Journal of Fluid Mechanics

Papers

Analytical approximations to the flow field induced by electroosmosis during isotachophoretic transport through a channel

TOBIAS BAIERa1 c1, FRIEDHELM SCHÖNFELDa2 and STEFFEN HARDTa1

a1 Center of Smart Interfaces, TU Darmstadt, Petersenstraße 32, 64287 Darmstadt, Germany

a2 Hochschule RheinMain, Fachbereich Ingenieurwissenschaften, Am Brückweg 26, 65428 Rüsselsheim, Germany

Abstract

An analytical approximation is derived for the flow field in the vicinity of a transition zone between electrolytes of different mobility in isotachophoretic transport through a channel. Due to the difference in electroosmotic mobility and electric field on both sides of the transition zone, the flow field consists of a superposition of electroosmotic and pressure-driven flow. The corresponding convective ion transport inherently reduces the resolution of isotachophoretic separation processes. The derived analytical result is adequate for both wide and narrow transition zones and valid in the limit of thin electric double layers, relevant for most situations where isotachophoresis is employed. In this way, it complements and generalizes the results obtained for wide transition zones in the lubrication approximation. The analysis is extended to multiple sample zones with ions of different electrophoretic mobility, a scenario characteristic for applications in the field of analytical chemistry. The results are validated by comparison to finite-element calculations accounting for the transport of different ionic species governed by the coupled Nernst–Planck and Stokes equations, both for situations with only a single transition zone as well as for several transition zones. Excellent agreement is obtained between the analytical and the numerical results for realistic parameter values encountered in ITP experiments. This suggests using the analytical expression for the flow field in the framework of numerical studies of species transport in ITP experiments, since the time-consuming computation of the velocity field is essentially eliminated. The latter is successfully demonstrated using an iterative procedure, numerically solving the Nernst–Planck equation for a given flow field, and using the resulting concentration fields as an input for the derived analytical expression.

(Received January 24 2011)

(Revised April 06 2011)

(Accepted May 30 2011)

(Online publication July 19 2011)

Key words:

  • low-Reynolds-number flows;
  • MHD and electrohydrodynamics;
  • microfluidics

Correspondence:

c1 Email address for correspondence: baier@csi.tu-darmstadt.de

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