Electroosmotic Fluid Motion and Late-Time Solute Transport for Large Zeta Potentials

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Abstract
Analytical and numerical methods are employed to determine the electric potential, fluid velocity, and late-time solute distribution for electroosmotic flow in a tube and channel at ζ potentials that are not necessarily small. The electric potential and fluid velocity are in general obtained by numerical means. In addition, new analytical solutions are presented for the velocity in a tube and channel in the extremes of large and small Debye layer thickness. The electroosmotic fluid velocity is used to analyze late-time transport of a neutral nonreacting solute. Zero- and first-order solutions describing axial variation of the solute concentration are determined analytically. The resulting expressions contain eigenvalues representing the dispersion and skewness of the axial concentration profiles. These eigenvalues and the functions describing transverse variation of the concentration field are determined numerically using a shooting technique. Results are presented for both tube and channel geometries over a wide range of the normalized Debye layer thickness and ζ potential. Simple analytical approximations to the eigenvalues are also provided for the limiting cases of large and small values of the Debye layer thickness.