Numerical study on the rotating electro-osmotic flow of third grade fluid with slip boundary condition
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Juan Song
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Moli Zhao
Abstract
Considering the slip boundary condition, the rotating electro-osmotic flow of a third grade fluid in a channel formed by two parallel plates is investigated in the present study. The charge distribution is treated with the Debye–Hückel approximation analytically. Based on the finite difference method, the velocity profile for rotating electro-osmotic flow of third grade fluid is obtained numerically. It is shown that the non-Newtonian parameter of third grade fluid and the velocity slip factor play the important roles for the rotating electro-osmotic flow. The increasing non-Newtonian parameter slows down the flow and decreases the velocity magnitude, and the increasing slip parameter β has the similar influence on the velocity profile. Furthermore, the effect of the inclusion of third grade on the velocity profile is more conspicuous in the area near the walls.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11672164
Award Identifier / Grant number: 41831278
Funding source: Taishan Scholar Foundation of Shandong Province
Acknowledgments
The authors are grateful to the anonymous reviewers for their careful reading, helpful comments and suggestions that really helped us to improve the presentation of the paper. This work is supported by the National Natural Science Foundation of China (Nos. 11672164, 41831278), and the Taishan Scholars Project Foundation of Shandong Province.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: This work is supported by the National Natural Science Foundation of China (Nos. 11672164, 41831278), and the Taishan Scholars Project Foundation of Shandong Province.
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Employment or leadership: None declared.
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Honorarium: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
[1] A. C. Ruo, M. H. Chang, and F. Chen, “Effect of rotation on the electrohydrodynamic instability of a fluid layer with an electrical conductivity gradient,” Phys. Fluids, vol. 22, 2010, Art no. 024102.10.1063/1.3308542Suche in Google Scholar
[2] A. Ajdari, “Transverse electrokinetic and microfluidic effects in micropatterned channels: lubrication analysis for slab geometries,” Phys. Rev. E, vol. 65, 2001, Art no. 016301.10.1103/PhysRevE.65.016301Suche in Google Scholar
[3] C. C. Chang and C. Y. Wang, “Rotating electro-osmotic flow over a plate or between two plates,” Phys. Rev. E, vol. 84, 2011, Art no. 056320.10.1103/PhysRevE.84.056320Suche in Google Scholar
[4] C. Fetecu, M. Imran, and C Fetecau, “Taylor-Couette flow of an oldroyd-B fluid in an annulus due to a time-dependent couple,” Z. Naturforsch., vol. 66a, pp. 40–46, 2011, https://doi.org/10.5560/zna.2011.66a0040.Suche in Google Scholar
[5] A. Mondal and G. C. Shit, “Transport of magneto-nanoparticles during electro-osmotic flow in a micro-tube in the presence of magnetic field for drug delivery application,” J. Magn. Magn Mater., vol. 442, no. 15, pp. 319–328, 2017, https://doi.org/10.1016/j.jmmm.2017.06.131.Suche in Google Scholar
[6] L. L. Ferrás, A. S. Cavadas, P. R. Resende, A. M. Afonso, and F. T. Pinho, “Effect of the solvent viscosity on pure electro-osmotic flow of viscoelastic fluids, J. Non-Newton. Fluid Mech., vol. 259, pp. 125–129, 2018, https://doi.org/10.1016/j.jnnfm.2018.04.008.Suche in Google Scholar
[7] N. Bag and S. Bhattacharyya, “Electroosmotic flow of a non-Newtonian fluid in a microchannel with heterogeneous surface potential,” J. Non-Newton. Fluid Mech., vol. 259, pp. 48–60, 2018, https://doi.org/10.1016/j.jnnfm.2018.05.005.Suche in Google Scholar
[8] Q. Zhu, S. Deng, and Y. Chen, “Periodical pressure-driven electrokinetic flow of power-law fluids through a rectangular microchannel,” J. Non-Newton. Fluid Mech., vol. 203, pp. 38–60, 2014, https://doi.org/10.1016/j.jnnfm.2013.10.003.Suche in Google Scholar
[9] G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford Engineering Science Series), 2nd ed. Oxford, Clarendon Press, 1994.10.1093/oso/9780198561958.001.0001Suche in Google Scholar
[10] J. Barrat and L. Bocquet, “Large slip effect at a nonwetting fluid solid interface,” Phys. Rev. Lett., vol. 82, pp. 4671–4674, 1999, https://doi.org/10.1103/physrevlett.82.4671.Suche in Google Scholar
[11] N. Churaev, V. Sobolev, and A. Somov, “Slippage of liquids over lyophobic solid surfaces,” J. Colloid Interface Sci., vol. 97, pp. 574–581, 1984, https://doi.org/10.1016/0021-9797(84)90330-8.Suche in Google Scholar
[12] D. C. Tretheway and C. D. Meinhart, “Apparent fluid slip at hydrophobic microchannel walls,” Phy. Fluids, vol. 14, pp. L9, 2002, https://doi.org/10.1063/1.1432696.Suche in Google Scholar
[13] D. C. Tretheway and C. D. Meinhart, “A generating mechanism for apparent fluid slip in hydrophobic microchannels,” Phy. Fluids, vol. 16, pp. 1509–1515, 2002, https://doi.org/10.1063/1.1669400.Suche in Google Scholar
[14] C. L. A. Berli and M. L. Olivares, “Electrokinetic flow of non-Newtonian fluids in microchannels,” J. Colloid Interface Sci., vol. 320, pp. 582–589, 2008, https://doi.org/10.1016/j.jcis.2007.12.032.Suche in Google Scholar PubMed
[15] P. Goswami and S. Chakraborty, “Semi-analytical solutions for electroosmotic flows with interfacial slip in microchannels of complex cross-sectional shapes,” Microfluid. Nanofluidics, vol. 11, pp. 255–267, 2011, https://doi.org/10.1007/s10404-011-0793-6.Suche in Google Scholar
[16] G. C. Shit, A. Mondal, A. Sinba, and P. K. Kundu, “Effects of slip velocity on rotating electro-osmotic flow in a slowly varying micro-channel,” Colloid. Surface A. Physicochem. Eng. Aspect., vol. 489, pp. 249–255, 2016, https://doi.org/10.1016/j.colsurfa.2015.10.036.Suche in Google Scholar
[17] Z. Tan and J. Liu, “Electro-osmotic flow of Eyring fluids in a circular microtube with Navier’s slip boundary condition,” Phys. Lett. A, vol. 381, no. 32, pp. 2573–2577, 2017, https://doi.org/10.1016/j.physleta.2017.06.004.Suche in Google Scholar
[18] D. C. Duffy, H. L. Gillis, and J. Lin, “Microfabricated centrifugalmicrofluidic systems: characterization and multiple enzymatic assays,” Anal. Chem., vol. 71, pp. 4669–4678, 1999, https://doi.org/10.1021/ac990682c.Suche in Google Scholar
[19] Y. Ren and W. F. Leung, “Flow and mixing in rotating zigzag microchannel,” Chem. Eng. J., vol. 215-216, pp. 561–578, 2013, https://doi.org/10.1016/j.cej.2012.09.136.Suche in Google Scholar
[20] P. Kaushik, P. Abhimanyu, and P. K. Mondal, “Confinement effects on the rotational microflows of a viscoelastic fluid under electrical double layer phenomenon,” J. Non-Newtonian Fluid Mech., vol. 244, pp. 123–137, 2017, https://doi.org/10.1016/j.jnnfm.2017.04.006.Suche in Google Scholar
[21] J. H. Lee, J. B. Ha, and Y. K. Bahk, “Microfluidic centrifuge of nano-particles using rotating flow in a microchamber,” Sens. Actuators B, vol. 132, pp. 525–530, 2008, https://doi.org/10.1016/j.snb.2007.11.027.Suche in Google Scholar
[22] P. Kaushik, P. K. Mondal, and S. Chakraborty, “Rotational electrohydrodynamics of a non-Newtonian fluid under electrical double-layer phenomenon: the role of lateral confinement,” Microfluid Nanofluid, vol. 21, pp. 122, 2017, https://doi.org/10.1007/s10404-017-1957-9.Suche in Google Scholar
[23] Z. Y. Xie and Y. J. Jian, “Rotating electroosmotic flow of power-law fluids at high zeta potentials,” Colloid. Surface A. Physicochem. Eng. Aspect., vol. 461, pp. 231–239, 2014, https://doi.org/10.1016/j.colsurfa.2014.07.051.Suche in Google Scholar
[24] S. Wang, N. Li, M. Zhao, M. N. Azese, “Effect of slip velocity on the rotating electro-osmotic flow of the power-law fluid in a slowly varying microchannel,” Z. Naturforsch., vol. 73, no. 9a, pp. 825–831, 2018, https://doi.org/10.1515/zna-2018-0034.Suche in Google Scholar
[25] W. B. Russel, D. A. Saville, and W. R. Schowalter, Collodial Dispersions, Cambridge, Cambridge University Press, 1992.Suche in Google Scholar
[26] M. Parida and S. Padhy, “Electro-osmotic flow of a third-grade fluid past a channel having stretching walls,” Nonlinear Eng., vol. 8, pp. 56–64, 2019, https://doi.org/10.1515/nleng-2017-0112.Suche in Google Scholar
[27] R. L. Fosdick and K. R. Rajagopal, “Thermodynamics and stability of fluids of third grade,” Proc. R. Soc. A., vol. 369, pp. 351–377, 1980, https://doi.org/10.1098/rspa.1980.0005.Suche in Google Scholar
[28] I. L. Animasaun, B. Mahanthesh, and O. K. Koriko, “On the motion of non-Newtonian Eyring Powell fluid conveying tiny gold particles due to generalized surface slip velocity and buoyancy,” Int. J. Appl. Comput. Math., vol. 4, pp. 137, 2018, https://doi.org/10.1007/s40819-018-0571-1.Suche in Google Scholar
[29] P. D. Ariel, “Flow of a third grade fluid through a porous flat channel,” Int. J. Engng. Sci., vol. 41, pp. 1267–1285, 2003, https://doi.org/10.1016/s0020-7225(02)00380-4.Suche in Google Scholar
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Artikel in diesem Heft
- Frontmatter
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- Dynamical Systems & Nonlinear Phenomena
- A modified simple chaotic hyperjerk circuit: coexisting bubbles of bifurcation and mixed-mode bursting oscillations
- Dynamics of a discrete-time system with Z-type control
- Dynamic response of axially loaded end-bearing rectangular closed diaphragm walls
- Hydrodynamics
- Admissibility conditions for Riemann data in shallow water theory
- Numerical study on the rotating electro-osmotic flow of third grade fluid with slip boundary condition
- Solid State Physics & Materials Science
- Ultrasonic study of Si-oil based magneto-rheological fluid
- Electromagnetic propagation characteristics of one-dimensional photonic crystals with metal layers in quasi-parity-time (PT)-symmetric system
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Artikel in diesem Heft
- Frontmatter
- General
- Remote magnetically controlled drug release from electrospun composite nanofibers: design of a smart platform for therapy of psoriasis
- Dynamical Systems & Nonlinear Phenomena
- A modified simple chaotic hyperjerk circuit: coexisting bubbles of bifurcation and mixed-mode bursting oscillations
- Dynamics of a discrete-time system with Z-type control
- Dynamic response of axially loaded end-bearing rectangular closed diaphragm walls
- Hydrodynamics
- Admissibility conditions for Riemann data in shallow water theory
- Numerical study on the rotating electro-osmotic flow of third grade fluid with slip boundary condition
- Solid State Physics & Materials Science
- Ultrasonic study of Si-oil based magneto-rheological fluid
- Electromagnetic propagation characteristics of one-dimensional photonic crystals with metal layers in quasi-parity-time (PT)-symmetric system
- Thermodynamics & Statistical Physics
- Combined influence of axial electron temperature and exponential plasma density ramp on the self-focusing of a chirped laser in plasma
