A thin film flow on a cylinder driven by electro-osmosis in direct current (DC) and alternating current (AC) electric field are analytically investigated respectively. Analytical solutions of electric potential and flow velocity are obtained by solving viscous incompressible hydrodynamic equations coupling with linearized
Possion-Boltzmann equation based on the leaky dielectric model and the Debye-H¨uckel approximation. In a DC electric field, the dimensionless flow velocity just differs from the electric potential by a constant. The flow velocity on free surface only depends on a ratio α between the electric potential on the free surface and the potential on the cylindrical surface. In an AC electric field, the results show the amplitude of flow velocity. The phase difference between flow velocity in flow field and that in the electrical double layer is closely related to the Reynolds number. Amplitude of flow velocity in an AC periodic electric field is similar to that in a DC steady electric field in low Reynolds number. With the increase of the Reynolds number, the amplitude of flow velocity decreases near the solid surface, while the phase difference increases. The amplitude of flow velocity on a free surface decreases/increases as the Reynolds number increases for low/high α.
LI Jun, HU Guo-hui
. Characteristics of Thin Film Flow on Cylinder Driven by Electro-osmosis[J]. Journal of Shanghai University, 2013
, 19(6)
: 579
-584
.
DOI: 10.3969/j.issn.1007-2861.2013.06.006
[1] Reuss F F. Charge-induced flow [C]//Proceedings of the Imperial Society of Naturalists of Moscow. 1809: 327-337.
[2] Burgreen D, Nakache F. Electrokinetic flow in ultrafine capillary slits [J]. The Journal of Physical Chemistry, 1964, 68(5): 1084-1091.
[3] Levine S, Marriott J R, Neale G, et al. Theory of electrokinetic flow in fine cylindrical capillaries at high zeta-potentials [J]. Journal of Colloid and Interface Science, 1975, 52: 136-149.
[4] Tsao H K.Electroosmoticflowthroughanannulus[J]. Journal of Colloid and Interface Science, 2000, 225: 247-250.
[5] Wang C Y, Liu Y H, Chang C C. Analytical solution of electro-osmotic flow in a semicircular microchannel [J]. Physics of Fluids, 2008, 20(6): 063105.
[6] Dutta P, Beskok A. Analytical solution of time periodic electroosmotic flows: analogies to stokes’ second problem [J]. Analytical Chemistry, 2001, 73: 5097-5102.
[7] Wang X, Chen B, Wu J. A semianalytical solution of periodical electro-osmosis in a rectangular microchannel [J]. Physics of Fluids, 2007, 19(12): 127101.
[8] Erickson D, Li D. Analysis of alternating current electroosmotic flows in a rectangular microchannel [J]. Langmuir, 2003, 19: 5421-5430.
[9] Brask A, Goranovi´c G, Jensen M J, et al. A novel electro-osmotic pump design for nonconducting liquids: theoretical analysis of flow rate-pressure characteristics and stability [J]. Journal of Micromechanics and Microengineering, 2005, 15: 883-891.
[10] Joo S W. A new hydrodynamic instability in ultrathin film flows induced by electro-osmosis [J]. Journal of Mechanical Science and Technology, 2008, 22: 382-386.
[11] Choi W, Sharma A, Qian S, et al. Is free surface free in micro-scale electrokinetic flows? [J]. Journal of Colloid and Interface Science, 2010, 347: 153-155.
[12] Taylor G. Disintegration of water drops in an electric field [J]. Mathematical and Physical Sciences: Series A, 1964, 280(1382): 383-397.
[13] Melcher J, Taylor G. Electrohydrodynamics: a review of the role of interfacial shear stresses [J]. Annual Review of Fluid Mechanics, 1969, 1: 111-146.
[14] 唐文跃, 胡国辉. 生物芯片中周期性电渗驱动液体薄膜的流动特性[J]. 力学学报, 2012, 44(3): 600-606.
[15] Dutta P, Beskok A, Warburton T C. Numerical simulation of mixed electroosmotic/pressure driven microflows [J]. Numerical Heat Transfer: Part A, 2002, 41(2): 131-148.
[16] Rice C, Whitehead R. Electrokinetic flow in a narrow cylindrical capillary [J]. The Journal of Physical Chemistry, 1965, 69: 4017-4024.
[17] Saville D. Electrohydrodynamics: the Taylor-Melcher leaky dielectric model [J]. Annual Review of Fluid Mechanics, 1997, 29: 27-64.
[18] Patankar N A, Hu H H. Numerical simulation of electroosmotic flow [J]. Analytical Chemistry, 1998, 70: 1870-1881.
