Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-25T01:08:56.741Z Has data issue: false hasContentIssue false
  • English
  • Français

Electrophoresis of a Cylinder in a Cylindrical Tube

Part of: Magnetohydrodynamics and electrohydrodynamics

Published online by Cambridge University Press:  28 July 2017

Huicheng Feng  and
Teck Neng Wong
Huicheng Feng*
Affiliation:
School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
Teck Neng Wong*
Affiliation:
School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
*
*Corresponding author. Email addresses:mtnwong@ntu.edu.sg (T. N. Wong), feng0050@e.ntu.edu.sg (H. Feng)
*Corresponding author. Email addresses:mtnwong@ntu.edu.sg (T. N. Wong), feng0050@e.ntu.edu.sg (H. Feng)
Get access

Abstract

Electrophoresis of a cylinder suspended in a cylindrical tube is analytically studied in the limit of thin electric double layer approximation. The electric and fluid flow fields within the annulus, and the cylinder velocities are analytically obtained in bipolar coordinates. The results are analyzed with various values of dimensionless parameters: eccentricity, cylinder-to-tube radius ratio and tube-to-cylinder zeta potential ratio (i.e., tube-to-cylinder velocity scale ratio). The analysis shows that microvortices are generated within the annulus. By changing the parameters, different flow patterns can be created, which shows potential for mixing enhancement in micro/nanofluidics. Moreover, the cylinder not only translates but also rotates when the cylinder and tube are eccentric. The cylinder rotation might be utilized as a micromotor or an electric field detector. The cylinder trajectories show that the cylinder may approach the tube wall or rest within the tube depending on the zeta potential ratio.

Keywords

Electrophoresiscylindrical tubevortex generationcylinder rotation

MSC classification

Secondary: 76W05: Magnetohydrodynamics and electrohydrodynamics
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 4 , October 2017 , pp. 1101 - 1122
Copyright
Copyright © Global-Science Press 2017 

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

[1] Berger, M. J. and Collela, P., Local adaptive mesh refinement for shock hydrodynamics, J. Comput. Phys. 82 (1989) 62–84.CrossRefGoogle Scholar
[2] Ajdari, A., Pumping liquids using asymmetric electrode arrays, Phys. Rev. E 61 (1) (2000) R45.Google Scholar
[3] Yoon, M. S., Kim, B. J., Sung, H. J., Pumping and mixing in a microchannel using ac asymmetric electrode arrays, Int. J. Heat Fluid Flow 29 (1) (2008) 269–280.Google Scholar
[4] Cartier, C. A., Drews, A. M., Bishop, K. J., Microfluidic mixing of nonpolar liquids by contact charge electrophoresis, Lab. Chip 14 (21) (2014) 4230–4236.Google Scholar
[5] Feng, H., Wong, T. N., Che, Z., Marcos, Chaotic micromixer utilizing electro-osmosis and induced charge electro-osmosis in eccentric annulus, Phys. Fluids 28 (6).Google Scholar
[6] Daghighi, Y., Li, D., Micro-valve using induced-charge electrokinetic motion of janus particle, Lab. Chip 11 (17) (2011) 2929–2940.Google Scholar
[7] Sugioka, H., Elastic valve using induced-charge electro-osmosis, Phys. Rev. Applied 3 (6) (2015) 064001.Google Scholar
[8] Ren, Y., Liu, W., Jia, Y., Tao, Y., Shao, J., Ding, Y., Jiang, H., Induced-charge electroosmotic trapping of particles, Lab. Chip 15 (10) (2015) 2181–2191.Google Scholar
[9] Schnitzer, O., Frankel, I., Yariv, E., Electrophoresis of bubbles, J. Fluid Mech. 753 (2014) 49–79.Google Scholar
[10] Schnitzer, O., Frankel, I., Yariv, E., Electrokinetic flows about conducting drops, J. Fluid Mech. 722 (2013) 394–423.Google Scholar
[11] Masliyah, J. H., Bhattacharjee, S., Electrokinetic Phenomena, John Wiley & Sons, Inc., 2005, Ch. 7, pp. 221–227.Google Scholar
[12] Ohshima, H., Electrophoresis of colloidal particles in a salt-free medium, Chem. Eng. Sci. 61 (7) (2006) 2104–2107.CrossRefGoogle Scholar
[13] Loewenberg, M., Davis, R. H., Near-contact electrophoretic particle motion, J. Fluid Mech. 288 (1995) 103–122.Google Scholar
[14] Yariv, E., Brenner, H., Near-contact electrophoretic motion of a sphere parallel to a planar wall, J. Fluid Mech. 484 (2003) 85–111.Google Scholar
[15] Lee, T. C., Keh, H. J., Electrophoresis of a spherical particle in a spherical cavity, Microfluid Nanofluid 16 (6) (2014) 1107–1115.CrossRefGoogle Scholar
[16] Hsu, J.-P., Yee, C.-P., Yeh, L.-H., Importance of electroosmotic flow and multiple ionic species on the electrophoresis of a rigid sphere in a charge-regulated zwitterionic cylindrical pore, Langmuir 28 (29) (2012) 10942–10947.Google Scholar
[17] Chiu, H. C., Keh, H. J., Electrophoresis of a colloidal sphere with double-layer polarization in a microtube, Microfluid Nanofluid 20 (4) (2016) 1–13.Google Scholar
[18] Unni, H. N., Keh, H. J., Yang, C., Analysis of electrokinetic transport of a spherical particle in a microchannel, Electrophoresis 28 (4) (2007) 658–664.Google Scholar
[19] Chang, Y. C., Keh, H. J., Diffusiophoresis and electrophoresis of a charged sphere perpendicular to two plane walls, J. Colloid Interface Sci. 322 (2) (2008) 634–653.Google Scholar
[20] Chen, W. J., Keh, H. J., Electrophoresis of a charged soft particle in a charged cavity with arbitrary double-layer thickness, J. Phys. Chem. B 117 (33) (2013) 9757–9767.Google Scholar
[21] Tseng, S., Hsu, J.-P., Lo, H.-M., Yeh, L.-H., Electrophoresis of a soft sphere in a necked cylindrical nanopore, Phys. Chem. Chem. Phys. 15 (28) (2013) 11758–11765.Google Scholar
[22] Hsu, J.-P., Kuo, C.-C., Electrophoresis of a soft toroid coaxially along the axis of a cylindrical pore, Chem. Eng. Sci. 64 (24) (2009) 5247–5254.CrossRefGoogle Scholar
[23] Keh, H. J., Horng, K. D., Kuo, J., Boundary effects on electrophoresis of colloidal cylinders, J. Fluid Mech. 231 (1991) 211–228.Google Scholar
[24] Feng, H., Wong, T. N., Pair interactions between conducting and non-conducting cylinders under uniform electric field, Chem. Eng. Sci. 142 (2016) 12–22.CrossRefGoogle Scholar
[25] Hsu, J.-P., Chen, Z.-S., Lee, D.-J., Tseng, S., Su, A., Effects of double-layer polarization and electroosmotic flow on the electrophoresis of a finite cylinder along the axis of a cylindrical pore, Chem. Eng. Sci. 63 (18) (2008) 4561–4569.Google Scholar
[26] He, Y.-Y., Wu, E., Lee, E., Electrophoresis in suspensions of charged porous spheres in salt-free media, Chem. Eng. Sci. 65 (20) (2010) 5507–5516.CrossRefGoogle Scholar
[27] Bhattacharyya, S., De, S., Gopmandal, P. P., Electrophoresis of a colloidal particle embedded in electrolyte saturated porous media, Chem. Eng. Sci. 118 (2014) 184–191.CrossRefGoogle Scholar
[28] Khair, A. S., Posluszny, D. E., Walker, L. M., Coupling electrokinetics and rheology: electrophoresis in non-newtonian fluids, Phys. Rev. E 85 (1) (2012) 016320.CrossRefGoogle ScholarPubMed
[29] Zhao, C., Yang, C., Electrokinetics of non-newtonian fluids: a review, Adv. Colloid Interface Sci. 201 (2013) 94–108.Google Scholar
[30] Squires, T. M., Bazant, M. Z., Breaking symmetries in induced-charge electro-osmosis and electrophoresis, J. Fluid Mech. 560 (2006) 65–101.Google Scholar
[31] Boymelgreen, A., Yossifon, G., Park, S., Miloh, T., Spinning janus doublets driven in uniform ac electric fields, Phys. Rev. E 89 (1) (2014) 011003.CrossRefGoogle ScholarPubMed
[32] Dose, E. V., Guiochon, G., Timescales of transient processes in capillary electrophoresis, J. Chromatogr. A 652 (1) (1993) 263–275.Google Scholar
[33] Söderman, O., Jönsson, B., Electro-osmosis: Velocity profiles in different geometries with both temporal and spatial resolution, J. Chem. Phys. 105 (23) (1996) 10300–10311.CrossRefGoogle Scholar
[34] Jackson, J. D., Classical Electrodynamics, Wiley, 1999.Google Scholar
[35] Jeffery, G., The rotation of two circular cylinders in a viscous fluid, Proc. R. Soc. London, Ser. A 101 (709) (1922) 169–174.Google Scholar
[36] Feng, H., Wong, T. N., Che, Z., Induced charge electrophoresis of a conducting cylinder in a nonconducting cylindrical pore and its micromotoring application, Phys. Rev. Fluids 1 (2016) 044103.Google Scholar
[37] Morrison, F., Electrophoresis of a particle of arbitrary shape, J. Colloid Interface Sci. 34 (2) (1970) 210–214.CrossRefGoogle Scholar
[38] Cummings, E. B., Griffiths, S., Nilson, R., Paul, P., Conditions for similitude between the fluid velocity and electric field in electroosmotic flow, Anal. Chem. 72 (11) (2000) 2526–2532.Google Scholar
[39] Yariv, E., The electrophoretic mobilities of a circular cylinder in close proximity to a dielectric wall, J. Fluid Mech. 804.Google Scholar
[40] Saintillan, D., Nonlinear interactions in electrophoresis of ideally polarizable particles, Phys. Fluids 20 (6) (2008) 067104.Google Scholar
[41] Feng, H., Wong, T.N., Marcos, Pair interactions in induced charge electrophoresis of conducting cylinders, Int. J. Heat Mass Trans. 88 (2015) 674–683.CrossRefGoogle Scholar