zbMATH — the first resource for mathematics

Alternating current electroosmotic flow of the Jeffreys fluids through a slit microchannel. (English) Zbl 1308.76327
Summary: Using the method of separation of variables, semi-analytical solutions are presented for the time periodic EOF flow of linear viscoelastic fluids between micro-parallel plates. The linear viscoelastic fluids used here are described by the Jeffreys model. The solution involves solving the Poisson-Boltzmann (PB) equation, together with the Cauchy momentum equation and the Jeffreys constitutive equation considering the depletion effect produced by the interaction between macro-molecules of the Jeffreys fluid and the channel surface. The overall flow is divided into depletion layer and bulk flow outside of depletion layer. The velocity expressions of these two layers were obtained, respectively. By numerical computations, the influence of oscillating Reynolds number, Re, normalized retardation time, \(\lambda_{2}\omega\), and normalized wall zeta potential, \(\psi=w\), on velocity amplitude is presented. Results show that the magnitude of the velocity amplitude becomes smaller with the increase of retardation time for small and intermediate Re. For large Re, the velocity is almost unchanged near the EDL with retardation time. Moreover, high zeta potential results in larger the magnitude of EOF velocity no matter whether the Re is large or not, especially within the depletion layer.{
©2011 American Institute of Physics}

76W05 Magnetohydrodynamics and electrohydrodynamics
35Q35 PDEs in connection with fluid mechanics
76M25 Other numerical methods (fluid mechanics) (MSC2010)
Full Text: DOI
[1] DOI: 10.1146/annurev.fluid.36.050802.122124 · Zbl 1076.76076
[2] DOI: 10.1016/j.ijheatmasstransfer.2005.11.007 · Zbl 1189.76433
[3] Hunter R. J., Zeta Potential in Colloid Science: Principles and Applications (1981)
[4] Karniadakis G., Microflows and Nanoflows: Fundamentals and Simulation (2005)
[5] DOI: 10.1021/j100787a019
[6] DOI: 10.1016/0021-9797(75)90310-0
[7] DOI: 10.1006/jcis.1999.6696
[8] DOI: 10.1006/jcis.2002.8453
[9] DOI: 10.1006/jcis.2001.8200
[10] DOI: 10.1016/S0017-9310(98)00125-2 · Zbl 0962.76614
[11] DOI: 10.1016/S0927-7757(99)00328-3
[12] DOI: 10.1021/ac991225z
[13] DOI: 10.1063/1.2939399 · Zbl 1182.76812
[14] DOI: 10.1021/ac015546y
[15] DOI: 10.1006/jcis.2001.7797
[16] DOI: 10.1016/S0020-7225(02)00143-X
[17] DOI: 10.1063/1.2784532 · Zbl 1182.76816
[18] DOI: 10.1063/1.2949306 · Zbl 1182.76135
[19] DOI: 10.1021/la702109c
[20] DOI: 10.1006/jcis.1999.6708
[21] DOI: 10.1063/1.3358473 · Zbl 1188.76065
[22] DOI: 10.1016/j.aca.2005.11.046
[23] DOI: 10.1016/j.aca.2007.10.049
[24] DOI: 10.1016/j.jcis.2008.06.028
[25] DOI: 10.1016/j.colsurfa.2010.07.014
[26] DOI: 10.1002/elps.200900564
[27] DOI: 10.1016/j.jnnfm.2008.11.002 · Zbl 1274.76379
[28] DOI: 10.1016/j.jcis.2007.09.027
[29] DOI: 10.1039/b800185e
[30] DOI: 10.1016/j.jnnfm.2011.02.003 · Zbl 1282.76053
[31] DOI: 10.1016/j.jnnfm.2009.01.006 · Zbl 1274.76085
[32] DOI: 10.1016/0377-0257(80)85007-5 · Zbl 0432.76012
[33] DOI: 10.1016/j.jcis.2010.01.025
[34] DOI: 10.1002/elps.200800578
[35] DOI: 10.1007/s10404-010-0651-y
[36] DOI: 10.1016/j.jcis.2007.12.032
[37] Bird R. B., Transport Phenomena, 2. ed. (2001)
[38] DOI: 10.1016/j.jcis.2007.07.007
[39] Li D., Electrokinetics in Microfluidics (2004)
[40] Bird R. B., Fluid Mechanics 1, 2. ed. (1987)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.