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Nonlinear Rupture of Thin Micropolar Liquid Film Under a Magnetic Field

  • P.-J. Cheng (a1), C.-K. Chen (a2), Y.-C. Wang (a2), M.-C. Lin (a3) and C.-K. Yang (a3)...


This paper investigates the rupture problem of a thin micropolar liquid film under a magnetic field on a horizontal plate, using long-wave perturbation to resolve nonlinear evolution equations with a free film interface. The governing equation is resolved using a finite difference method as part of an initial value problem for spatial periodic boundary conditions. The effect of a micropolar liquid under a magnetic field on the nonlinear rupture mechanism is studied in terms of the micropolar parameter, R, the Hartmann constant, m and the initial disturbance amplitude, H 0. Modeling results indicate that the R, m and H 0 parameters strongly affect the film flow. Enhancing the micropolar and magnetic effects is found to delay the rupture time. In addition, the results show that the film rupture time increases as the values of initial disturbance magnitude decrease. The micropolar and magnetic parameters indeed play a significant role in the film flow on a horizontal plate. Moreover, the optimum conditions can be found to alter stability of the film flow by controlling the applied magnetic field.


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1. Ruiz, D. E., Cammi, A. and Luzzi, L., “Dynamic stability of natural circulation loops for single phase fluids with internal heat generation,” Journal of Mathematical Analysis and Applications, 425, pp. 307336 (2015).
2. Lin, M. C., “Surface instability of thin polymer resist films with phase change effects on coating flow using numerical approximation techniques,” Computers & Mathematics with Applications, 68, pp. 847858 (2014).
3. Jin, C., You, I.-K. and Kim, H.K., “Effect of rapid thermal annealing on the properties of spin-coated In-Zn-Sn-O films,” Current Applied Physics, 13, pp. 177181 (2013).
4. Sheludko, A., “Thin liquid film,” Advanced Sciences Colloid Interface, 1, pp. 391494 (1967).
5. Ruckenstein, E. and Jain, R. K., “Spontaneous rupture of thin liquid films,” Journal of the Chemical Society, Faraday Transactions, 270, pp. 132146 (1974).
6. Williams, M. B. and Davis, S. H., “Nonlinear theory of film rupture,” Journal of Colloid and Interface Science, 90, pp. 220228 (1982).
7. Hwang, C. C. and Chang, S. H., “Rupture theory of thin power-law liquid film,” Journal of Applied Physics, 74, pp. 29652967 (1993).
8. Prokopiou, Th., Cheng, M. and Chang, H. C., “Long waves on inclined films at high Reynolds number,” Journal of Fluid Mechanics, 222, pp. 665691 (1991).
9. Alekseenko, S. V., Narkoryakov, V. Y. and Pokusaev, B. G., “Wave formation on a vertical falling liquid film,” AIChE Journal, 31, pp. 14461460 (1991).
10. Hwang, C. C., Chen, J. L. and Shen, L. F., “Strong nonlinear dynamic rupture theory of thin liquid film,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 54, pp. 30133016 (1996).
11. Eringen, A. C., “Theory of micropolar fluids,” Journal of Applied Mathematics and Mechanics, 16, pp. 118 (1967).
12. Liu, C. Y., “Initiation of instability in micropolar fluids,” Physics of Fluids, 14, pp. 18081809 (1970).
13. Hung, C. I., Tsai, J. S., Chen, C. K., “Nonlinear Stability of the thin micropolar liquid film flowing down on a vertical plate,” Journal of Fluids Engineering, 118, pp. 498505 (1996).
14. Hung, C. I. and Tsai, J. S., “Rupture of thin micropolar liquid film,” Acta Mechanica, 122, pp. 217223 (1997).
15. Hsieh, D. Y., “Stability of conducting fluid flowing down an inclined plane in a magnetic field,” Physics of Fluids, 8, pp. 17851791 (1965).
16. Hung, C. I. and Tsai, J.S., “Rupture of thin liquid film under the magnetic field,” Journal of Applied Physics, 80, pp. 42204222 (1996).
17. Edwards, D. A., Brenner, H. and Wasan, D. T., Interfacial Transport Processes and Rheology, Butterworth-Heinemann, Oxford (1991).
18. Stokes, V. K., “Couple stress in fluids,” Physics of Fluids, 9, pp. 17091715 (1966).
19. Burelbach, J. P., Bankoff, S. G. and Davis, S. H., “Nonlinear Stability of Vaporizing/condensing liquid films,” Journal of Fluid Mechanics, 195, pp. 463494 (1988).
20. Chen, J. L. and Hwang, C. C., “Effects of inertia on the rupture process of a thin liquid film,” Journal of Colloid and Interface Science, 167, pp. 214216 (1994)



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