Analytical solutions for species transport in a T‐sensor at low peclet numbers

Abstract

A 3D analytical solution is presented for the problem of mass transport in a T‐sensor by taking the axial diffusion effects into account. The solution methodology is based on an eigenfunction expansion of the solute concentration and enjoys the variational calculus for the solution of the associated eigenvalue problem. The method is capable of handling a mixed electroosmotic and pressure‐driven velocity profile and is executed assuming a rectangular channel cross‐section although it can be easily extended to more complex geometries. Two simplified models, one based on a uniform velocity profile, valid for the channel half height to Debye length ratios of above 100, and the other based on a depthwise averaging of the species concentration to be used for cases in which the channel width to height ratio is above 5 are also presented. As a part of the latter, expressions are derived for the Taylor dispersion coefficient of the mixed flow in a slit microconduit. The most interesting finding of this study is that, when the diffusion mechanism significantly contributes to the axial movement of the species, the well‐known heterogeneous mass transport evolves into a nearly uniform pattern in the depthwise direction and the mixing length noticeably increases. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4119–4130, 2016