# zbMATH — the first resource for mathematics

Numerical analysis for rotating electro-osmotic flow of fractional Maxwell fluids. (English) Zbl 1450.76039
Summary: In this paper, a rotating electro-osmotic flow of a fractional Maxwell fluid in a parallel plate microchannel with high zeta potentials is examined. The Navier’s slip law at walls is considered. The electric double layer potential distribution is derived by using the nonlinear Poisson-Boltzmann equation. Based on the $$L 1$$ approximation of the Caputo derivative, a Crank-Nicolson numerical scheme is developed for obtaining the numerical solutions of the rotating electro-osmotic flow velocity profiles. With a purpose to verify the correctness of our numerical results, a comparison has been made with the analytical solutions of the Newtonian fluid given by the previous work, and the excellent agreement between the solutions is clear. Finally, the influence of the fractional parameters $$\alpha$$ and $$\beta$$, the slip length $$d$$ and the wall zeta potential $$\zeta$$ on the velocity distribution is also discussed in detail.

##### MSC:
 76U05 General theory of rotating fluids 76W05 Magnetohydrodynamics and electrohydrodynamics 76A10 Viscoelastic fluids 76M20 Finite difference methods applied to problems in fluid mechanics 26A33 Fractional derivatives and integrals
Full Text:
##### References:
  Bruus, H., Theoretical Microfluidics (2008), Oxford University Press: Oxford University Press New York  Sarma, R.; Deka, N.; Sarma, K.; Mondal, P. K., Electroosmotic flow of Phan-Thien-Tanner fluids at high zeta potentials: An exact analytical solution, Phys. Fluids, 30, Article 062001 pp. (2018)  Peralta, M.; Bautista, O.; Méndez, F.; Bautista, E., Pulsatile electroosmotic flow of a Maxwell fluid in a parallel flat plate microchannel with asymmetric zeta potentials, Appl. Math. Mech. -Engl. Ed., 39, 667-684 (2018)  Wang, X. P.; Qi, H. T.; Yu, B.; Xiong, Z.; Xu, H. Y., Analytical and numerical study of electroosmotic slip flows of fractional second grade fluids, Commun. Nonlinear. Sci. Numer. Simul., 50, 77-87 (2017)  Wang, S. W.; Zhao, M. L., Analytical solution of the transient electro-osmotic flow of a generalized fractional Maxwell fluid in a straight pipe with a circular cross-section, Euro. J. Mech. B/Fluids, 54, 82-86 (2015) · Zbl 1408.76018  Yang, X.; Qi, H. T.; Jiang, X. Y., Numerical analysis for electroosmotic flow of fractional Maxwell fluids, Appl. Math. Lett., 78, 1-8 (2018) · Zbl 1457.76115  Zhao, C. L.; Yang, C., Exact solutions for electro-osmotic flow of viscoelastic fluids in rectangular micro-channels, Appl. Math. Comput., 211, 502-509 (2009) · Zbl 1162.76007  Chang, C. C.; Wang, C. Y., Rotating electro-osmotic flow over a plate or between two plates, Phys. Rev. E, 84, Article 056320 pp. (2011)  Li, S. X.; Jian, Y. J.; Xie, Z. Y.; Liu, Q. S.; Li, F. Q., Rotating electro-osmotic flow of third grade fluids between two microparallel plates, Colloids Surf. A, 470, 240-247 (2015)  Kaushik, P.; Mandal, S.; Chakraborty, S., Transient electroosmosis of a Maxwell fluid in a rotating microchannel, Electrophoresis, 38, 2741-2748 (2017)  Xie, Z. Y.; Jian, Y. J., Rotating electroosmotic flow of power-law fluids at high zeta potentials, Colloid Surf. A, 461, 231-239 (2014)  Xu, M. Z.; Jian, Y. J., Unsteady rotating electroosmotic flow with time-fractional Caputo-Fabrizio derivative, Appl. Math. Lett., 100, Article 106015 pp. (2020) · Zbl 1425.76316  Matías, A.; Sánchez, S.; Méndez, F.; Bautista, O., Influence of slip wall effect on a non-isothermal electro-osmotic flow of a viscoelastic fluid, Int. J. Thermal Sci., 98, 352-363 (2015)  Shit, G. C.; Mondal, A.; Sinha, A.; Kundu, P. K., Effects of slip velocity on rotating electro-osmotic flow in a slowly varying micro-channel, Colloid Surf. A, 489, 249-255 (2016)  Wang, S. W.; Li, N.; Zhao, M.; Azese, M. N., Effects of slip velocity on the rotating electro-osmotic flow of the power-law fluid in a slowly varying microchannel, Z. Nat.forsch., 73, 825-831 (2018)  Tan, W.; Pan, W.; Xu, M., A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates, Int. J. Non-Linear Mech., 38, 645-650 (2003) · Zbl 1346.76009  Christov, I. C.; Christov, C. I., Comment on “On a class of exact solutions of the equations of motion of a second grade fluid” by C. Fetecǎu and J. Zierep (Acta Mech. 150 (2001) 135-138), Acta Mech., 215, 25-28 (2010)
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.