Skip to main content Accessibility help
×
Home

Electromagnetohydrodynamic Flow of Powell-Eyring Fluids in a Narrow Confinement

  • F.-Q. Li (a1), Y.-J. Jian (a1), Z.-Y. Xie (a1) and L. Wang (a1)

Abstract

In this work, we investigate electromagnetohydrodynamic (EMHD) flow of Powell-Eyring fluid through a slit confinement. The approximate analytical solution and numerical result of EMHD velocity are obtained by using homotopy perturbation method and Chebyshev spectral method, respectively. The analytical solutions are found to be in good agreement with numerical results under the same conditions. The influences of Hartmann number Ha, electrical field strength parameter S, the Powell-Eyring fluid parameters γ and β on velocity are discussed in detail. It is found that the volume flow rate of Newtonian fluid is always larger than that of Powell-Eyring fluid. The results reveal the intricate interaction between EMHD effect and fluid rheology involving non-Newtonian fluid. Therefore, the results are useful in dealing with some non-Newtonian biomicrofluidic systems.

Copyright

Corresponding author

*Corresponding author (jianyj@imu.edu.cn)

References

Hide All
1. Stone, H. A., Stroock, A. D. and Ajdari, A., “Engineering flows in small devices: Microfluidics toward a lab-on-a-chip,” Annual Review of Fluid Mechanics, 36, pp. 381411 (2004).
2. Das, S. and Chakraborty, S., “Analytical solutions for velocity, temperature and concentration distribution in electroosmotic microchannel flows of a non-Newtonian bio-fluid,” Analytica Chimica Acta, 559, pp. 1524 (2006).
3. Ghosal, S., “Lubrication theory for electro-osmotic flow in a microfluidic channel of slowly varying cross-section and wall charge.” Journal of Fluid Mechanics, 459, pp. 103128 (2002).
4. Wang, C. Y., Liu, Y. H. and Chang, C. C., “Analytical solution of electro-osmotic flow in a semicircular microchannel,” Physics of Fluids, 20, 063105 (2008).
5. Li, S. X., Jian, Y. J., Xie, Z. Y., Liu, Q. S. and Li, F. Q., “Rotating electro-osmotic flow of third grade fluids between two microparallel plates,” Colloids and Surfaces A: Physicochemical and Engineering Aspects, 470, pp. 240247 (2015).
6. Jian, Y. J., Su, J., Chang, L., Liu, Q. S. and He, G. W., “Transient electroosmotic flow of general Maxwell fluids through a slit microchannel,” Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 65, pp. 435447 (2014).
7. Lemoff, A. V. and Lee, A. P., “An AC magnetohydrodynamic micropump,” Sensors and Actuators B: Chemical, 63, pp. 178185 (2000).
8. Bau, H. H., Zhu, J., Qian, S. and Xiang, Y., “A magneto-hydrodynamically controlled fluidic network,” Sensors Actuators B, 88, pp. 205216 (2003).
9. Qian, S. Z. and Bau, H. H., “Magneto-hydrodynamics based microfluidics,” Mechanics Research Communications, 36, pp. 1021 (2009).
10. Gelb, A., Gleeson, J. P., West, J. and Roche, O. M., “Modeling annular micromixers,” SIAM Journal on Applied Mathematics, 64, pp. 12941310 (2004).
11. Pamme, N., “Magnetism and microfluidics,” Lab on a Chip, 6, pp. 2438 (2006).
12. Peter, L. O. and Sedat, B., “Direct numerical simulations of low Reynolds number turbulent channel flow with EMHD control,” Physics of Fluids, 10, pp. 11691181 (1998).
13. Abdullah, M. and Duwairi, H. M., “Thermal and flow analysis of two-dimensional fully developed flow in an AC magneto-hydrodynamic micropump,” Microsystem technologies, 14, pp. 11171123 (2008).
14. Buren, M., Jian, Y. J. and Chang, L., “Electromagnetohydrodynamic flow through a microparallel channel with corrugated walls,” Journal of Physics D: Applied Physics, 47, 425501 (2014).
15. Reddy, P. D. S., Bandyopadhyay, D., Joo, S. W., Sharma, A. and Qian, S., “Parametric study on instabilities in a two-layer electromagnetohydrodynamic channel flow confined between two parallel electrodes,” Physical Review E, 83, 036313 (2011).
16. Shojaeian, M. and Shojaeian, M., “Analytical solution of mixed electromagnetic/pressure driven gaseous flows in microchannel,” Microfluidics and nanofluidics, 12, pp. 553564 (2012).
17. Si, D. Q. and Jian, Y. J., “Electromagnetohydrodynamic (EMHD) micropump of Jeffrey fluids through two parallel microchannels with corrugated walls,” Journal of Physics D: Applied Physics, 48, 085501 (2015).
18. Duwairi, H. M. and Abdullah, M., “Numerical computation of fluid flow in a magnetohydrodynamic micropump,” Turkish Journal of Engineering and Environmental Sciences, 32, pp. 15 (2008).
19. Jang, J. and Lee, S. S., “Theoretical and experimental study of MHD magnetohydrodynamic micropump,” Sensors and Actuators A: Physical, 80, pp. 8489 (2000).
20. Chakraborty, S. and Paul, D., “Microchannel flow control through a combined electromagnetohydrodynamic transport,” Journal of Physics D: Applied Physics, 39, pp. 53645371 (2006).
21. Jian, Y. J. and Chang, L., “Electromagnetohydrodynamic (EMHD) micropumps under a spatially nonuniform magnetic field,” AIP Advances, 5, 057121 (2015).
22. Tso, C. P. and Sundaravadivelu, K., “Capillary flow between parallel plates in the presence of an electromagnetic field,” Journal of Physics D: Applied Physics, 34, pp. 35223527 (2001).
23. Sun, Y. J., Jian, Y. J., Chang, L. and Liu, Q. S., “Thermally fully developed electroosmotic flow of power-law fluids in a circular microchannel,” Journal of Mechanics, 29, pp. 609616 (2013).
24. Jian, Y. J., Liu, Q. S. and Yang, L. G., “AC electroosmotic flow of generalized Maxwell fluids in a rectangular microchannel,” Journal of Non-Newtonian Fluid Mechanics, 166, pp. 13041314 (2011).
25. Liu, Q. S., Jian, Y. J. and Yang, L. G., “Alternating current electroosmotic flow of the Jeffreys fluids through a slit microchannel,” Physics of Fluids, 23, 102001 (2011).
26. Sun, L. X., Jian, Y. J., Chang, L., Zhang, H. Y. and Liu, Q. S., “Alternating current electro-osmotic flow of the Maxwell fluids through a circular micro-pipe,” Journal of Mechanics, 29, pp. 233240 (2013).
27. Powell, R. E. and Eyring, H., “Mechanism for the relaxation theory of viscosity,” Nature, 154, pp. 427428 (1944).
28. Islam, S., Shah, A., Zhou, C. Y. and Ali, I., “Homotopy perturbation analysis of slider bearing with Powell-Eyring fluid,” Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 60, pp. 11781193 (2009).
29. Patel, M. and Timol, M. G., “Numerical treatment of Powell–Eyring fluid flow using Method of Satisfaction of Asymptotic Boundary Conditions (MSABC),” Applied Numerical Mathematics, 59, pp. 25842592 (2009)
30. Hayat, T., Iqbal, Z., Qasim, M. and Obaidat, S., “Steady flow of an Eyring Powell fluid over a moving surface with convective boundary conditions,” International Journal of Heat and Mass Transfer, 55, pp. 18171822 (2012).
31. Hayat, T., Shah, S. I., Ahmad, B. and Mustafa, M., “Effect of slip on peristaltic flow of Powell-Eyring fluid in a symmetric channel,” Applied Bionics and Biomechanics, 11, pp. 6979 (2014).
32. Goswami, P., Mondal, P. K., Dutta, S. and Chakraborty, S., “Electroosmosis of Powell–Eyring fluids under interfacial slip,” Electrophoresis, 36, pp. 703711 (2015).
33. He, J. H., “A review on some new recently developed nonlinear analytical techniques,” International Journal of Nonlinear Sciences and Numerical Simulation, 1, pp. 5170 (2000).
34. He, J. H., “Homotopy perturbation method, a new analytical technique,” Applied Mathematics and computation, 135, pp. 7379 (2003).
35. Peyret, R., Spectral methods for incompressible viscous flow, Springer, New York, pp. 4670 (2001).
36. Trefethen, L. N., Spectral methods in MATLAB, SIAM, Philadelphia, pp. 7178 (2000).

Keywords

Electromagnetohydrodynamic Flow of Powell-Eyring Fluids in a Narrow Confinement

  • F.-Q. Li (a1), Y.-J. Jian (a1), Z.-Y. Xie (a1) and L. Wang (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed