to the Navier‐Stokes equations assuming a fixed volumetric axial flow, a constant electric field, and thin symmetric double layers. The resulting biharmonic equation is solved using a double‐sided Laplace transformation, which is then inverted by Heaviside expansion. The resulting series solution provides closed‐form expressions for the velocity and pressure fields that help explain how the recirculating flows generated by an abrupt change in the surface potential may contribute both locally and globally to the hydrodynamic dispersion in straight microchannels. © 2007 American Institute of Chemical Engineers AIChE J, 2007