Hostname: page-component-7bb8b95d7b-nptnm Total loading time: 0 Render date: 2024-09-08T05:17:35.111Z Has data issue: false hasContentIssue false
  • English
  • Français

Sheltering the perturbed vortical layer of electroconvection under shear flow

Published online by Cambridge University Press:  26 January 2017

Rhokyun Kwak ,
Van Sang Pham  and
Jongyoon Han
Rhokyun Kwak*
Affiliation:
Center for BioMicrosystems, Korea Institute of Science and Technology, Seoul, 02792, Republic of Korea
Van Sang Pham
Affiliation:
Department of Fluid Mechanics and Ship Engineering, Hanoi University of Science and Technology, No1 DaiCoViet, Hanoi, Vietnam Singapore-MIT Alliance for Research and Technology (SMART) Centre, Singapore
Jongyoon Han
Affiliation:
Singapore-MIT Alliance for Research and Technology (SMART) Centre, Singapore Department of Electrical Engineering and Computer Science Department of Biological Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
*
†Email address for correspondence: rhokyun@kist.re.kr
Get access Rights & Permissions [Opens in a new window]

Abstract

Sheltering of a perturbed vortical layer by a shear flow is a common method to control turbulence and transport in plasma physics. Despite the desire to exploit this phenomenon in wider engineering applications, shear sheltering has rarely been observed in general non-ionized fluids. In this study, we visualize this shear sheltering in a generic neutral-fluid situation in electromembrane desalination: electroconvection (EC) under the Hagen–Poiseuille flow initiated by ion concentration polarization. Our work is the first demonstration of shear sheltering in electrochemical systems. Experiment, numerical simulation and scaling analysis accurately capture the effect by pinpointing the threshold for shear suppression. Determined by balancing the velocity fluctuation (with EC vortices) and the flow shear (with no-slip walls), the threshold for shear suppression is scaled as the EC height. Stable EC with coherent unidirectional vortices occurs under the threshold height, whereas chaotic EC occurs beyond this height as the EC-induced vortical perturbation overwhelms the flow shear. Attractors in a time-delay phase space illustrate this sequence of steady–periodic (stable EC)–chaotic transitions precisely. Going one step further, the shear sheltering effect is decoupled from the shear-independent mechanism of vortex suppression, i.e. vortex sweeping by the mean flow. In the frequency domain, this shear-independent effect is negligible for stable EC (when shear sheltering dominates), whereas it can reduce the level of chaotic fluctuations of chaotic EC (when shear sheltering weakens). Lastly, taken together, we describe the EC-induced convective ion transport by the new scaling law for the electric Nusselt number as a function of the electric Rayleigh number and the Reynolds number. This work not only expands the scientific understanding of EC and the shear sheltering effect, but also affects a broad range of electrochemical applications, including desalination, energy harvesting and sensors.

JFM classification

Instability: Instability Drops and Bubbles: Electrohydrodynamic effects Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 813 , 25 February 2017 , pp. 799 - 823
Check for updates
Copyright
© 2017 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

Bassett, M. R. & Hudson, J. L. 1989 Quasiperiodicity and chaos during an electrochemical reaction. J. Phys. Chem. 93 (7), 2731–2737.Google Scholar
Beyer, P., Benkadda, S., Fuhr-Chaudier, G., Garbet, X., Ghendrih, Ph. & Sarazin, Y. 2005 Nonlinear dynamics of transport barrier relaxations in tokamak edge plasmas. Phys. Rev. Lett. 94, 105001.CrossRefGoogle ScholarPubMed
Choi, J.-H., Lee, H.-J. & Moon, S.-H. 2001 Effects of electrolytes on the transport phenomena in a cation-exchange membrane. J. Colloid Interface Sci. 238 (1), 188–195.CrossRefGoogle Scholar
Cross, M. C. & Hohenberg, P. C. 1993 Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112.CrossRefGoogle Scholar
Dritschel, D. G. 1989 On the stabilization of a two-dimensional vortex strip by adverse shear. J. Fluid. Mech. 206, 193–221.Google Scholar
Druzgalski, C. L., Andersen, M. B. & Mani, A. 2013 Direct numerical simulation of electroconvective instability and hydrodynamic chaos near an ion-selective surface. Phys. Fluids 25 (11), 110804.CrossRefGoogle Scholar
Dukhin, S. S. 1991 Electrokinetic phenomena of the second kind and their applications. Adv. Colloid Interface Sci. 35, 173–196.Google Scholar
Gollub, J. P. & Benson, S. V. 1980 Many routes to turbulent convection. J. Fluid Mech. 100 (3), 449–470.Google Scholar
Grossmann, S. & Lohse, D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 27–56.Google Scholar
Hunt, J. C. R. & Durbin, P. A. 1999 Perturbed vortical layers and shear sheltering. Fluid Dyn. Res. 24 (6), 375–404.Google Scholar
Kim, S. J., Wang, Y.-C., Lee, J. H., Jang, H. & Han, J. 2007 Concentration polarization and nonlinear electrokinetic flow near a nanofluidic channel. Phys. Rev. Lett. 99, 044501.Google Scholar
Kwak, R., Guan, G., Peng, W. K. & Han, J. 2013a Microscale electrodialysis: concentration profiling and vortex visualization. Desalination 308, 138–146.CrossRefGoogle Scholar
Kwak, R., Pham, V. S., Lim, K. M. & Han, J. 2013b Shear flow of an electrically charged fluid by ion concentration polarization: scaling laws for electroconvective vortices. Phys. Rev. Lett. 110 (11), 114501.Google Scholar
Kwak, R., Pham, V. S., Kim, B., Chen, L. & Han, J. 2016 Enhanced salt removal by unipolar ion conduction in ion concentration polarization desalination. Sci. Rep. 6, 25349.Google Scholar
Mishchuk, N., Gonzalez-Caballero, F. & Takhistov, P. 2001 Electroosmosis of the second kind and current through curved interface. Colloid Surface A 181, 131–144.CrossRefGoogle Scholar
Mishchuk, N. A. & Takhistov, P. V. 1995 Electroosmosis of the second kind. Colloid Surfaces A 95 (2), 119–131.CrossRefGoogle Scholar
Packard, N. H., Crutchfield, J. P., Farmer, J. D. & Shaw, R. S. 1980 Geometry from a time series. Phys. Rev. Lett. 45, 712–716.Google Scholar
Pham, V. S., Li, Z., Lim, K. M., White, J. K. & Han, J. 2012 Direct numerical simulation of electroconvective instability and hysteretic current–voltage response of a permselective membrane. Phys. Rev. E 86, 046310.Google ScholarPubMed
Posner, J. D., Pérez, C. L. & Santiago, J. G. 2012 Electric fields yield chaos in microflows. Proc. Natl Acad. Sci. USA 109 (36), 14353–14356.CrossRefGoogle ScholarPubMed
Probstein, R. 2003 Physicochemical Hydrodynamics: An Introduction. Wiley.Google Scholar
Rubinstein, I. & Shtilman, L. 1979 Voltage against current curves of cation exchange membranes. J. Chem. Soc., Faraday Transactions 2: Molecular Chem. Phys. 75, 231–246.Google Scholar
Rubinstein, I. & Zaltzman, B. 2000 Electro-osmotically induced convection at a permselective membrane. Phys. Rev. E 62, 2238–2251.Google Scholar
Rubinstein, S. M., Manukyan, G., Staicu, A., Rubinstein, I., Zaltzman, B., Lammertink, R. G. H., Mugele, F. & Wessling, M. 2008 Direct observation of a nonequilibrium electro-osmotic instability. Phys. Rev. Lett. 101, 236101.Google Scholar
Schoch, R. B., Han, J. & Renaud, P. 2008 Transport phenomena in nanofluidics. Rev. Mod. Phys. 80, 839–883.CrossRefGoogle Scholar
Shats, M. G., Xia, H., Punzmann, H. & Falkovich, G. 2007 Suppression of turbulence by self-generated and imposed mean flows. Phys. Rev. Lett. 99, 164502.Google Scholar
Sinha, M., Kevrekidis, I. G. & Smits, A. J. 2006 Experimental study of a Neimark–Sacker bifurcation in axially forced Taylor–Couette flow. J. Fluid Mech. 558, 1–32.Google Scholar
Stevens, R. J. A. M., van der Poel, E. P., Grossmann, S. & Lohse, D. 2013 The unifying theory of scaling in thermal convection: the updated prefactors. J. Fluid Mech. 730, 295–308.Google Scholar
Strugarek, A., Sarazin, Y., Zarzoso, D., Abiteboul, J., Brun, A. S., Cartier-Michaud, T., Dif-Pradalier, G., Garbet, X., Ghendrih, Ph., Grandgirard, V., Latu, G., Passeron, C. & Thomine, O. 2013 Unraveling quasiperiodic relaxations of transport barriers with gyrokinetic simulations of tokamak plasmas. Phys. Rev. Lett. 111, 145001.Google Scholar
Swinney, H. L. 1983 Observations of order and chaos in nonlinear systems. Physica D 7 (1), 3–15.Google Scholar
Terry, P. W. 2000a Does flow shear suppress turbulence in nonionized flows? Phys. Plasmas 7, 1653–1661.Google Scholar
Terry, P. W. 2000b Suppression of turbulence and transport by sheared flow. Rev. Mod. Phys. 72, 109–165.Google Scholar
Urtenov, M. K., Uzdenova, A. M., Kovalenko, A. V., Nikonenko, V. V., Pismenskaya, N. D., Vasil’eva, V. I., Sistat, P. & Pourcelly, G. 2013 Basic mathematical model of overlimiting transfer enhanced by electroconvection in flow-through electrodialysis membrane cells. J. Membr. Sci. 447, 190–202.CrossRefGoogle Scholar
Vastano, J. A. & Moser, R. D. 1991 Short-time Lyapunov exponent analysis and the transition to chaos in Taylor–Couette flow. J. Fluid Mech. 233, 83–118.CrossRefGoogle Scholar
Wulf, P., Egbers, C. & Rath, H. J. 1999 Routes to chaos in wide-gap spherical Couette flow. Phys. Fluids 11 (6), 1359–1372.CrossRefGoogle Scholar

Kwak et al. supplementary movie

Supporting Video of diffusion-dominant cases (2.5-3.75V), stable EC (7.5V), and chaotic EC (15V)

Download Kwak et al. supplementary movie(Video)
Video 4.7 MB

Kwak et al. supplementary movie

Supporting Video of the stable and chaotic ECs at the threshold

Download Kwak et al. supplementary movie(Video)
Video 1.3 MB
Supplementary material: File

Kwak supplementary material

Supplementary information

Download Kwak supplementary material(File)
File 6.2 MB