Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-24T22:41:31.109Z Has data issue: false hasContentIssue false
  • English
  • Français

Tuning the dispersion of reactive solute by steady and oscillatory electroosmotic–Poiseuille flows in polyelectrolyte-grafted micro/nanotubes

Published online by Cambridge University Press:  07 October 2019

Milad Reshadi Open the ORCID record for Milad Reshadi [Opens in a new window]  and
Mohammad Hassan Saidi Open the ORCID record for Mohammad Hassan Saidi [Opens in a new window]
Milad Reshadi
Affiliation:
Center of Excellence in Energy Conversion (CEEC), Department of Mechanical Engineering, Sharif University of Technology, Tehran 11155-9567, Iran
Mohammad Hassan Saidi*
Affiliation:
Center of Excellence in Energy Conversion (CEEC), Department of Mechanical Engineering, Sharif University of Technology, Tehran 11155-9567, Iran Sharif Energy Research Institute (SERI), Sharif University of Technology, Tehran 14597-77611, Iran
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper extends the analysis of solute dispersion in electrohydrodynamic flows to the case of band broadening in polyelectrolyte-grafted (soft) capillaries by accounting for the effects of ion partitioning, irreversible catalytic reaction and pulsatile flow actuation. In the Debye–Hückel limit, we present the benchmark solutions of electric potential and velocity distribution pertinent to steady and oscillatory mixed electroosmotic–pressure-driven flows in soft capillaries. Afterwards, the mathematical models of band broadening based on the Taylor–Aris theory and generalized dispersion method are presented to investigate the late-time asymptotic state and all-time evolution of hydrodynamic dispersion, respectively. Also, to determine the heterogeneous dispersion behaviour of solute through all spatiotemporal stages and to relax the constraint of small zeta potentials, a full-scale numerical simulation of time-dependent solute transport in soft capillaries is presented by employing the second-order-accurate finite difference method. Then, by inspecting the dispersion of passive tracer particles in Poiseuille flows, we examine the accuracy of two analytical approaches against the simulation results of a custom-built numerical algorithm. Our findings from hydrodynamic dispersion in Poiseuille flows reveal that, compared to rigid capillaries, more time is required to approach the longitudinal normality and transverse uniformity of injected solute in soft capillaries. For the case of dispersion in mixed electrohydrodynamic flows, it is found that the characteristics of the soft interface, including the thickness, permittivity, fixed charge density and friction coefficient of the polymer coating layer, play a significant role in determining the Taylor diffusion coefficient, advection speed and dispersion rate of solutes in soft capillaries.

JFM classification

Drops and Bubbles: Electrohydrodynamic effects
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 880 , 10 December 2019 , pp. 73 - 112
Copyright
© 2019 Cambridge University Press 

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

Ali, M., Yameen, B., Cervera, J., Ramiìrez, P., Neumann, R., Ensinger, W., Knoll, W. & Azzaroni, O. 2010 Layer-by-layer assembly of polyelectrolytes into ionic current rectifying solid-state nanopores: insights from theory and experiment. J. Am. Chem. Soc. 132 (24), 8338–8348.Google Scholar
Ali, M., Yameen, B., Neumann, R., Ensinger, W., Knoll, W. & Azzaroni, O. 2008 Biosensing and supramolecular bioconjugation in single conical polymer nanochannels. Facile incorporation of biorecognition elements into nanoconfined geometries. J. Am. Chem. Soc. 130 (48), 16351–16357.Google Scholar
Alipanah, M. & Ramiar, A. 2017 High efficiency micromixing technique using periodic induced charge electroosmotic flow: a numerical study. Colloids Surf. A 524, 53–65.Google Scholar
Ananthakrishnan, V., Gill, W. N. & Barduhn, A. J. 1965 Laminar dispersion in capillaries. Part I. Mathematical analysis. AICHE J. 11 (6), 1063–1072.Google Scholar
Arcos, J., MÉNDEZ, F., Bautista, E. & Bautista, O. 2018 Dispersion coefficient in an electro-osmotic flow of a viscoelastic fluid through a microchannel with a slowly varying wall zeta potential. J. Fluid Mech. 839, 348–386.Google Scholar
Aris, R. 1956 On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. Lond. A 235 (1200), 67–77.Google Scholar
Barker, S. L., Ross, D., Tarlov, M. J., Gaitan, M. & Locascio, L. E. 2000 Control of flow direction in microfluidic devices with polyelectrolyte multilayers. Anal. Chem. 72 (24), 5925–5929.Google Scholar
Behrens, S. H. & Grier, D. G. 2001 The charge of glass and silica surfaces. J. Chem. Phys. 115 (14), 6716–6721.Google Scholar
Bhattacharyya, S. & De, S. 2016 Influence of rigid core permittivity and double layer polarization on the electrophoresis of a soft particle: a numerical study. Phys. Fluids 28 (1), 012001.Google Scholar
Born, M. 1920 Volumen und Hydratationswärme der Ionen. Z. Phys. 1 (1), 45–48.Google Scholar
Chakraborty, S. & Ray, S. 2008 Mass flow-rate control through time periodic electro-osmotic flows in circular microchannels. Phys. Fluids 20 (8), 083602.Google Scholar
Chanda, S., Sinha, S. & Das, S. 2014 Streaming potential and electroviscous effects in soft nanochannels: towards designing more efficient nanofluidic electrochemomechanical energy converters. Soft Matt. 10 (38), 7558–7568.Google Scholar
Chen, G. & Das, S. 2015a Electroosmotic transport in polyelectrolyte-grafted nanochannels with pH-dependent charge density. J. Appl. Phys. 117 (18), 185304.Google Scholar
Chen, G. & Das, S. 2015b Streaming potential and electroviscous effects in soft nanochannels beyond Debye–Hückel linearization. J. Colloid Interface Sci. 445, 357–363.Google Scholar
Choi, C.-H., Ulmanella, U., Kim, J., Ho, C.-M. & Kim, C.-J. 2006 Effective slip and friction reduction in nanograted superhydrophobic microchannels. Phys. Fluids 18 (8), 087105.Google Scholar
Chun, K.-Y. & Stroeve, P. 2002 Protein transport in nanoporous membranes modified with self-assembled monolayers of functionalized thiols. Langmuir 18 (12), 4653–4658.Google Scholar
Das, S., Banik, M., Chen, G., Sinha, S. & Mukherjee, R. 2015 Polyelectrolyte brushes: theory, modelling, synthesis and applications. Soft Matt. 11 (44), 8550–8583.Google Scholar
Datta, R. & Kotamarthi, V. R. 1990 Electrokinetic dispersion in capillary electrophoresis. AICHE J. 36 (6), 916–926.Google Scholar
Datta, S. & Ghosal, S. 2008 Dispersion due to wall interactions in microfluidic separation systems. Phys. Fluids 20 (1), 012103.Google Scholar
Datta, S. & Ghosal, S. 2009 Characterizing dispersion in microfluidic channels. Lab on a Chip 9 (17), 2537–2550.Google Scholar
Debesset, S., Hayden, C., Dalton, C., Eijkel, J. C. & Manz, A. 2004 An AC electroosmotic micropump for circular chromatographic applications. Lab on a Chip 4 (4), 396–400.Google Scholar
Dutta, D. 2015 An analytic description of electrodynamic dispersion in free-flow zone electrophoresis. J. Chromatogr. A 1404, 124–130.Google Scholar
Duval, J. F., Wilkinson, K. J., Van Leeuwen, H. P. & Buffle, J. 2005 Humic substances are soft and permeable: evidence from their electrophoretic mobilities. Environ. Sci. Technol. 39 (17), 6435–6445.Google Scholar
Eijkel, J. C., Van Den Berg, A. & Manz, A. 2004 Cyclic electrophoretic and chromatographic separation methods. Electrophoresis 25 (2), 243–252.Google Scholar
Faure, B., Salazar-Alvarez, G., Ahniyaz, A., Villaluenga, I., Berriozabal, G., De Miguel, Y. R. & Bergström, L. 2013 Dispersion and surface functionalization of oxide nanoparticles for transparent photocatalytic and UV-protecting coatings and sunscreens. Sci. Technol. Adv. Mater. 14 (2), 023001.Google Scholar
Fife, P. & Nicholes, K. 1975 Dispersion in flow through small tubes. Proc. R. Soc. Lond. A 344 (1636), 131–145.Google Scholar
Gervais, T. & Jensen, K. F. 2006 Mass transport and surface reactions in microfluidic systems. Chem. Engng Sci. 61 (4), 1102–1121.Google Scholar
Ghosal, S. 2003 The effect of wall interactions in capillary-zone electrophoresis. J. Fluid Mech. 491, 285–300.Google Scholar
Gill, W. & Sankarasubramanian, R. 1970 Exact analysis of unsteady convective diffusion. Proc. R. Soc. Lond. A 316 (1526), 341–350.Google Scholar
Griffiths, I., Howell, P. & Shipley, R. 2013 Control and optimization of solute transport in a thin porous tube. Phys. Fluids 25 (3), 033101.Google Scholar
Griffiths, S. K. & Nilson, R. H. 2000 Electroosmotic fluid motion and late-time solute transport for large zeta potentials. Anal. Chem. 72 (20), 4767–4777.Google Scholar
Griffiths, S. K. & Nilson, R. H. 2006 Charged species transport, separation, and dispersion in nanoscale channels: autogenous electric field-flow fractionation. Anal. Chem. 78 (23), 8134–8141.Google Scholar
Grimes, B., Lüdtke, S., Unger, K. & Liapis, A. 2002 Novel general expressions that describe the behavior of the height equivalent of a theoretical plate in chromatographic systems involving electrically-driven and pressure-driven flows. J. Chromatogr. A 979 (1–2), 447–466.Google Scholar
Heyde, M., Peters, C. & Anderson, J. 1975 Factors influencing reverse osmosis rejection of inorganic solutes from aqueous solution. J. Colloid Interface Sci. 50 (3), 467–487.Google Scholar
Hoogeveen, N. G., Cohen Stuart, M. A., Fleer, G. J. & Böhmer, M. R. 1996 Formation and stability of multilayers of polyelectrolytes. Langmuir 12 (15), 3675–3681.Google Scholar
Hoshyargar, V., Ashrafizadeh, S. N. & Sadeghi, A. 2017 Mass transport characteristics of diffusioosmosis: potential applications for liquid phase transportation and separation. Phys. Fluids 29 (1), 012001.Google Scholar
Hoshyargar, V., Khorami, A., Ashrafizadeh, S. N. & Sadeghi, A. 2018 Solute dispersion by electroosmotic flow through soft microchannels. Sensors Actuators B 255, 3585–3600.Google Scholar
Houseworth, J. 1984 Shear dispersion and residence time for laminar flow in capillary tubes. J. Fluid Mech. 142, 289–308.Google Scholar
Huang, H.-F. & Lai, C.-L. 2006 Enhancement of mass transport and separation of species by oscillatory electroosmotic flows. Proc. R. Soc. Lond. A 462 (2071), 2017–2038.Google Scholar
Huiqian, Y., Nguyen, N.-T. & Huang, X. 2006 Micromixer based on Taylor dispersion. J. Phys.: Conf. Ser. 34, 136–141.Google Scholar
Hunter, R. 1988 Zeta Potential in Colloid Science: Principles and Applications. Academic Press.Google Scholar
Hyväluoma, J. & Harting, J. 2008 Slip flow over structured surfaces with entrapped microbubbles. Phys. Rev. Lett. 100 (24), 246001.Google Scholar
Israelachvili, J. N. 2011 Intermolecular and Surface Forces. Academic Press.Google Scholar
Jorgenson, J. W. & Lukacs, K. D. 1981 High-resolution separations based on electrophoresis and electroosmosis. J. Chromatogr. A 218, 209–216.Google Scholar
Karniadakis, G., Beskok, A. & Aluru, N. R. 2006 Microflows and Nanoflows: Fundamentals and Simulation. Springer.Google Scholar
Khodabandehloo, A. & Chen, D. D. 2017 Electroosmotic flow dispersion of large molecules in electrokinetic migration. Anal. Chem. 89 (15), 7823–7827.Google Scholar
Kirby, B. J. & Hasselbrink, E. F. 2004 Zeta potential of microfluidic substrates: 1. Theory, experimental techniques, and effects on separations. Electrophoresis 25 (2), 187–202.Google Scholar
Lee, J., Panzer, M. J., He, Y., Lodge, T. P. & Frisbie, C. D. 2007 Ion gel gated polymer thin-film transistors. J. Am. Chem. Soc. 129 (15), 4532–4533.Google Scholar
Leong, J.-C., Tsai, C.-H., Chang, C.-L., Lin, C.-F. & Fu, L.-M. 2007 Rapid microfluidic mixers utilizing dispersion effect and interactively time-pulsed injection. Japan. J. Appl. Phys. 46, 5345.Google Scholar
Li, D. 2004 Electrokinetics in Microfluidics. Academic Press.Google Scholar
Li, F., Jian, Y., Chang, L., Zhao, G. & Yang, L. 2016 Alternating current electroosmotic flow in polyelectrolyte-grafted nanochannel. Colloids Surfaces B 147, 234–241.Google Scholar
Li, H. & Jian, Y. 2017 Dispersion for periodic electro-osmotic flow of Maxwell fluid through a microtube. Intl J. Heat Mass Transfer. 115, 703–713.Google Scholar
Lighthill, M. 1966 Initial development of diffusion in Poiseuille flow. IMA J. Appl. Maths 2 (1), 97–108.Google Scholar
Lim, C. Y. & Lam, Y. C. 2012 Analysis on micro-mixing enhancement through a constriction under time periodic electroosmotic flow. Microfluid. Nanofluid. 12 (1–4), 127–141.Google Scholar
Lim, C. Y., Lam, Y. C. & Yang, C. 2010 Mixing enhancement in microfluidic channel with a constriction under periodic electro-osmotic flow. Biomicrofluidics 4 (1), 014101.Google Scholar
Ling, B., Tartakovsky, A. M. & Battiato, I. 2016 Dispersion controlled by permeable surfaces: surface properties and scaling. J. Fluid Mech. 801, 13–42.Google Scholar
López-Viota, J., Mandal, S., Delgado, A. V., Toca-Herrera, J. L., Möller, M., Zanuttin, F., Balestrino, M. & Krol, S. 2009 Electrophoretic characterization of gold nanoparticles functionalized with human serum albumin (HSA) and creatine. J. Colloid Interface Sci. 332 (1), 215–223.Google Scholar
Loucaides, N., Ramos, A. & Georghiou, G. E. 2007 Novel systems for configurable AC electroosmotic pumping. Microfluid. Nanofluid. 3 (6), 709–714.Google Scholar
Martin, M. & Guiochon, G. 1984 Axial dispersion in open-tubular capillary liquid chromatography with electroosmotic flow. Anal. Chem. 56 (4), 614–620.Google Scholar
Masliyah, J. H. & Bhattacharjee, S. 2006 Electrokinetic and Colloid Transport Phenomena. Wiley.Google Scholar
Mazumder, B. & Mondal, K. K. 2005 On solute transport in oscillatory flow through an annular pipe with a reactive wall and its application to a catheterized artery. Q. J. Mech. Appl. Maths 58 (3), 349–365.Google Scholar
McEldoon, J. P. & Datta, R. 1992 Analytical solution for dispersion in capillary liquid chromatography with electroosmotic flow. Anal. Chem. 64 (2), 227–230.Google Scholar
Medina, I., Toledo, M., MÉNDEZ, F. & Bautista, O. 2018 Pulsatile electroosmotic flow in a microchannel with asymmetric wall zeta potentials and its effect on mass transport enhancement and mixing. Chem. Engng Sci. 184, 259–272.Google Scholar
Mei, C. C., Auriault, J.-L. & Ng, C.-O. 1996 Some applications of the homogenization theory. Adv. Appl. Mech. 32, 277–348.Google Scholar
Meller, A., Nivon, L. & Branton, D. 2001 Voltage-driven DNA translocations through a nanopore. Phys. Rev. Lett. 86 (15), 3435–3438.Google Scholar
Mertz, D., HEMMERLÉ, J., Mutterer, J., Ollivier, S., Voegel, J.-C., Schaaf, P. & Lavalle, P. 2007 Mechanically responding nanovalves based on polyelectrolyte multilayers. Nano Lett. 7 (3), 657–662.Google Scholar
Moles, D. R.2002 Electroosmotic flow controlled microfluidic devices. U.S. Patent no. 6406605.Google Scholar
Morita, K., Muramatsu, N., Ohshima, H. & Kondo, T. 1991 Electrophoretic behavior of rat lymphocyte subpopulations. J. Colloid Interface Sci. 147 (2), 457–461.Google Scholar
Mukherjee, A. & Mazumder, B. 1988 Dispersion of contaminant in oscillatory flows. Acta Mech. 74 (1–4), 107–122.Google Scholar
Ng, C.-O. 2011 How does wall slippage affect hydrodynamic dispersion? Microfluid. Nanofluid. 10 (1), 47–57.Google Scholar
Ng, C.-O. & Rudraiah, N. 2008 Convective diffusion in steady flow through a tube with a retentive and absorptive wall. Phys. Fluids 20 (7), 073604.Google Scholar
Patwary, J., Chen, G. & Das, S. 2016 Efficient electrochemomechanical energy conversion in nanochannels grafted with polyelectrolyte layers with pH-dependent charge density. Microfluid. Nanofluid. 20 (2), 37.Google Scholar
Paul, S. & Ng, C.-O. 2012 Dispersion in electroosmotic flow generated by oscillatory electric field interacting with oscillatory wall potentials. Microfluid. Nanofluid. 12 (1–4), 237–256.Google Scholar
Phillips, C., Kaye, S. & Robinson, C. 1995 Time-dependent transport by convection and diffusion with exchange between two phases. J. Fluid Mech. 297, 373–401.Google Scholar
Poddar, A., Maity, D., Bandopadhyay, A. & Chakraborty, S. 2016 Electrokinetics in polyelectrolyte grafted nanofluidic channels modulated by the ion partitioning effect. Soft Matt. 12 (27), 5968–5978.Google Scholar
Pretorius, V., Hopkins, B. J. & Schieke, J. 1974 Electro-osmosis: a new concept for high-speed liquid chromatography. J. Chromatogr. A 99, 23–30.Google Scholar
Probstein, R. F. 2005 Physicochemical Hydrodynamics: An Introduction. Wiley.Google Scholar
Ramon, G., Agnon, Y. & Dosoretz, C. 2011 Solute dispersion in oscillating electro-osmotic flow with boundary mass exchange. Microfluid. Nanofluid. 10 (1), 97–106.Google Scholar
Ramon, G. Z. 2017 Solute transport under oscillating electro-osmotic flow in a closed-ended cylindrical pore. J. Engng Maths 110 (1), 195–205.Google Scholar
Rana, J. & Murthy, P. 2016 Solute dispersion in pulsatile Casson fluid flow in a tube with wall absorption. J. Fluid Mech. 793, 877–914.Google Scholar
Reshadi, M. & Saidi, M. H. 2018 The role of ion partitioning in electrohydrodynamic characteristics of soft nanofluidics: inclusion of EDL overlap and steric effects. Chem. Engng Sci. 190, 443–458.Google Scholar
Sankarasubramanian, R. & Gill, W. N. 1973 Unsteady convective diffusion with interphase mass transfer. Proc. R. Soc. Lond. A 333 (1592), 115–132.Google Scholar
Sasaki, N., Kitamori, T. & Kim, H.-B. 2006 AC electroosmotic micromixer for chemical processing in a microchannel. Lab on a Chip 6 (4), 550–554.Google Scholar
Sbragaglia, M., Benzi, R., Biferale, L., Succi, S. & Toschi, F. 2006 Surface roughness-hydrophobicity coupling in microchannel and nanochannel flows. Phys. Rev. Lett. 97 (20), 204503.Google Scholar
Sharp, K. A. & Brooks, D. E. 1985 Calculation of the electrophoretic mobility of a particle bearing bound polyelectrolyte using the nonlinear Poisson–Boltzmann equation. Biophys. J. 47 (4), 563–566.Google Scholar
Shaw, D. 1992 Introduction to Colloid and Surface Chemistry (Colloid and Surface Engineering). Butterworth-Heinemann.Google Scholar
Song, H., Wang, Y. & Pant, K. 2012 Cross-stream diffusion under pressure-driven flow in microchannels with arbitrary aspect ratios: a phase diagram study using a three-dimensional analytical model. Microfluid. Nanofluid. 12 (1–4), 265–277.Google Scholar
Song, J., Ng, C.-O. & Law, W.-K. A. 2014 Dispersion in oscillatory electro-osmotic flow through a parallel-plate channel with kinetic sorptive exchange at walls. J. Hydrodyn. 26 (3), 363–373.Google Scholar
Steinberger, A., Cottin-Bizonne, C., Kleimann, P. & Charlaix, E. 2007 High friction on a bubble mattress. Nat. Mater. 6 (9), 665–668.Google Scholar
Steitz, R., Gutberlet, T., Hauss, T., Klösgen, B., Krastev, R., Schemmel, S., Simonsen, A. C. & Findenegg, G. H. 2003 Nanobubbles and their precursor layer at the interface of water against a hydrophobic substrate. Langmuir 19 (6), 2409–2418.Google Scholar
Stokes, A. & Barton, N. 1990 The concentration distribution produced by shear dispersion of solute in Poiseuille flow. J. Fluid Mech. 210, 201–221.Google 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.Google Scholar
Taylor, G. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219 (1137), 186–203.Google Scholar
Teo, C. J. & Khoo, B. C. 2010 Flow past superhydrophobic surfaces containing longitudinal grooves: effects of interface curvature. Microfluid. Nanofluid. 9 (2–3), 499–511.Google Scholar
Tretheway, D. C. & Meinhart, C. D. 2004 A generating mechanism for apparent fluid slip in hydrophobic microchannels. Phys. Fluids 16 (5), 1509–1515.Google Scholar
Tsuda, T., Nomura, K. & Nakagawa, G. 1982 Open-tubular microcapillary liquid chromatography with electro-osmosis flow using a UV detector. J. Chromatogr. A 248 (2), 241–247.Google Scholar
Tyrrell, J. W. & Attard, P. 2001 Images of nanobubbles on hydrophobic surfaces and their interactions. Phys. Rev. Lett. 87 (17), 176104.Google Scholar
Van Theemsche, A., Gzil, P., Dan, C., Deconinck, J., De Smet, J., Vervoort, N. & Desmet, G. 2004 Theoretical comparison of the band broadening in nonretained electrically and pressure-driven flows through an ordered chromatographic pillar packing. Anal. Chem. 76 (14), 4030–4037.Google Scholar
Vedel, S. & Bruus, H. 2012 Transient Taylor–Aris dispersion for time-dependent flows in straight channels. J. Fluid Mech. 691, 95–122.Google Scholar
Vilozny, B., Wollenberg, A. L., Actis, P., Hwang, D., Singaram, B. & Pourmand, N. 2013 Carbohydrate-actuated nanofluidic diode: switchable current rectification in a nanopipette. Nanoscale 5 (19), 9214–9221.Google Scholar
Wu, J. H. & Keh, H. J. 2003 Diffusioosmosis and electroosmosis in a capillary slit with surface charge layers. Colloids Surf. A 212 (1), 27–42.Google Scholar
Wu, Z. & Chen, G. 2014 Approach to transverse uniformity of concentration distribution of a solute in a solvent flowing along a straight pipe. J. Fluid Mech. 740, 196–213.Google Scholar
Wu, Z., Fu, X. & Wang, G. 2016 On spatial pattern of concentration distribution for Taylor dispersion process. Sci. Rep. 6, 20556.Google Scholar
Xuan, X. 2008 Solute transport and separation in nanochannel chromatography. J. Chromatogr. A 1187 (1–2), 289–292.Google Scholar
Xuan, X. & Li, D. 2004 Joule heating effects on peak broadening in capillary zone electrophoresis. J. Micromech. Microengng 14 (8), 1171–1180.Google Scholar
Yameen, B., Ali, M., Neumann, R., Ensinger, W., Knoll, W. & Azzaroni, O. 2009 Synthetic proton-gated ion channels via single solid-state nanochannels modified with responsive polymer brushes. Nano Lett. 9 (7), 2788–2793.Google Scholar
Zhao, H. & Bau, H. H. 2007 Effect of secondary flows on Taylor–Aris dispersion. Anal. Chem. 79 (20), 7792–7798.Google Scholar
Zholkovskij, E. K. & Masliyah, J. H. 2004 Hydrodynamic dispersion due to combined pressure-driven and electroosmotic flow through microchannels with a thin double layer. Anal. Chem. 76 (10), 2708–2718.Google Scholar
Zholkovskij, E. K., Masliyah, J. H. & Czarnecki, J. 2003 Electroosmotic dispersion in microchannels with a thin double layer. Anal. Chem. 75 (4), 901–909.Google Scholar
Zholkovskij, E. K., Masliyah, J. H. & Yaroshchuk, A. E. 2013 Broadening of neutral analyte band in electroosmotic flow through slit channel with different zeta potentials of the walls. Microfluid. Nanofluid. 15 (1), 35–47.Google Scholar