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Hydrodynamic bifurcation in electro-osmotically driven periodic flows
Phys. Rev. Fluids 3, 063702 – Published 8 June, 2018
DOI: https://doi.org/10.1103/PhysRevFluids.3.063702
Abstract
In this paper, we report an inertial instability that occurs in electro-osmotically driven channel flows. We assume that the charge motion under the influence of an externally applied electric field is confined to a small vicinity of the channel walls that, effectively, drives a bulk flow through a prescribed slip velocity at the boundaries. Here, we study spatially periodic wall velocity modulations in a two-dimensional straight channel numerically. At low slip velocities, the bulk flow consists of a set of vortices along each wall that are left-right symmetric, while at sufficiently high slip velocities, this flow loses its stability through a supercritical bifurcation. Surprisingly, the flow state that bifurcates from a left-right symmetric base flow has a rather strong mean component along the channel, which is similar to pressure-driven velocity profiles. The instability sets in at rather small Reynolds numbers of about 20–30, and we discuss its potential applications in microfluidic devices.
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References (19)
- V. Pretorius, B. J. Hopkins, and J. D. Schieke, Electro-osmosis: A new concept for high-speed liquid chromatograph, J. Chromatogr. A 99, 23 (1974).
- R. Probstein, Physicochemical Hydrodynamics (Wiley, New York, 1994).
- R. B. Schoch, J. Han, and P. Renaud, Transport phenomena in nanofluidics, Rev. Mod. Phys. 80, 839 (2008).
- X. Wang, C. Cheng, S. Wang, and S. Liu, Electroosmotic pumps and their applications in microfluidic systems, Microfluid. Nanofluid. 6, 145 (2009).
- C.-Y. Lee, C.-L. Chang, Y.-N. Wang, and L.-M. Fu, Microfluidic mixing: A review, Int. J. Mol. Sci. 12, 3263 (2011).
- V. Murlidhar, M. Zeinali, S. Grabauskiene, M. Ghannad-Rezaie, M. S. Wicha, D. M. Simeone, N. Ramnath, R. M. Reddy, and S. Nagrath, A radial flow microfluidic device for ultra-high-throughput affinity-based isolation of circulating tumor cells, Small 10, 4895 (2014).
- A. Ajdari, Electro-osmosis on inhomogeneously charged surfaces, Phys. Rev. Lett. 75, 755 (1995).
- S. Mandal, U. Ghosh, A. Bandopadhyay, and S. Chakraborty, Electro-osmosis of superimposed fluids in the presence of modulated charged surfaces in narrow confinements, J. Fluid Mech. 776, 390 (2015).
- A. Bandopadhyay, U. Ghosh, and S. Chakraborty, Time periodic electroosmosis of linear viscoelastic liquids over patterned charged surfaces in microfluidic channels, J. Non-Newtonian Fluid Mech. 202, 1 (2013).
- C.-C. Chang and R.-J. Yang, Chaotic mixing in a microchannel utilizing periodically switching electro-osmotic recirculating rolls, Phys. Rev. E 77, 056311 (2008).
- J. B. Zhang, G. W. He, and F. Liu, Electro-osmotic flow and mixing in heterogeneous microchannels, Phys. Rev. E 73, 056305 (2006).
- T. Zhao, X. Wang, L. Jiang, and R. G. Larson, Assessment of mesoscopic particle-based methods in microfluidic geometries, J. Chem. Phys. 139, 084109 (2013).
- M. H. Oddy, J. G. Santiago, and J. C. Mikkelson, Electrokinetic instability micromixing, Anal. Chem. 73, 5822 (2001).
- J. D. Posner and J. G. Santiago, Convective instability of electrokinetic flows in a cross-shaped microchannel, J. Fluid Mech. 555, 1 (2006).
- H. Lin, Electrokinetic instability in microchannel flows: A review, Mech. Res. Commun. 36, 33 (2009).
- J. D. Posner, C. L. Perez, and J. G. Santiago, Electric fields yield chaos in microflows, Proc. Natl. Acad. Sci. U.S.A. 109, 14353 (2012).
- J. P. Boyd, Chebyshev and Fourier Spectral Methods, 2nd ed., Dover Books on Mathematics (Dover, New York, 2013).
- C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics (Springer-Verlag, Berlin, 1987).
- H. Rezvantalab, G. Zhu, and R. G. Larson, The effect of wall depletion and hydrodynamic interactions on stress-gradient-induced polymer migration, Soft Matter 12, 5883 (2016).
