Transient Electro-Osmotic and Pressure Driven Flows through a Microannulus

Affiliation(s)

School of Mathematical Science, Inner Mongolia University, Hohhot, China.

School of Mathematics and Statistics, Inner Mongolia University of Finance and Economics, Hohhot, China.

School of Mathematical Science, Inner Mongolia University, Hohhot, China.

School of Mathematics and Statistics, Inner Mongolia University of Finance and Economics, Hohhot, China.

ABSTRACT

Flow behavior of transient mixed electro-osmotic and pressure driven flows (EOF/PDF) through a microannulus is investigated based on a linearized Poisson-Boltzmann equation and Navier-Stokes equation. A semi-analytical solution of EOF velocity distribution as functions of relevant parameters is derived by *β*, the normalized pressure gradient Ω* *and the inner to outer radius ratio *α* on transient EOF velocity are presented.

Cite this paper

R. Na, Y. Jian, L. Chang, J. Su and Q. Liu, "Transient Electro-Osmotic and Pressure Driven Flows through a Microannulus,"*Open Journal of Fluid Dynamics*, Vol. 3 No. 2, 2013, pp. 50-56. doi: 10.4236/ojfd.2013.32007.

R. Na, Y. Jian, L. Chang, J. Su and Q. Liu, "Transient Electro-Osmotic and Pressure Driven Flows through a Microannulus,"

References

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[8] J. P. Hsu, C. Y. Kao, S. J. Tseng and C. J. Chen, “Electrokinetic Flow through an Elliptical Microchannel: Effects of Aspect Ratio and Electrical Boundary Conditions,” The Journal of Physical Chemistry, Vol. 248, No. 1, 2002, pp. 176-184.

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[12] C. Y. Wang, Y. H. Liu and C. C. Chang, “Analytical Solution of Electroosmotic Flow in a Semicircular Microchannel,” Physical of Fluids, Vol. 20, No. 6, 2008, Article ID: 063105. doi:10.1063/1.2939399

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[16] Y. J. Jian, L. G. Yang and Q. S. Liu. “Time Periodic Electro-Osmotic Flow through a Microannulus,” Physical of Fluids, Vol. 22, No. 4, 2010, Article ID: 042001. doi:10.1063/1.3358473

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[18] Y. J. Kang, C. Yang and X. Y. Huang, “Dynamic Aspects of Electroosmotic Flow in a Cylindrical Microcapillary,” International Journal of Engineering Science, Vol. 40, No. 20, 2002, pp. 2203-2221. doi:10.1016/S0020-7225(02)00143-X

[19] C. C. Chang and C. Y. Wang, “Starting Electro-Osmotic Flow in an Annulus and in a Rectangular Channel,” Electrophoresis, Vol. 29, No. 14, 2008, pp. 2970-2979. doi:10.1002/elps.200800041

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[1] H. A. Stone, A. D. Stroock and A. Ajdar, “Engineering Flows in Small Devices: Microfluidics toward a Lab-On-a-Chip,” Annual Review of Fluid Mechanics, Vol. 36, No. 1, 2004, pp. 381-411. doi:10.1146/annurev.fluid.36.050802.122124

[2] R. J. Hunter, “Zeta Potential in Colloid Science,” Academic Press, San Diego, 1981.

[3] G. Karniadakis, A. Beskok and N. Aluru, “Micorflows and Nanoflows: Fundamentals and Simulation,” Springer, New York, 2005.

[4] D. Burgreen and F. R. Nakache, “Electrokinetic Flow in Ultrafine Capillary Slits,” The Journal of Physical Chemistry, Vol. 68, No. 5, 1964, pp. 1084-1091.

[5] S. Levine, J. R. Marriott, G. Neale and N. Epstein, “Theory of Electrokinetic Flow in Fine Cylindrical Capillaries at High Zeta-Potentials,” The Journal of Physical Chemistry, Vol. 52, No. 1, 1975, pp. 136-149.

[6] H. K. Tsao, “Electroosmotic Flow through an Annulus,” The Journal of Physical Chemistry, Vol. 225, No. 1, 2000, pp. 247-250.

[7] Y. J. Kang, C. Yang and X. Y. Huang, “Electroosmotic Flow in a Capillary Annulus with High Zeta Potentials,” The Journal of Physical Chemistry, Vol. 253, No. 1, 2002, pp. 285-294.

[8] J. P. Hsu, C. Y. Kao, S. J. Tseng and C. J. Chen, “Electrokinetic Flow through an Elliptical Microchannel: Effects of Aspect Ratio and Electrical Boundary Conditions,” The Journal of Physical Chemistry, Vol. 248, No. 1, 2002, pp. 176-184.

[9] C. Yang, D. Li and J. H. Masliyah, “Modeling Forced Liquid Convection in Rectangular Microchannels with Electrokinetic Effects,” International Journal of Heat and Mass Transfer, Vol. 41, No. 24, 1998, pp. 4229-4249. doi:10.1016/S0017-9310(98)00125-2

[10] S. Arulanandam and D. Li, “Liquid Transport in Rectangular Microchannels by Electroosmotic Pumping,” Colloids and Surfaces A: Physicochemical and Engineering Aspects, Vol. 161, No. 1, 2000, pp. 89-102. doi:10.1016/S0927-7757(99)00328-3

[11] F. Bianchi, R. Ferrigno and H. H. Girault, “Finite Element Simulation of an Electroosmotic Driven Flow Division at a t-Junction of Microscale Dimensions,” Analytical Chemistry, Vol. 72, No. 9, 2000, pp. 1987-1993. doi:10.1021/ac991225z

[12] C. Y. Wang, Y. H. Liu and C. C. Chang, “Analytical Solution of Electroosmotic Flow in a Semicircular Microchannel,” Physical of Fluids, Vol. 20, No. 6, 2008, Article ID: 063105. doi:10.1063/1.2939399

[13] P. Dutta and A. Beskok, “Analytical Solution of Time Periodic Electroosmotic Flows: Analogies to Stokes’s Econd Problem,” Analytical Chemistry, Vol. 73, No. 21, 2001, pp. 5097-5102. doi:10.1021/ac015546y

[14] X. M. Wang, B. Chen and J. K. Wu, “A Semianalytical Solution of Periodical Electro-Osmosis in a Rectangular Microchannel,” Physical of Fluids, Vol. 19, No. 12, 2007, Article ID: 127101. doi:10.1063/1.2784532

[15] S. Chakraborty and S. Ray, “Mass Flow-Rate Control through Time Periodic Electro-Osmotic Flows in Circular Microchannels,” Physical of Fluids, Vol. 20, No. 8, 2008, Article ID: 083602. doi:10.1063/1.2949306

[16] Y. J. Jian, L. G. Yang and Q. S. Liu. “Time Periodic Electro-Osmotic Flow through a Microannulus,” Physical of Fluids, Vol. 22, No. 4, 2010, Article ID: 042001. doi:10.1063/1.3358473

[17] H. J. Keh and H. C. Tseng, “Transient Electrokinetic Flow in Fine Capillaries,” Journal Colloid Interface Science, Vol. 242, No. 2, 2001, pp. 450-459. doi:10.1006/jcis.2001.7797

[18] Y. J. Kang, C. Yang and X. Y. Huang, “Dynamic Aspects of Electroosmotic Flow in a Cylindrical Microcapillary,” International Journal of Engineering Science, Vol. 40, No. 20, 2002, pp. 2203-2221. doi:10.1016/S0020-7225(02)00143-X

[19] C. C. Chang and C. Y. Wang, “Starting Electro-Osmotic Flow in an Annulus and in a Rectangular Channel,” Electrophoresis, Vol. 29, No. 14, 2008, pp. 2970-2979. doi:10.1002/elps.200800041

[20] F. R. De Hoog, J. H. Knight and A. N. Stokes, “An Improved Method for Numerical Inversion of Laplace Transforms,” SIAM Journal on Scientific and Statistical Computing, Vol. 3, No. 3, 1982, pp. 357-366. doi:10.1137/0903022