On the time development of dispersion in electroosmotic flow through a rectangular channel

Abstract

This is an analytical study on the time development of hydrodynamic dispersion of an inert species in electroosmotic flow through a rectangular channel. The objective is to determine how the channel side walls may affect the dispersion coefficient at different instants of time. To this end, the generalized dispersion model, which is valid for short and long times, is employed in the present study. Analytical expressions are derived for the convection and dispersion coefficients as functions of time, the aspect ratio of the channel, and the Debye-Huckel parameter representing the thickness of the electric double layer. For transport in a channel of large aspect ratio, the dispersion may undergo several stages of transience. The initial, fast time development is controlled by molecular diffusion across the narrow channel height, while the later, slower time development is governed by diffusion across the wider channel breadth. For a sufficiently large aspect ratio, there can be an interlude between these two periods during which the coefficient is nearly steady, signifying the resemblance of the transport to that in a parallel-plate channel. Given a sufficiently long time, the dispersion coefficient will reach a fully-developed steady value that may be several times higher than that without the side wall effects. The time scales for these periods of transience are identified in this paper.