Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-06T06:48:00.620Z Has data issue: false hasContentIssue false
  • English
  • Français

Lubrication theory for electro-osmotic flow in a non-uniform electrolyte

Published online by Cambridge University Press:  28 March 2007

T. L. SOUNART  and
J. C. BAYGENTS
T. L. SOUNART*
Affiliation:
Department of Chemical and Environmental Engineering, The University of Arizona, Tucson, AZ 85721, USA
J. C. BAYGENTS
Affiliation:
Department of Chemical and Environmental Engineering, The University of Arizona, Tucson, AZ 85721, USA
*
†Author to whom correspondence should be addressed. Present address: Intel Corporation, 4500 Dobson Rd, Chandler, AZ 85248, USA. [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A lubrication theory has been developed for the electro-osmotic flow of non-uniform buffers in narrow rectilinear channels. The analysis applies to systems in which the transverse dimensions of the channel are large compared with the Debye screening length of the electrolyte. In contrast with related theories of electrokinetic lubrication, here the streamwise variations of the velocity field stem from, and are nonlinearly coupled to, spatiotemporal variations in the electrolyte composition. Spatially non-uniform buffers are commonly employed in electrophoretic separation and transport schemes, including iso-electric focusing (IEF), isotachophoresis (ITP), field-amplified sample stacking (FASS), and high-ionic-strength electro-osmotic pumping. The fluid dynamics of these systems is controlled by a complex nonlinear coupling to the ion transport, driven by an applied electric field. Electrical conductivity gradients, attendent to the buffer non-uniformities, result in a variable electro-osmotic slip velocity and, in electric fields approaching 1 kV cm−1, Maxwell stresses drive the electrohydrodynamic circulation. Explicit semi-analytic expressions are derived for the fluid velocity, stream function, and electric field. The resulting approximations are found to be in good agreement with full numerical solutions for a prototype buffer, over a range of conditions typical of microfluidic systems. The approximations greatly simplify the computational analysis, reduce computation times by a factor 4–5, and, for the first time, provide general insight on the dominant fluid physics of two-dimensional electrically driven transport.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 576 , 10 April 2007 , pp. 139 - 172
Copyright
Copyright © Cambridge University Press 2007

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: Electroosmosis on charge-modulated and undulated surfaces. Phys. Rev. E 53, 4996–5005.Google ScholarPubMed
Anderson, J. L. & Idol, W. K. 1985 Electroosmosis through pores with non-uniformly charged walls. Chem. Engng Commun. 38, 93–106.CrossRefGoogle Scholar
Beckers, J. L. & Boček, P. 2000 Sample stacking in capillary zone electrophoresis: Principles, advantages and limitations. Electrophoresis 21, 2747–2767.3.0.CO;2-Z>CrossRefGoogle ScholarPubMed
Bharadwaj, R. & Santiago, J. G. 2005 Dynamics of field amplified sample stacking. J. Fluid Mech. 543, 57–92.CrossRefGoogle Scholar
Bier, M., Palusinski, O. A., Mosher, R. A. & Saville, D. A. 1983 Electrophoresis: Mathematical modeling and computer simulation. Science 219, 1281–1287.CrossRefGoogle ScholarPubMed
Bjorstad, P. 1983 Fast numerical-solution of the biharmonic Dirichlet problem on rectangles. SIAM J. Numer. Anal. 20, 59–71.CrossRefGoogle Scholar
Boris, J. P., Landsberg, A. M., Oran, E. S. & Gardner, J. H. 1993 LCPFCT – Flux-Corrected Transport Algorithm for Solving Generalized Continuity Equations. NRL Mem. Rep. 6410-93-7192. Naval Research Laboratory, Washington.CrossRefGoogle Scholar
Bousse, L., Cohen, C., Nikiforov, T., Chow, A., Kopf-Sill, A. R., Dubrow, R. & Parce, J. W. 2000 Electrokinetically controlled microfluidic analysis systems. Annu. Rev. Biophys. Biom. 29, 155–181.CrossRefGoogle ScholarPubMed
Burgi, D. S. & Chien, R.-L. 1991 Optimization in sample stacking for high-performance capillary electrophoresis. Anal. Chem. 63, 2043–2047.CrossRefGoogle Scholar
Gebauer, P. & Bocek, P. 2002 Recent progress in capillary isotachophoresis. Electrophoresis 23, 3858–3864.CrossRefGoogle ScholarPubMed
Ghosal, S. 2002 Lubrication theory for electro-osmotic flow in a microfluidic channel of slowly varying cross-section and wall charge. J. Fluid Mech. 459, 103–128.CrossRefGoogle Scholar
Ghosal, S. 2003 The effect of wall interactions in capillary-zone electrophoresis. J. Fluid Mech. 491, 285–300.CrossRefGoogle Scholar
Ghosal, S. 2004 Fluid mechanics of electro-osmotic flow and its effect on band broadening in capillary electrophoresis. Electrophoresis 25, 214–228.CrossRefGoogle Scholar
Gottlieb, D. 1972 Strang-type difference schemes for multidimensional problems. SIAM J. Numer. Anal. 9, 650–661.CrossRefGoogle Scholar
von Helmholtz, H. 1879 Stüdien Über electrische grenschichten. Ann. Phys. 7, 337–387.CrossRefGoogle Scholar
Ikuta, N. & Hirokawa, T. 1998 Numerical simulation for capillary electrophoresis I. Development of a simulation program with high numerical stability. J. Chromatogr. A 802, 49–57.CrossRefGoogle Scholar
Kasicka, V. 1997 Theoretical bases and separation principles of capillary electromigration methods. Chemicke Listy 91, 320–329.Google Scholar
Leal, L. G. 1992 Laminar Flow and Convective Transport Processes. Butterworth-Heinemann.Google Scholar
Long, D., Stone, H. A. & Ajdari, A. 1999 Electro-Osmotic flows created by surface defects in capillary electrophoresis. J. Colloid Interface Sci. 212, 338–349.CrossRefGoogle Scholar
Martens, J. H. P., Reijenga, A., BoonkkampJ. C., ten Thije J. C., ten Thije, Mattheij, J. H. M., , R. M. M. & Everaerts, F. M. 1997 Transient modelling of capillary electrophoresis isotachophoresis. J. Chromatogr. A 772, 49–62.CrossRefGoogle Scholar
Mitchell, P. 2001 Microfluidics—downsizing large-scale biology. Nature Biotechnol. 19, 717–721.CrossRefGoogle ScholarPubMed
Mosher, R. A., Saville, D. A. & Thormann, W. 1992 The Dynamics of Electrophoresis. VCH, Weinheim.Google Scholar
Palusinski, O. A., Graham, A., Mosher, R. Bier, A., , M. & Saville, D. A. 1986 Theory of electrophoretic separations. Part II: Construction of a numerical scheme and its applications. AIChE J. 32, 215–223.CrossRefGoogle Scholar
Russel, W. B., Saville, D. A. & Schowalter, W. R. 1989 Colloidal Dispersions. Cambridge University Press.CrossRefGoogle Scholar
Saville, D. A. & Palusinski, O. A. 1986 Theory of electrophoretic separations. Part I: Formulation of a mathematical model. AIChE J. 32, 207–214.CrossRefGoogle Scholar
von Smoluchowski, M. 1903 Contribution ‘a la théorie de l'endosmose électrique et de quelques phenom énes corrélatifs. Bull. Intl Acadé. Sci. Cracovie 8, 182–200.Google Scholar
Sounart, T. L. 2001 Electrokinetic transport and fluid motion in microanalytical electrolyte systems. PhD Dissertation, The University of Arizona.Google Scholar
Sounart, T. L. & Baygents, J. C. 2000 Simulation of electrophoretic separations by the flux-corrected transport method. J. Chromatogr. A 890, 321–336.CrossRefGoogle ScholarPubMed
Sounart, T. L. & Baygents, J. C. 2001 Electrically-driven fluid motion in channels with streamwise gradients in the electrical conductivity. Colloids Surfaces A: Physicochem. Engng Aspects 195, 59–75.CrossRefGoogle Scholar
Stone, H. A., Stroock, A. D. & Ajdari, A. 2004 Engineering flows in small devices: Microfluidics toward a lab-on-a-chip. Annu. Rev. Fluid Mech. 36, 381–411.CrossRefGoogle Scholar
Sweby, P. K. 1984 High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal. 21, 995–1011.CrossRefGoogle Scholar
Taylor, G. I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219, 186–203.Google Scholar
Thormann, W., Zhang, C.-X., Caslavska, J., Gebauer, P. & Mosher, R. A. 1998 Modeling of the impact of ionic strength on the electro-osmotic flow in capillary electrophoresis with uniform and discontinuous buffer systems. Anal. Chem 70, 549–562.CrossRefGoogle Scholar
de Zeeuw, P. M. 1990 Matrix-dependent prolongations and restrictions in a blackbox multigrid solver. J. Comput. Appl. Math. 33, 1–27.CrossRefGoogle Scholar