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研究了微平行管道内线性黏弹性流体的非定常电渗流动, 其中线性黏弹性流体的本构关系是由Jeffrey流体模型来描述的. 利用Laplace变换法, 求解了线性化的Poisson-Boltzmann方程、 非定常的柯西动量方程和Jeffrey流体本构方程, 给出了黏弹性Jeffrey流体电渗速度的解析表达式, 分析了无量纲弛豫时间λ1和滞后时间λ2对速度剖面的影响. 发现滞后时间为零时, 弛豫时间越小, 速度剖面图越接近牛顿流体的速度剖面图; 随着弛豫时间和滞后时间的增加, 速度振幅也变得越来越大, 随着时间的增加, 速度逐渐趋于恒定.In this study, analytical solutions are presented for the unsteady electroosmotic flow of linear viscoelastic fluid between micro-parallel plates. The linear viscoelastic fluid used here is described by the general Jeffrey model. Using Laplace transform method, the solution involves analytically solving the linearized Poisson-Boltzmann equation, together with the Cauchy momentum equation and the general Jeffrey constitutive equation. By numerical computations, the influences of the dimensionless relaxation time λ1 and retardation time λ2 on velocity profile are presented. In addition, we find that when the retardation time is zero, the smaller the relaxation time, the more close to the Newtonian fluid velocity profile the velocity profile is. With the increases of the relaxation time and the retardation time, the velocity amplitude also becomes bigger and bigger. As time goes by, the velocity tends to be stable gradually.
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Keywords:
- electric double-layer /
- micro-parallel plates /
- Jeffrey fluids /
- unsteady electroosmotic flow
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[8] Yang C, Li D, Masliyah J H 1998 Int. J. Heat Mass Transfer 41 4229
[9] Bianchi F, Ferrigno R, Girault H H 2000 Anal. Chem. 72 1987
[10] Wang C Y, Liu Y H, Chang C C 2008 Phys. Fluids 20 063105
[11] Dutta P, Beskok A 2001 Anal. Chem. 73 5097
[12] Keh H J, Tseng H C 2001 J. Colloid Interface Sci. 242 450
[13] Kang Y J, Yang C, Huang X Y 2002 Int. J. Eng. Sci. 40 2203
[14] Wang X M, Chen B, Wu J K 2007 Phys. Fluids 19 127101
[15] Jian Y J, Yang L G, Liu Q S 2010 Phys. Fluids 22 042001
[16] Das S, Chakraborty S 2006 Anal. Chim. Acta 559 15
[17] Vasu N, De S 2010 Colloids and Surfaces A: Physicochem. Eng. Aspects 368 44
[18] Tang G H, Li X F, He Y L, Tao W Q 2009 J. Non-Newtonian Fluid Mech. 157 133
[19] Wang R J, Lin J Z, Li Z H 2005 Binmedical Microdevices 7 131
[20] Zhang K, Lin J Z, Li Z H 2006 Appl. Math. Mech. (English Edition) 27 575
[21] Lin J Z, Zhang K, Li H J 2006 Chin. Phys. 15 2688
[22] Liu Q S, Jian Y J, Yang L G 2011 J. Non-Newtonian Fluid Mech.166 478
[23] Chang L, Jian Y J 2012 Acta Phys. Sin. 61 124702 (in Chinese) [长龙, 菅永军 2012 61 124702]
[24] Jian Y J, Liu Q S, Yang L G 2011 J. Non-Newtonian Fluid Mech. 166 1304
[25] Liu Q S, Jian Y J, Yang L G 2011 Phys. Fluids 23 102001
[26] Jian Y J, Liu Q S, Duan H Z, Chang L, Yang L G 2011 The Sixth International Conference on Fluid Mechanics (ICFM6) Guang Zhou, June 30-July 3, 2011 p616
[27] Deng S Y, Jian Y J, Bi Y H, Chang L, Wang H J, Liu Q S 2012 Mech. Res. Commun. 39 9
[28] Jiang H Y, Li S S, Hou Z X, Ren Y K, Sun Y J 2011 Acta Phys. Sin. 60 020702 (in Chinese) [姜洪源, 李姗姗, 侯珍秀, 任玉坤, 孙永军 2011 60 020702]
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[1] Stone H A, Stroock A D, Ajdari A 2004 Ann. Rev. Fluid Mech. 36 381
[2] Bayraktar T, Pidugu S B 2006 Int. J. Heat Mass Trans. 49 815
[3] Squires T M, Quake S R 2005 Rev. Mod. Phys. 77 977
[4] Hunter R J 1981 Zeta Potential in Colloid Science (New York: Academic Press) p15
[5] Levine S, Marriott J R, Neale G, Epstein N 1975 J. Colloid Interface Sci. 52 136
[6] Tsao H K 2000 J. Colloid Interface Sci. 225 247
[7] Hsu J P, Kao C Y, Tseng S J, Chen C J 2002 J. Colloid Interface Sci. 248 176
[8] Yang C, Li D, Masliyah J H 1998 Int. J. Heat Mass Transfer 41 4229
[9] Bianchi F, Ferrigno R, Girault H H 2000 Anal. Chem. 72 1987
[10] Wang C Y, Liu Y H, Chang C C 2008 Phys. Fluids 20 063105
[11] Dutta P, Beskok A 2001 Anal. Chem. 73 5097
[12] Keh H J, Tseng H C 2001 J. Colloid Interface Sci. 242 450
[13] Kang Y J, Yang C, Huang X Y 2002 Int. J. Eng. Sci. 40 2203
[14] Wang X M, Chen B, Wu J K 2007 Phys. Fluids 19 127101
[15] Jian Y J, Yang L G, Liu Q S 2010 Phys. Fluids 22 042001
[16] Das S, Chakraborty S 2006 Anal. Chim. Acta 559 15
[17] Vasu N, De S 2010 Colloids and Surfaces A: Physicochem. Eng. Aspects 368 44
[18] Tang G H, Li X F, He Y L, Tao W Q 2009 J. Non-Newtonian Fluid Mech. 157 133
[19] Wang R J, Lin J Z, Li Z H 2005 Binmedical Microdevices 7 131
[20] Zhang K, Lin J Z, Li Z H 2006 Appl. Math. Mech. (English Edition) 27 575
[21] Lin J Z, Zhang K, Li H J 2006 Chin. Phys. 15 2688
[22] Liu Q S, Jian Y J, Yang L G 2011 J. Non-Newtonian Fluid Mech.166 478
[23] Chang L, Jian Y J 2012 Acta Phys. Sin. 61 124702 (in Chinese) [长龙, 菅永军 2012 61 124702]
[24] Jian Y J, Liu Q S, Yang L G 2011 J. Non-Newtonian Fluid Mech. 166 1304
[25] Liu Q S, Jian Y J, Yang L G 2011 Phys. Fluids 23 102001
[26] Jian Y J, Liu Q S, Duan H Z, Chang L, Yang L G 2011 The Sixth International Conference on Fluid Mechanics (ICFM6) Guang Zhou, June 30-July 3, 2011 p616
[27] Deng S Y, Jian Y J, Bi Y H, Chang L, Wang H J, Liu Q S 2012 Mech. Res. Commun. 39 9
[28] Jiang H Y, Li S S, Hou Z X, Ren Y K, Sun Y J 2011 Acta Phys. Sin. 60 020702 (in Chinese) [姜洪源, 李姗姗, 侯珍秀, 任玉坤, 孙永军 2011 60 020702]
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