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Transient electroosmotic flow of general Maxwell fluids through a slit microchannel. (English) Zbl 1302.76011
Summary: Using the Laplace transform method, semi-analytical solutions are presented for transient electroosmotic flow of Maxwell fluids between micro-parallel plates. The solution involves solving the linearized Poisson-Boltzmann equation, together with the Cauchy momentum equation and the Maxwell constitutive equation considering the depletion effect produced by the interaction between macro-molecules of the Maxwell fluids and the channel surface. The overall flow is divided into depletion layer and bulk flow outside of depletion layer. In addition, the Maxwell stress is incorporated to describe the boundary condition at the interface. The velocity expressions of these two layers were obtained respectively. By numerical computations of inverse Laplace transform, the influences of viscosity ratio \(\mu\), density ratio \(\rho\), dielectric constant ratio \(\epsilon\) of layer II to layer I, relaxation time \(\bar\lambda_1\), interface charge density jump \(Q\), and interface zeta potential difference \(\Delta\bar\psi\) on transient velocity amplitude are presented.

MSC:
76A05 Non-Newtonian fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
76W05 Magnetohydrodynamics and electrohydrodynamics
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[1] Stone, H.A.; Stroock, A.D.; Ajdari, A., Engineering flows in small devices: microfluidics toward a lab-on-a-chip, Ann. Rev. Fluid Mech., 36, 381-411, (2004) · Zbl 1076.76076
[2] Bayraktar, T.; Pidugu, S.B., Characterization of liquid flows in microfluidic systems, Int. J. Heat Mass Trans., 49, 815-824, (2006) · Zbl 1189.76433
[3] Li D.: Electrokinetics in Microfluidics. Elsevier, Amsterdam (2004)
[4] Karniadakis G., Beskok A., Aluru N.: Micorflows and Nanoflows: Fundamentals and Simulation. Springer, New York (2005) · Zbl 1115.76003
[5] Levine, S.; Marriott, J.R.; Neale, G.; Epstein, N., Theory of electrokinetic flow in fine cylindrical capillaries at high zeta potentials, J. Colloid Interface Sci., 52, 136-149, (1975)
[6] Tsao, H.K., Electroosmotic flow through an annulus, J. Colloid Interface Sci., 225, 247-250, (2000)
[7] Hsu, J.P.; Kao, C.Y.; Tseng, S.J.; Chen, C.J., Electrokinetic flow through an elliptical microchannel: effects of aspect ratio and electrical boundary conditions, J. Colloid Interface Sci., 248, 176-184, (2002)
[8] Yang, C.; Li, D.; Masliyah, J.H., Modeling forced liquid convection in rectangular microchannels with electrokinetic effects, Int. J. Heat Mass Transf., 41, 4229-4249, (1998) · Zbl 0962.76614
[9] Bianchi, F.; Ferrigno, R.; Girault, H.H., Finite element simulation of an electroosmotic driven flow division at a t-junction of microscale dimensions, Anal. Chem., 72, 1987-1993, (2000)
[10] Wang, C.Y.; Liu, Y.H.; Chang, C.C., Analytical solution of electro-osmotic flow in a semicircular microchannel, Phys. Fluids, 20, 063105, (2008) · Zbl 1182.76812
[11] Dutta, P.; Beskok, A., Analytical solution of time periodic electroosmotic flows: analogies to stokes’ second problem, Anal. Chem., 73, 5097-5102, (2001)
[12] Keh, H.J.; Tseng, H.C., Transient electrokinetic flow in fine capillaries, J. Colloid Interface Sci., 242, 450-459, (2001)
[13] Kang, Y.J.; Yang, C.; Huang, X.Y., Dynamic aspects of electroosmotic flow in a cylindrical microcapillary, Int. J. Eng. Sci., 40, 2203-2221, (2002)
[14] Wang, X.M.; Chen, B.; Wu, J.K., A semianalytical solution of periodical electro-osmosis in a rectangular microchannel, Phys. Fluids, 19, 127101, (2007) · Zbl 1182.76816
[15] Chakraborty, S.; Ray, S., Mass flow-rate control through time periodic electro-osmotic flows in circular microchannels, Phys. Fluids, 20, 083602, (2008) · Zbl 1182.76135
[16] Jian, Y.J.; Yang, L.G.; Liu, Q.S., Time periodic electro-osmotic flow through a microannulus, Phys. Fluids, 22, 042001, (2010) · Zbl 1188.76065
[17] Deng, S.Y.; Jian, Y.J.; Bi, Y.H.; Chang, L.; Wang, H.J.; Liu Q., S., Unsteady electroosmotic flow of power-law fluid in a rectangular microchannel, Mech. Res. Commun., 39, 9-14, (2010) · Zbl 1291.76352
[18] Das, S.; Chakraborty, S., Analytical solutions for velocity, temperature and concentration distribution in electroosmotic microchannel flows in a non-Newtonian bio-fluid, Anal. Chim. Acta, 559, 15-24, (2006)
[19] Chakraborty, S., Electroosmotically driven capillary transport of typical non-Newtonian biofluids in rectangular microchannels, Anal. Chim. Acta, 605, 175-184, (2007)
[20] Zhao, C.; Zholkovskij, E.; Masliyah, J.H.; Yang, C., Analysis of electroosmotic flow of power-law fluids in a slit microchannel, J. Colloid Interface Sci., 326, 503-510, (2008)
[21] Zhao, C.; Yang, C., Nonlinear Smoluchowski velocity for electroosmosis of power-law fluids over a surface with arbitrary zeta potentials, Electrophoresis, 31, 973-979, (2010)
[22] Tang, G.H.; Li, X.F.; He, Y.L.; Tao, W.Q., Electroosmotic flow of non-Newtonian fluid in microchannels, J. Non-Newton. Fluid Mech., 157, 133-137, (2009) · Zbl 1274.76379
[23] Park, H.M.; Lee, W.M., Helmholtz-Smoluchowski velocity for viscoelastic electroosmotic flows, J. Colloid Interface Sci., 317, 631-636, (2008)
[24] Park, H.M.; Lee, W.M., Effect of viscoelasticity on the flow pattern and the volumetric flow rate in electroosmotic flows through a microchannel, Lab Chip, 8, 1163-1170, (2008)
[25] Zhao, C.; Yang, C., Exact solutions for electro-osmotic flow of viscoelastic fluids in rectangular micro-channels, Appl. Math. Comput., 211, 502-509, (2009) · Zbl 1162.76007
[26] Afonso, A.M.; Alves, M.A.; Pinho, F.T., Analytical solution of mixed electro-osmotic pressure driven flows of viscoelastic fluids in microchannels, J. Non-Newton. fluid Mech., 159, 50-63, (2009) · Zbl 1274.76085
[27] Liu, Q.S.; Jian, Y.J.; Yang, L.G., Time periodic electroosmotic flow of the generalized Maxwell fluids between two micro-parallel plates, J. Non-Newton. fluid Mech., 166, 478-486, (2011) · Zbl 1282.76053
[28] Jian, Y.J.; Liu, Q.S.; Yang, L.G., AC electroosmotic flow of generalized Maxwell fluids in a rectangular microchannel, J. Non-Newton. fluid Mech., 166, 1304-1314, (2011) · Zbl 1282.76051
[29] Berli, C.L.A.; Olivares, M.L., Electrokinetic flow of non-Newtonian fluids on microchannels, J. Colloid Interface Sci., 320, 582-589, (2008)
[30] Sousa, J.J.; Afonso, A.M.; Pinho, F.T., Effect of the skimming layer on electro- osmotic-Poiseuille flows of viscoelastic fluids, Microfluid Nanofluid, 10, 107-122, (2011)
[31] Liu, Q.S.; Jian, Y.J.; Yang, L.G., Alternating current electroosmotic flow of the Jeffreys fluids through a slit microchannel, Phys. fluids, 23, 102001, (2011) · Zbl 1308.76327
[32] Volkov, A.G.; Deamer, D.W.; Tanelian, D.L.; Markin, V.S., Electrical double layers at the oil/water interface, Prog. Surf. Sci., 53, 1-134, (1996)
[33] Choi, W.; Sharma, A.; Qian, S.Z.; Lim, G.; Joo, S.W., On steady two-fluid electroosmotic flow with full interfacial electrostatics, J. Colloid Interface Sci., 357, 521-526, (2008)
[34] Mayur, M.; Amiroudine, S.; Lasseux, D., Free-surface instability in electro-osmotic flows of ultrathin liquid films, Phys. Rev. E, 85, 046301, (2012)
[35] De Hoog, F.R.; Knight, J.H.; Stokes, A.N., An improved method for numerical inversion of Laplace transforms, SIAM J. Sci. Stat. Comput., 3, 357-366, (1982) · Zbl 0482.65066
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