Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-27T03:50:50.069Z Has data issue: false hasContentIssue false
  • English
  • Français

Unsteady solute dispersion by electrokinetic flow in a polyelectrolyte layer-grafted rectangular microchannel with wall absorption

Published online by Cambridge University Press:  23 January 2020

Morteza Sadeghi ,
Mohammad Hassan Saidi ,
Ali Moosavi  and
Arman Sadeghi Open the ORCID record for Arman Sadeghi [Opens in a new window]
Morteza Sadeghi*
Affiliation:
Center of Excellence in Energy Conversion (CEEC), School of Mechanical Engineering, Sharif University of Technology, Tehran11155-9567, Iran
Mohammad Hassan Saidi*
Affiliation:
Center of Excellence in Energy Conversion (CEEC), School of Mechanical Engineering, Sharif University of Technology, Tehran11155-9567, Iran
Ali Moosavi
Affiliation:
Center of Excellence in Energy Conversion (CEEC), School of Mechanical Engineering, Sharif University of Technology, Tehran11155-9567, Iran
Arman Sadeghi
Affiliation:
Department of Mechanical Engineering, University of Kurdistan, Sanandaj66177-15175, Iran
*
†Email address for correspondence: saman@sharif.edu
†Email address for correspondence: saman@sharif.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

The dispersion of a neutral solute band by electrokinetic flow in polyelectrolyte layer (PEL)-grafted rectangular/slit microchannels is theoretically studied. The flow is assumed to be both steady and fully developed and a first-order irreversible reaction is considered at the wall to account for probable surface adsorption of solutes. Considering low electric potentials, analytical solutions are obtained for electric potential, fluid velocity and solute concentration. Special solutions are also obtained for the case without wall adsorption. To track the dispersion properties of the solute band, the generalized dispersion model is adopted by considering the exchange, the convection and the dispersion coefficients. The solutions developed are validated by comparing the results with the predictions of finite-element-based numerical simulations. Even though the solutions can take any form of initial solute concentration into account, the results are presented by considering a solute band of rectangular shape. The results reveal that, while the short-term transport coefficients are strongly affected by the initial concentration profile, the long-term values are not dependent upon the initial conditions. In addition, it is shown that the mass transport coefficients are strong functions of the channel aspect ratio; hence, approximating a rectangular geometry by the space between two parallel plates may lead to considerable errors in the estimation of mass transport characteristics. This is particularly important for the dispersion coefficient for which the long-term values for a slit microchannel are quite different from those for a rectangular channel of very high aspect ratio. It is also illustrated that the exchange and convection coefficients increase on increasing the Damköhler number, whereas the opposite is true for the dispersion coefficient. The convection and dispersion coefficients are generally increasing functions of the PEL fixed charge density and the PEL thickness and decreasing functions of the PEL friction coefficient. Last but not least, a thicker electric double layer is found to provide a larger degree of solute dispersion, which is the opposite of that observed in a microchannel with bare walls.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Reacting Flows: Laminar reacting flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 887 , 25 March 2020 , A13
Copyright
© The Author(s), 2020. Published by 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

Abdollahzadeh, M., Saidi, M. S. & Sadeghi, A. 2017 Enhancement of surface adsorption-desorption rates in microarrays invoking surface charge heterogeneity. Sensors Actuators B 242, 956–964.CrossRefGoogle Scholar
Andreev, V. P. & Lisin, E. E. 1993 On the mathematical model of capillary electrophoresis. Chromatographia 37 (3), 202–210.CrossRefGoogle Scholar
Archer, D. G. & Wang, P. 1990 The dielectric constant of water and Debye–Hückel limiting law slopes. J. Phys. Chem. Ref. Data 19 (2), 371–411.CrossRefGoogle 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
Chiari, M., Cretich, M., Damin, F., Ceriotti, L. & Consonni, R. 2000 New adsorbed coatings for capillary electrophoresis. Electrophoresis 21 (5), 909–916.3.0.CO;2-L>CrossRefGoogle ScholarPubMed
Datta, R. & Kotamarthi, V. R. 1990 Electrokinetic dispersion in capillary electrophoresis. AIChE J. 36 (6), 916–926.CrossRefGoogle Scholar
Datta, S. & Ghosal, S. 2009 Characterizing dispersion in microfluidic channels. Lab on a Chip 9 (17), 2537–2550.CrossRefGoogle ScholarPubMed
Dautzenberg, H.1985 Polymeric stabilization of colloidal dispersions. Von Donald H. Napper. ISBN 0-12-513980-2. London/New York/etc.: Academic Press Inc. 1983. XVIII, 428 S., Lwd. Acta Polymerica 36 (8) 457–457.CrossRefGoogle Scholar
Dutta, D. 2007 Electroosmotic transport through rectangular channels with small zeta potentials. J. Colloid Interface Sci. 315 (2), 740–746.CrossRefGoogle ScholarPubMed
Feltkamp, H.1966 Dynamics of Chromatography. Part 1, Principles and Theory. Von J. Calvin Giddings. 323 Seiten. Marcel Dekker, Inc., New York 1965. Preis: $11.50. Archiv der Pharmazie 299 (7) 651–652.Google Scholar
Garcia, A. L., Ista, L. K., Petsev, D. N., O’Brien, M. J., Bisong, P., Mammoli, A. A., Brueck, S. R. J. & López, G. P. 2005 Electrokinetic molecular separation in nanoscale fluidic channels. Lab on a Chip 5 (11), 1271–1276.CrossRefGoogle ScholarPubMed
Gill, W. N. & Sankarasubramanian, R. 1970 Exact analysis of unsteady convective diffusion. Proc. R. Soc. Lond. A 316 (1526), 341–350.CrossRefGoogle Scholar
Gill, W. N. & Sankarasubramanian, R. 1971 Dispersion of a non-uniform slug in time-dependent flow. Proc. R. Soc. Lond. A 322 (1548), 101–117.CrossRefGoogle Scholar
Gill, W. N. & Sankarasubramanian, R. 1972 Dispersion of non-uniformly distributed time-variable continuous sources in time-dependent flow. Proc. R. Soc. Lond. A 327 (1569), 191–208.CrossRefGoogle Scholar
Griffiths, S. K. & Nilson, R. H. 1999 Hydrodynamic dispersion of a neutral nonreacting solute in electroosmotic flow. Analyt. Chem. 71 (24), 5522–5529.CrossRefGoogle Scholar
Griffiths, S. K. & Nilson, R. H. 2000 Electroosmotic fluid motion and late-time solute transport for large zeta potentials. Analyt. Chem. 72 (20), 4767–4777.CrossRefGoogle ScholarPubMed
Hickey, O. A., Harden, J. L. & Slater, G. W. 2009 Molecular dynamics simulations of optimal dynamic uncharged polymer coatings for quenching electro-osmotic flow. Phys. Rev. Lett. 102 (10), 108304.CrossRefGoogle ScholarPubMed
Holden, M. A., Kumar, S., Castellana, E. T., Beskok, A. & Cremer, P. S. 2003 Generating fixed concentration arrays in a microfluidic device. Sensors Actuators B 92 (1), 199–207.CrossRefGoogle 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.CrossRefGoogle Scholar
Karniadakis, G. E., Beskok, A. & Aluru, N. 2005 Microflows and Nanoflows, Fundamentals and Simulation. Springer.Google Scholar
Keramati, H., Sadeghi, A., Saidi, M. H. & Chakraborty, S. 2016 Analytical solutions for thermo-fluidic transport in electroosmotic flow through rough microtubes. Intl J. Heat Mass Transfer 92, 244–251.CrossRefGoogle Scholar
Louie, S. M., Phenrat, T., Small, M. J., Tilton, R. D. & Lowry, G. V. 2012 Parameter identifiability in application of soft particle electrokinetic theory to determine polymer and polyelectrolyte coating thicknesses on colloids. Langmuir 28 (28), 10334–10347.CrossRefGoogle ScholarPubMed
Masliyah, J. H. & Bhattacharjee, S. 2006 Electrokinetic and Colloid Transport Phenomena. John Wiley & Sons.CrossRefGoogle Scholar
Matsunaga, T., Lee, H.-J. & Nishino, K. 2013 An approach for accurate simulation of liquid mixing in a T-shaped micromixer. Lab on a Chip 13 (8), 1515–1521.CrossRefGoogle Scholar
Monteferrante, M., Melchionna, S., Marconi, U. M. B., Cretich, M., Chiari, M. & Sola, L. 2015 Electroosmotic flow in polymer-coated slits: a joint experimental/simulation study. Microfluid Nanofluid 18 (3), 475–482.CrossRefGoogle Scholar
Nagarani, P., Sarojamma, G. & Jayaraman, G. 2004 Effect of boundary absorption in dispersion in Casson fluid flow in a tube. Ann. Biomed. Engng 32, 706–719.CrossRefGoogle Scholar
Ng, C.-O. 2006 Dispersion in steady and oscillatory flows through a tube with reversible and irreversible wall reactions. Proc. R. Soc. Lond. A 462 (2066), 481–515.CrossRefGoogle Scholar
Ng, C.-O. & Zhou, Q. 2012 Dispersion due to electroosmotic flow in a circular microchannel with slowly varying wall potential and hydrodynamic slippage. Phys. Fluids 24 (11), 112002.CrossRefGoogle Scholar
Nguyen, N.-T. & Wu, Z. 2004 Micromixers – a review. J. Micromech. Microengng 15 (2), R1–R16.CrossRefGoogle Scholar
Paul, S. & Ng, C.-O. 2012 On the time development of dispersion in electroosmotic flow through a rectangular channel. Acta Mechanica Sin. 28 (3), 631–643.CrossRefGoogle Scholar
Paumier, G., Sudor, J., Gue, A.-M., Vinet, F., Li, M., Chabal, Y. J., Estève, A. & Djafari-Rouhani, M. 2008 Nanoscale actuation of electrokinetic flows on thermoreversible surfaces. Electrophoresis 29 (6), 1245–1252.CrossRefGoogle ScholarPubMed
Phillips, C. G. & Kaye, S. R. 1998 Approximate solutions for developing shear dispersion with exchange between phases. J. Fluid Mech. 374, 195–219.CrossRefGoogle Scholar
Ratner, B., Hoffman, A., Schoen, F. & Lemons, J. 2004 Biomaterials Science: An Introduction to Materials in Medicine. Academic Press.Google Scholar
Sadeghi, A. 2016 Analytical solutions for species transport in a T-sensor at low peclet numbers. AIChE J. 62 (11), 4119–4130.CrossRefGoogle Scholar
Sadeghi, A. 2019 Analytical solutions for mass transport in hydrodynamic focusing by considering different diffusivities for sample and sheath flows. J. Fluid Mech. 862, 517–551.CrossRefGoogle Scholar
Sadeghi, A., Amini, Y., Saidi, M. H. & Chakraborty, S. 2014 Numerical modeling of surface reaction kinetics in electrokinetically actuated microfluidic devices. Anal. Chim. Acta 838, 64–75.CrossRefGoogle ScholarPubMed
Sadeghi, A., Azari, M. & Hardt, S. 2019 Electroosmotic flow in soft microchannels at high grafting densities. Phys. Rev. Fluids 4 (6), 063701.CrossRefGoogle Scholar
Sadeghi, M., Sadeghi, A. & Saidi, M. H. 2016 Electroosmotic flow in hydrophobic microchannels of general cross section. Trans. ASME J. Fluids Engng 138 (3), 031104.CrossRefGoogle Scholar
Sadeghi, M., Saidi, M. H., Moosavi, A. & Sadeghi, A. 2017 Geometry effect on electrokinetic flow and ionic conductance in pH-regulated nanochannels. Phys. Fluids 29 (12), 122006.Google Scholar
Sadeghi, M., Saidi, M. H. & Sadeghi, A. 2017 Electroosmotic flow and ionic conductance in a pH-regulated rectangular nanochannel. Phys. Fluids 29 (6), 062002.Google Scholar
Sankarasubramanian, R. & Gill, W. N. 1972 Dispersion from a prescribed concentration distribution in time variable flow. Proc. R. Soc. Lond. A 329 (1579), 479–492.CrossRefGoogle Scholar
Sankarasubramanian, R. & Gill, W. N. 1973 Unsteady convective diffusion with interphase mass transfer. Proc. R. Soc. Lond. A 333 (1592), 115–132.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 (1), 381–411.CrossRefGoogle Scholar
Taylor, G. I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219 (1137), 186–203.Google Scholar
Tripathi, A., Bozkurt, O. & Chauhan, A. 2005 Dispersion in microchannels with temporal temperature variations. Phys. Fluids 17 (10), 103607.CrossRefGoogle Scholar
Vafai, K. 2005 Handbook of Porous Media. CRC Press.CrossRefGoogle Scholar
Vedel, S. & Bruus, H. 2011 Transient Taylor–Aris dispersion for time-dependent flows in straight channels. J. Fluid Mech. 691, 95–122.CrossRefGoogle Scholar
Vennela, N., Mondal, S., De, S. & Bhattacharjee, S. 2012 Sherwood number in flow through parallel porous plates (microchannel) due to pressure and electroosmotic flow. AIChE J. 58 (6), 1693–1703.CrossRefGoogle Scholar
White, F. 2011 Fluid Mechanics. McGraw-Hill.Google Scholar
Wu, D., Qin, J. & Lin, B. 2008 Electrophoretic separations on microfluidic chips. J. Chromatogr. A 1184 (1), 542–559.CrossRefGoogle ScholarPubMed
Wu, Z. & Nguyen, N.-T. 2005 Convective–diffusive transport in parallel lamination micromixers. Microfluid Nanofluid 1 (3), 208–217.CrossRefGoogle Scholar
Yeh, L.-H., Zhang, M., Hu, N., Joo, S. W., Qian, S. & Hsu, J.-P. 2012 Electrokinetic ion and fluid transport in nanopores functionalized by polyelectrolyte brushes. Nanoscale 4 (16), 5169–5177.CrossRefGoogle ScholarPubMed