Rotating electroosmotic flow of an Eyring fluid.

*(English)*Zbl 1372.76113Summary: A perturbation analysis is presented in this paper for the electroosmotic (EO) flow of an Eyring fluid through a wide rectangular microchannel that rotates about an axis perpendicular to its own. Mildly shear-thinning rheology is assumed such that at the leading order the problem reduces to that of Newtonian EO flow in a rotating channel, while the shear thinning effect shows up in a higher-order problem. Using the relaxation time as the small ordering parameter, analytical solutions are deduced for the leading- as well as first-order problems in terms of the dimensionless Debye and rotation parameters. The velocity profiles of the Ekman-electric double layer (EDL) layer, which is the boundary layer that arises when the Ekman layer and the EDL are comparably thin, are also deduced for an Eyring fluid. It is shown that the present perturbation model can yield results that are close to the exact solutions even when the ordering parameter is as large as order unity. By this order of the relaxation time parameter, the enhancing effect on the rotating EO flow due to shear-thinning Eyring rheology can be significant.

PDF
BibTeX
Cite

\textit{C. Qi} and \textit{C.-O. Ng}, Acta Mech. Sin. 33, No. 2, 295--315 (2017; Zbl 1372.76113)

Full Text:
DOI

##### References:

[1] | Zhao, C; Yang, C, Electrokinetics of non-Newtonian fluids: a review, Adv. Colloid Interface Sci., 201-202, 94-108, (2013) |

[2] | Chakraborty, S, Electroosmotically driven capillary transport of typical non-Newtonian biofluids in rectangular microchannels, Anal. Chim. Acta, 605, 175-184, (2007) |

[3] | Zhao, C; Zholkovskij, E; Masliyah; etal., Analysis of electroosmotic flow of power-law fluids in a slit microchannel, J. Colloid Interface Sci., 326, 503-510, (2008) |

[4] | 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) |

[5] | Zhao, C; Yang, C, An exact solution for electroosmosis of non-Newtonian fluids in microchannels, J. Non-Newton. Fluid Mech., 166, 1076-1079, (2011) · Zbl 1282.76044 |

[6] | Babaie, A; Sadeghi, A; Saidi, MH, Combined electroosmotically and pressure driven flow of power-law fluids in a slit microchannel, J. Non-Newton. Fluid Mech., 166, 792-798, (2011) · Zbl 1282.76023 |

[7] | Deng, SY; Jian, YJ; Bi, YH; etal., Unsteady electroosmotic flow of power-law fluid in a rectangular microchannel, Mech. Res. Commun., 39, 9-14, (2012) · Zbl 1291.76352 |

[8] | Dhar, J; Ghosh, U; Chakraborty, S, Alterations in streaming potential in presence of time periodic pressure-driven flow of a power law fluid in narrow confinements with nonelectrostatic ion-ion interactions, Electrophoresis, 35, 662-669, (2014) |

[9] | Ng, CO; Qi, C, Electroosmotic flow of a power-law fluid in a non-uniform microchannel, J. Non-Newton. Fluid Mech., 208-209, 118-125, (2014) |

[10] | Dhinakaran, S; Afonso, AM; Alves, MA; etal., Steady viscoelastic fluid flow between parallel plates under electro-osmotic forces: phan-thien-tanner model, J. Colloid Interface Sci., 344, 513-520, (2010) |

[11] | Sadeghi, A; Saidi, MH; Mozafari, AA, Heat transfer due to electroosmotic flow of viscoelastic fluids in a slit microchannel, Int. J. Heat Mass Transf., 54, 4069-4077, (2011) · Zbl 1219.80084 |

[12] | Abhimanyu, P; Kaushik, P; Mondal, PK; etal., Transiences in rotational electro-hydrodynamics microflows of a viscoelastic fluid under electric double layer phenomena, J. Non-Newton. Fluid Mech., 231, 56-67, (2016) |

[13] | Ng, CO, Combined pressure-driven and electroosmotic flow of Casson fluid through a slit microchannel, J. Non-Newton. Fluid Mech., 198, 1-9, (2013) |

[14] | Ng, CO; Qi, C, Electroosmotic flow of a viscoplastic material through a slit channel with walls of arbitrary zeta potential, Phys. Fluids, 25, 103102, (2013) |

[15] | Berli, CLA; Olivares, ML, Electrokinetic flow of non-Newtonian fluids in microchannels, J. Colloid Interface Sci., 320, 582-589, (2008) |

[16] | Goswami, P; Mondal, PK; Dutta, S; etal., Electroosmosis of powell-Eyring fluids under interfacial slip, Electrophoresis, 36, 703-711, (2015) |

[17] | Duffy, DC; Gillis, HL; Lin, J; etal., Microfabricated centrifugal microfluidic systems: characterization and multiple enzymatic assays, Anal. Chem., 71, 4669-4678, (1999) |

[18] | Gorkin, R; Park, J; Siegrist, J; etal., Centrifugal microfluidics for biomedical applications, Lab Chip, 10, 1758-1773, (2010) |

[19] | DucrĂ©e, J; Haeberle, S; Lutz, S; etal., The centrifugal microfluidic bio-disk platform, J. Micromech. Microeng., 17, s103-s115, (2007) |

[20] | Grumann, M; Geipel, A; Riegger, L; etal., Batch-mode mixing on centrifugal microfluidic platforms, Lab Chip, 5, 560-565, (2005) |

[21] | Madou, M; Zoval, J; Jia, G; etal., Lab on a CD, Annu. Rev. Biomed. Eng., 8, 601-628, (2006) |

[22] | Noroozi, Z; Kido, H; Micic, M; etal., Reciprocating flow-based centrifugal microfluidics mixer, Rev. Sci. Instrum., 80, 075102, (2009) |

[23] | Chakraborty, D; Madou, M; Chakraborty, S, Anomalous mixing behaviour in rotationally actuated microfluidic devices, Lab Chip, 11, 2823-2826, (2011) |

[24] | Brenner, T; Glatzel, T; Zengerle, R; etal., Frequency-dependent transversal flow control in centrifugal microfluidics, Lab Chip, 5, 146-150, (2004) |

[25] | Kim, J; Kido, H; Rangel, RH; etal., Passive flow switching valves on a centrifugal microfluidic platform, Sens. Actuators B Chem., 128, 613-621, (2008) |

[26] | Wang, GJ; Hsu, WH; Chang, YZ; etal., Centrifugal and electric field forces dual-pumping CD-like microfluidic platform for biomedical separation, Biomed. Microdevices, 6, 47-53, (2004) |

[27] | Soong, CY; Wang, SH, Analysis of rotation-driven electrokinetic flow in microscale gap regions of rotating disk systems, J. Colloid Interface Sci., 269, 484-498, (2004) |

[28] | Boettcher, M; Jaeger, M; Riegger, L; etal., Lab-on-chip-based cell separation by combining dielectrophoresis and centrifugation, Biophys. Rev. Lett., 1, 443-451, (2006) |

[29] | Martinez-Duarte, R; Gorkin, RA; Abi-Samrab, K; etal., The integration of 3D carbon-electrode dielectrophoresis on a CD-like centrifugal microfluidic platform, Lab Chip, 10, 1030-1043, (2010) |

[30] | Chang, CC; Wang, CY, Rotating electro-osmotic flow over a plate or between two plates, Phys. Rev. E, 84, 056320, (2011) |

[31] | Xie, ZY; Jian, YJ, Rotating electroosmotic flow of power-law fluids at high zeta potentials, Colloids Surf. A Physicochem. Eng. Asp., 461, 231-239, (2014) |

[32] | Li, SX; Jian, YJ; Xie, ZY; etal., Rotating electro-osmotic flow of third grade fluids between two microparallel plates, Colloids Surf. A Physicochem. Eng. Asp., 470, 240-247, (2015) |

[33] | Ng, CO; Qi, C, Electro-osmotic flow in a rotating rectangular microchannel, Proc. R. Soc. A, 471, 20150200, (2015) · Zbl 1371.76156 |

[34] | Powell, RE; Eyring, HJ, Mechanisms for the relaxation theory of viscosity, Nature, 154, 427-428, (1944) |

[35] | Qi, C; Ng, CO, Rotating electroosmotic flow of viscoplastic material between two parallel plates, Colloids Surf. A Physicochem. Eng. Asp., 513, 355-366, (2017) |

[36] | Pedlosky, J.: Geophysical Fluid Dynamics, 2nd edn. Springer, New York (1987) · Zbl 0713.76005 |

[37] | Chakraborty, S, Generalization of interfacial electrohydrodynamics in the presence of hydrophobic interactions in narrow fluidic confinements, Phys. Rev. Lett., 100, 097801, (2008) |

[38] | Ng, CO; Chu, HCW, Electrokinetic flows through a parallel-plate channel with slipping stripes on walls, Phys. Fluids, 23, 102002, (2011) |

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.