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Electroosmotic flow of non-Newtonian fluid in microchannels. (English) Zbl 1274.76379
Summary: Understanding electroosmotic flow of non-Newtonian fluid in microchannels is of both fundamental and practical significance for optimal design and operation of various microfluidic devices. A numerical study of electroosmotic flow in microchannels considering the non-Newtonian behavior has been carried out for the first time. One lattice Boltzmann equation is solved to obtain the electric potential distribution in the electrolyte, and another lattice Boltzmann equation which avoids the derivations of the velocity data to calculate the shear is applied to obtain the flow field for commonly used power-law non-Newtonian model. The simulation results show that the fluid rheological behavior is capable of changing the electroosmotic flow pattern significantly and the power-law exponent $$n$$ plays an important role. For the shear thinning fluid of $$n<1$$, the electrical double layer effect is confined to a smaller zone close to the wall surface and it is more inclined to develop into a plug-like flow whilst the shear thickening fluid of $$n>1$$ is more difficult to grow into the plug-like flow compared to Newtonian fluid.

##### MSC:
 76W05 Magnetohydrodynamics and electrohydrodynamics 76A05 Non-Newtonian fluids 76M28 Particle methods and lattice-gas methods
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##### References:
 [1] Karniadakis, G.; Beskok, A.; Aluru, N.: Microflows and nanoflows fundamentals and simulation, (2004) · Zbl 1115.76003 [2] P. Dutta, Numerical modeling of electroosmotically driven flows in complex micro-geometries, Ph. D. thesis, Texas A&M University, College Station, 2001. [3] Ren, L. Q.; Li, D. Q.: Electroosmotic flow in heterogeneous microchannels, J. colloid interface sci. 243, 255 (2001) [4] Chen, S.; Doolen, G. D.: Lattice Boltzmann method for fluid flows, Annu. rev. Fluid. mech. 30, 329 (1998) · Zbl 0919.76068 [5] Li, B. M.; Kwok, D. Y.: Lattice Boltzmann model of microfluidics in the presence of external forces, J. colloid interface sci. 263, 144 (2003) · Zbl 1065.76165 [6] Li, B. M.; Kwok, D. Y.: Electrokinetic microfluidic phenomena by a lattice Boltzmann model using a modified Poisson-Boltzmann equation with an excluded volume effect, J. chem. Phys. 120, 947 (2004) [7] Tian, F. Z.; Kwok, D. Y.: On the surface conductance, flow rate, and current continuities of microfluidics with nonuniform surface potentials, Langmuir 21, 2192 (2005) [8] Wang, J. K.; Wang, M.; Li, Z. X.: Lattice Poisson – Boltzmann simulations of electro-osmotic flows in microchannels, J. colloid interface sci. 296, 729 (2006) [9] Melchionna, S.; Succi, S.: Electrorheology in nanopores via lattice Boltzmann simulation, J. chem. Phys. 120, 4492 (2004) [10] Guo, Z. L.; Zhao, T. S.; Shi, Y.: A lattice Boltzmann algorithm for electro-osmotic flows in microfluidic devices, J. chem. Phys. 122, 144907 (2005) [11] Chai, Z. H.; Guo, Z. L.; Shi, B. C.: Study of electro-osmotic flows in microchannels packed with variable porosity media via lattice Boltzmann method, J. appl. Phys. 101, 104913 (2007) [12] Boek, E. S.; Chiny, J.; Coveney, P. V.: Lattice Boltzmann simulations of the flow of non-Newtonian fluids in porous media, Int. J. Mod. phys. B 17, 99 (2003) [13] Gabbanelli, S.; Drazer, G.; Koplik, J.: Lattice Boltzmann method for non-Newtonian (power-law) fluids, Phys. rev. E 72, 046312 (2005) [14] Boyd, J.; Buick, J.; Green, S.: A second-order accurate lattice Boltzmann non-Newtonian flow model, J. phys. A 39, 1424 (2006) · Zbl 1148.82314 [15] Sullivan, S. P.; Gladden, L. F.; Johns, M. L.: Simulation of power-law fluid flow through porous media using lattice Boltzmann techniques, J. non-Newtonian fluid mech. 133, 91 (2006) · Zbl 1195.76391 [16] Sullivan, S. P.; Gladden, L. F.; Johns, M. L.; Gladden, L. F.: Verification of shear-thinning LB simulations in complex geometries, J. non-Newtonian fluid mech. 143, 59 (2007) · Zbl 1195.76056 [17] Wang, C. H.; Ho, J. R.: Lattice Boltzmann modeling of Bingham plastics, Physica A 387, 4740 (2008) [18] He, X. Y.; Luo, L. S.: Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation, Phys. rev. E 56, 6811 (1997) [19] Qian, Y. H.; D’humieres, D.; Lallemand, P.: Lattice BGK models for Navier – Stokes equation, Europhys. lett. 17, 479 (1992) · Zbl 1116.76419 [20] Artoli, A. M.: Mesoscopic computational haemodynamics, (2003) [21] Artoli, A. M.; Hoekstra, A. G.; Sloot, P. M. A.: Optimizing lattice Boltzmann simulations for unsteady flows, Comput. fluids 35, 227 (2006) · Zbl 1099.76051 [22] Tang, G. H.; Li, Z.; He, Y. L.; Zhao, C. Y.; Tao, W. Q.: Experimental observations and lattice Boltzmann method study of the electroviscous effect for liquid flow in microchannels, J. micromech. Microeng. 17, 539 (2007) [23] Ren, C. L.; Li, D. Q.: Improved understanding of the effect of electrical double layer on pressure-driven flow in microchannels, Anal. chim. Acta 531, 15 (2005) [24] Tang, G. H.; Li, Z.; Wang, J. K.; He, Y. L.; Tao, W. Q.: Electroosmotic flow and mixing in microchannels with the lattice Boltzmann method, J. appl. Phys. 100, 094908 (2006) [25] Tang, G. H.; Tao, W. Q.; He, Y. L.: Thermal boundary condition for the thermal lattice Boltzmann equation, Phys. rev. E 72, 016703 (2005) [26] Zou, Q.; He, X. Y.: On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Phys. fluids 9, 1591 (1997) · Zbl 1185.76873 [27] Rakotomalala, N.; Salin, D.; Watzky, P.: Simulations of viscous flows of complex fluids with a Bhatnagar, Gross, and Krook lattice gas, Phys. fluids 8, 3200 (1996) · Zbl 1027.76633
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