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The electro-osmotic flow of a non-Newtonian fluid in a slit micro-channel under the Navier's slip boundary condition is investigated. The Eyring constitutive relationship model is adopted to describe the non-Newtonian characteristics of the flow driven by the applied electric field force and pressure. In consideration of the micro-scale effects, electric field, non-Newtonian behavior and slip boundary condition, a mechanical model is built and the effects of these factors on the flow are studied. Analytical expressions are derived for the electric potential and velocity profile by solving the linearized Poisson-Boltzmann equation and the modified Cauchy equation. Approximate expressions of the velocity distribution are also given and discussed. Furthermore, by comparing the effects of electric force with that of pressure on the velocity distribution, some meaningful conclusions are drawn from the obtained graphics.
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Keywords:
- Eyring fluid /
- electro-osmotic flow /
- slip boundary /
- exact solutions
[1] Hunter R J 1981 Zeta Potential in Colloid Science (New York: Academic Press) p15
[2] Stone H A, Stroock A D, Ajdari A 2004 Ann. Rev. Fluid Mech. 36 381
[3] Rice C L, Whitehead R 1965 J. Phys. Chem. 69 4017
[4] Levine S, Marriott J R, Neale G, Epstein N 1975 J. Colloid Interface Sci. 52 136
[5] Wang X M, Chen B, Wu J K 2007 Phys. Fluids 19 127101
[6] Santiago J G 2001 Anal. Chem. 73 2353
[7] Das S, Chakraborty S 2006 Anal. Chim. Acta 559 15
[8] Chakraborty S 2007 Anal. Chim. Acta 605 175
[9] Zhao C L, Zholkovskij E, Masliyah J H, Yang C 2008 J. Colloid Interface Sci. 326 503
[10] Zhao C L, Yang C 2011 J. Non-Newtonian Fluid Mech. 166 1076
[11] Berli C L A, Olivares M L 2008 J. Colloid Interface Sci. 320 582
[12] Tang G H, Li X F, He Y L, Tao W Q 2009 J. Non-Newtonian Fluid Mech. 157 133
[13] Hayat T, Afzal S, Hendi A 2011 App. Math. Mech. Engl. Ed. 32 1119
[14] Chang L, Jian Y J 2012 Acta Phys. Sin. 61 124702 (in Chinese) [长龙, 菅永军 2012 61 124702]
[15] Liu Q S, Yang L G, Su J 2013 Acta Phys. Sin. 62 144702 (in Chinese) [刘全生, 杨连贵, 苏洁 2013 62 144702]
[16] Zheng L C, Zhang C L, Zhang X X, Zhang J H 2013 J. Franklin I. 350 990
[17] Zhao M L, Wang S W, Wei S S 2013 J. Non-Newtonian Fluid Mech. 201 135
[18] Xu S F, Wang J G 2013 Acta Phys. Sin. 62 124701 (in Chinese) [许少峰, 汪久根 2013 62 124701]
[19] Niu J, Fu C J, Tan W C 2012 PLoS ONE 7 e37274
[20] Tan Z, Qi H T, Jiang X Y 2014 App. Math. Mech. Engl. Ed. 35 689
[21] Kang J H, Zhou F B, Tan W C, Xia T Q 2014 J. Non-Newtonian Fluid Mech. 213 50
[22] Ng C O, Qi C 2014 J. Non-Newtonian Fluid Mech. 208 118
[23] Wang S W, Zhao M L, Li X C 2014 Cent. Eur. J. Phys. 12 445
[24] Mondal M, Misra R P, De S 2014 Int. J. Therm Sci. 86 48
[25] Xie Z Y, Jian Y J 2014 Colloids Surf. A 461 231
[26] Yang F Q 2007 Appl. Phys. Lett. 90 133105
[27] Eyring H 1936 J. Chem. Phys. 4 283
[28] Bird R B, Armstrong R, Hassager O 1987 Dynamics of Polymeric Liquids (New York: John Wiley & Sons) pp169-253
[29] Liu X L, Jiang M, Yang P R, Kaneta M 2005 ASME J. Tribology 127 70
[30] Bosse M A, Araya H, Troncoso S A, Arce P E 2002 Electrophoresis 23 2149;
[31] Afonso A M, Ferrás L L, Nóbrega J M, Alves M A, Pinho F T 2014 Microfluid. Nanofluid. 16 1131
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[1] Hunter R J 1981 Zeta Potential in Colloid Science (New York: Academic Press) p15
[2] Stone H A, Stroock A D, Ajdari A 2004 Ann. Rev. Fluid Mech. 36 381
[3] Rice C L, Whitehead R 1965 J. Phys. Chem. 69 4017
[4] Levine S, Marriott J R, Neale G, Epstein N 1975 J. Colloid Interface Sci. 52 136
[5] Wang X M, Chen B, Wu J K 2007 Phys. Fluids 19 127101
[6] Santiago J G 2001 Anal. Chem. 73 2353
[7] Das S, Chakraborty S 2006 Anal. Chim. Acta 559 15
[8] Chakraborty S 2007 Anal. Chim. Acta 605 175
[9] Zhao C L, Zholkovskij E, Masliyah J H, Yang C 2008 J. Colloid Interface Sci. 326 503
[10] Zhao C L, Yang C 2011 J. Non-Newtonian Fluid Mech. 166 1076
[11] Berli C L A, Olivares M L 2008 J. Colloid Interface Sci. 320 582
[12] Tang G H, Li X F, He Y L, Tao W Q 2009 J. Non-Newtonian Fluid Mech. 157 133
[13] Hayat T, Afzal S, Hendi A 2011 App. Math. Mech. Engl. Ed. 32 1119
[14] Chang L, Jian Y J 2012 Acta Phys. Sin. 61 124702 (in Chinese) [长龙, 菅永军 2012 61 124702]
[15] Liu Q S, Yang L G, Su J 2013 Acta Phys. Sin. 62 144702 (in Chinese) [刘全生, 杨连贵, 苏洁 2013 62 144702]
[16] Zheng L C, Zhang C L, Zhang X X, Zhang J H 2013 J. Franklin I. 350 990
[17] Zhao M L, Wang S W, Wei S S 2013 J. Non-Newtonian Fluid Mech. 201 135
[18] Xu S F, Wang J G 2013 Acta Phys. Sin. 62 124701 (in Chinese) [许少峰, 汪久根 2013 62 124701]
[19] Niu J, Fu C J, Tan W C 2012 PLoS ONE 7 e37274
[20] Tan Z, Qi H T, Jiang X Y 2014 App. Math. Mech. Engl. Ed. 35 689
[21] Kang J H, Zhou F B, Tan W C, Xia T Q 2014 J. Non-Newtonian Fluid Mech. 213 50
[22] Ng C O, Qi C 2014 J. Non-Newtonian Fluid Mech. 208 118
[23] Wang S W, Zhao M L, Li X C 2014 Cent. Eur. J. Phys. 12 445
[24] Mondal M, Misra R P, De S 2014 Int. J. Therm Sci. 86 48
[25] Xie Z Y, Jian Y J 2014 Colloids Surf. A 461 231
[26] Yang F Q 2007 Appl. Phys. Lett. 90 133105
[27] Eyring H 1936 J. Chem. Phys. 4 283
[28] Bird R B, Armstrong R, Hassager O 1987 Dynamics of Polymeric Liquids (New York: John Wiley & Sons) pp169-253
[29] Liu X L, Jiang M, Yang P R, Kaneta M 2005 ASME J. Tribology 127 70
[30] Bosse M A, Araya H, Troncoso S A, Arce P E 2002 Electrophoresis 23 2149;
[31] Afonso A M, Ferrás L L, Nóbrega J M, Alves M A, Pinho F T 2014 Microfluid. Nanofluid. 16 1131
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