Analytical solution of time periodic electroosmotic flows: Analogies to Stokes' second problem

被引:172
作者
Dutta, P
Beskok, A [1 ]
机构
[1] Texas A&M Univ, Dept Mech Engn, Microfluid Lab, College Stn, TX 77843 USA
[2] Washington State Univ, Sch Mech & Mat Engn, Pullman, WA 99164 USA
关键词
D O I
10.1021/ac015546y
中图分类号
O65 [分析化学];
学科分类号
070302 ; 081704 ;
摘要
Analytical solutions of time periodic electroosmotic flows in two-dimensional straight channels are obtained as a function of a nondimensional parameter kappa, which is based on the electric double-layer (EDL) thickness, kinematic viscosity, and frequency of the externally applied electric field. A parametric study as a function of kappa reveals interesting physics, ranging from oscillatory "pluglike" flows to cases analogous to the oscillating flat plate in a semi-infinite flow domain (Stokes' second problem). The latter case differs from the Stokes' second solution within the EDI, since the flow is driven with an oscillatory electric field rather than an oscillating plate. The analogous case of plate oscillating with the Helmholtz-Smoluchowski velocity matches our analytical solution in the bulk flow region. This indicates that the instantaneous Hehnholtz-Smoluchowski velocity is the appropriate electroosmotic slip condition even for high-frequency excitations. The velocity profiles for large Ic values show inflection points very near the walls with localized vorticity extrema that are stronger than the Stokes layers. This have the potential to result in low Reynolds number flow instabilities. It is also shown that, unlike the steady pure electroosmotic flows, the bulk flow region of time periodic electroosmotic flows are rotational when the diffusion length scales are comparable to and less than the half channel height.
引用
收藏
页码:5097 / 5102
页数:6
相关论文
共 19 条
[1]  
Anderson GP, 1999, FIELD ANAL CHEM TECH, V3, P307, DOI 10.1002/(SICI)1520-6521(1999)3:4/5<307::AID-FACT9>3.0.CO
[2]  
2-M
[3]   Electroosmosis through a cation-exchange membrane:: Effect of an ac perturbation on the electroosmotic flow [J].
Barragán, VM ;
Bauzá, CR .
JOURNAL OF COLLOID AND INTERFACE SCIENCE, 2000, 230 (02) :359-366
[4]   ELECTROKINETIC FLOW IN ULTRAFINE CAPILLARY SLITS [J].
BURGREEN, D ;
NAKACHE, FR .
JOURNAL OF PHYSICAL CHEMISTRY, 1964, 68 (05) :1084-&
[5]   Frequency-wavenumber migration of ultrasonic data [J].
Chang, YF ;
Chern, CC .
JOURNAL OF NONDESTRUCTIVE EVALUATION, 2000, 19 (01) :1-10
[6]  
Chapra S.C., 2010, Numerical Methods for Engineers, V6
[7]  
CHEN CH, 2000, P ASME INT MECH ENG, P523
[8]   TIMESCALES OF TRANSIENT PROCESSES IN CAPILLARY ELECTROPHORESIS [J].
DOSE, EV ;
GUIOCHON, G .
JOURNAL OF CHROMATOGRAPHY A, 1993, 652 (01) :263-275
[9]   Analytical solution of combined eloectoossmotic/pressure driven flows in two-dimensional straight channels: Finite debye layer effects [J].
Dutta, P ;
Beskok, A .
ANALYTICAL CHEMISTRY, 2001, 73 (09) :1979-1986
[10]  
DUTTA P, 2001, THESIS TEXAS A M U C