Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-22T14:16:26.307Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  19 July 2011

TOBIAS BAIER ,
FRIEDHELM SCHÖNFELD  and
STEFFEN HARDT
TOBIAS BAIER*
Affiliation:
Center of Smart Interfaces, TU Darmstadt, Petersenstraße 32, 64287 Darmstadt, Germany
FRIEDHELM SCHÖNFELD
Affiliation:
Hochschule RheinMain, Fachbereich Ingenieurwissenschaften, Am Brückweg 26, 65428 Rüsselsheim, Germany
STEFFEN HARDT
Affiliation:
Center of Smart Interfaces, TU Darmstadt, Petersenstraße 32, 64287 Darmstadt, Germany
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows MHD and Electrohydrodynamics: MHD and Electrohydrodynamics Micro-/Nano-fluid dynamics: Microfluidics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 682 , 10 September 2011 , pp. 101 - 119
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ajdari, A. 1996 Generation of transverse fluid currents and forces by an electric field: Electro-osmosis on charge-modulated and undulated surfaces. Phys. Rev. E 53 (5), 4996–5005.Google ScholarPubMed
Bharadwaj, R. & Santiago, J. G. 2005 Dynamics of field-amplified sample stacking. J. Fluid Mech. 543, 57–92.CrossRefGoogle Scholar
Chen, L., Prest, J. E., Fielden, P. R., Goddard, N. J., Manz, A. & Day, P. J. R. 2006 Miniaturised isotachophoresis analysis. Lab Chip 6, 474–487.CrossRefGoogle ScholarPubMed
Cui, H., Dutta, P. & Ivory, C. F. 2007 Isotachophoresis of proteins in a networked microfluidic chip: Experiment and 2-D simulation. Electrophoresis 28, 1138–1145.Google Scholar
Everaerts, F. M., Beckers, J. L. & Verheggen, T. P. 1976 Isotachophoresis. Elsevier.Google Scholar
Gebauer, P., Mala, Z. & Bocek, P. 2009 Recent progress in analytical capillary ITP. Electrophoresis 30 (1), 29–35.Google Scholar
Ghosal, S. 2002 a Band broadening in a microcapillary with a stepwise change in the ζ-potential. Anal. Chem. 74 (16), 4198–4203.CrossRefGoogle Scholar
Ghosal, S. 2002 b Lubrication theory for electro-osmotic flow in a microfluidic channel of slowly varying cross-section and wall charge. J. Fluid Mech. 459, 103–128.Google Scholar
Ghosal, S. 2006 Electrokinetic flow and dispersion in capillary electrophoresis. Annu. Rev. Fluid Mech. 38, 309–338.CrossRefGoogle Scholar
Graß, B., Neyer, A., Jöhnck, M., Siepe, D., Eisenbeiss, F., Weber, G. & Hergenröder, R., 2001 A new PMMA-microchip device for isotachophoresis with integrated conductivity detector. Sensors Actuators B 72 249–258.CrossRefGoogle Scholar
Herr, A. H., Molho, J. I., Santiago, J. G., Mungal, M. G., Kenny, T. W. & Garguilo, M. G. 2000 Electroosmotic capillary flow with non-uniform ζ-potential. Anal. Chem. 72 (5), 1053–1057.CrossRefGoogle Scholar
Horiuchi, K., Dutta, P. & Ivory, C. F. 2007 Electroosmosis with step changes in zeta potential in microchannel electrophoresis. AIChE J. 53 (10), 2521–2533.Google Scholar
Hruška, V. & Gaš, B. 2007 Kohlrausch regulating function and other conservation laws in electrophoresis. Electrophoresis 28, 3–14.CrossRefGoogle ScholarPubMed
Huang, H., Xu, F., Dai, Z. & Lin, B. 2005 On-line isotachophoretic preconcentration and gel electrophoretic separation of sodium dodecyl sulfate-proteins on a microchip. Electrophoresis 26, 2254–2260.Google Scholar
Joseph, D. D. 1977 The convergence of biorthogonal series for biharmonic and Stokes flow edge problems, Part I. SIAM J. Appl. Math. 33, 337–347.CrossRefGoogle Scholar
Jung, B., Bharadwaj, R. & Santiago, J. G. 2006 On-chip millionfold sample stacking using transient isotachophoresis. Anal. Chem. 78, 2319–2327.CrossRefGoogle ScholarPubMed
Khurana, T. K. & Santiago, J. G. 2008 a Preconcentration, separation, and indirect detection of nonfluorescent analytes using fluorescent mobility markers. Anal. Chem. 80, 279–287.Google Scholar
Khurana, T. K. & Santiago, J. G. 2008 b Sample zone dynamics in peak mode isotachophoresis. Anal. Chem. 80, 6300–6307.CrossRefGoogle ScholarPubMed
Kirby, B. J. & Hasselbrink, E. F. 2004 a Zeta potential of microfluidic substrates: 1. Theory, experimental techniques, and effects on separations. Electrophoresis 25, 187–202.CrossRefGoogle ScholarPubMed
Kirby, B. J. & Hasselbrink, E. F. 2004 b Zeta potential of microfluidic substrates: 2. Data for polymers. Electrophoresis 25, 203–213.CrossRefGoogle ScholarPubMed
Kohlrausch, F. 1897 Über Concentrations-Verschiebungen durch Electrolyse im Innern von Lösungen und Lösungsgemischen. Ann. Phys. 298 (10), 209–239.CrossRefGoogle Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics, 2nd edn (revised). Pergamon.Google Scholar
Lin, C. C., Hsu, B. K. & Chen, S. H. 2008 Integrated isotachophoretic stacking and gel electrophoresis on a plastic substrate and variations in detection dynamic range. Electrophoresis 29, 1228–1236.CrossRefGoogle ScholarPubMed
Long, D., Stone, H. A. & Ajdari, A. 1999 Electroosmotic flows created by surface defects in capillary electrophoresis. J. Colloid Interface Sci. 212, 338–349.CrossRefGoogle ScholarPubMed
MacInnes, D. A. & Longsworth, L. G. 1932 Transference numbers by the method of moving boundaries. Chem. Rev. 11, 171–230.CrossRefGoogle Scholar
Meleshko, V. V. 1996 Steady stokes flow in a rectangular cavity. Proc. R. Soc. Lond. A 452, 1999–2022.Google Scholar
Newman, J. S. & Thomas-Alyea, K. E. 2004 Electrochemical Systems, 3rd edn. Wiley.Google Scholar
Ölvecka, E., Masar, M., Kaniansky, D., Jöhnck, M. & Stanislawski, B. 2001 Isotachophoresis separations of enantiomers on a planar chip with coupled separation channels. Electrophoresis 22, 3347–3353.3.0.CO;2-F>CrossRefGoogle ScholarPubMed
Qian, S. & Bau, H. H. 2002 A chaotic electroosmotic stirrer. Anal. Chem. 74, 3616–3625.Google Scholar
Reza Mohamadi, M., Kaji, N., Tokeshi, M. & Baba, Y. 2007 Online preconcentration by transient isotachophoresis in linear polymer on a poly(methyl methacrylate) microchip for separation of human serum albumin immunoassay mixtures. Anal. Chem. 79, 3667–3672.CrossRefGoogle Scholar
Saville, D. A. 1990 The effects of electroosmosis on the structure of isotachophoresis boundaries. Electrophoresis 11, 899–902.CrossRefGoogle ScholarPubMed
Schönfeld, F., Goet, G., Baier, T. & Hardt, S. 2009 Transition zone dynamics in combined isotachophoretic and electroosmotic transport. Phys. Fluids 21, 092002.CrossRefGoogle Scholar
Smith, R. T. C. 1952 The bending of a semi-infinite strip. Austral. J. Sci. Res. A 5, 227–237.Google Scholar
Sounart, T. L. & Baygents, J. C. 2001 Electrically-driven fluid motion in channels with streamwise gradients of the electrical conductivity Colloids Surf. A 195, 59–75.CrossRefGoogle Scholar
Sounart, T. L. & Baygents, J. C. 2007 Lubrication theory for electro-osmotic flow in a non-uniform electrolyte. J. Fluid Mech. 576, 139–172.Google Scholar
Towns, J. K. & Regnier, F. E. 1992 Impact of polycation adsorption on efficiency and electroosmotically driven transport in capillary electrophoresis. Anal. Chem. 64, 2473–2478.Google Scholar
Walker, P. A., Morris, M. D., Burns, M. A. & Johnson, B. N. 1998 Isotachophoretic separations on a microchip. Normal Raman spectroscopy detection Anal. Chem. 70, 3766–3769.Google Scholar
Supplementary material: PDF

Baier et al. supplementary material

Appendices

Download Baier et al. supplementary material(PDF)
PDF 569.1 KB