Hydraulic-jump behavior of a thin film flowing down an inclined plane under an electrostatic field

Kwang Seok Kim; Hyo Kim

Korean Journal of Chemical Engineering, Vol.25, No.1, 25-33, January, 2008

DOI10.1007/s11814-008-0005-6 Export Citation

Hydraulic-jump behavior of a thin film flowing down an inclined plane under an electrostatic field

Kwang Seok Kim, and Hyo Kim^{1, †}

Otto H. York Department of Chemical Engineering, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, United States
¹Department of Chemical Engineering, University of Seoul, 90 Jeonnong-dong, Dongdaemun-gu, Seoul 130-743, Korea

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The hydraulic-jump phenomenon of a thin fluid layer flowing down an inclined plane under an electrostatic field is explored by using a global bifurcation theory. First, the existence of hydraulic-hump wave has been found from heteroclinic trajectories of an associated ordinary differential equation. Then, the jump behavior has been characterized by introducing an intensity function on the variations of Reynolds number and surfave-wave speed. Finally, we have investigated the nonlinear stability of traveling shock waves triggered from a hydraulic jump by integrating the initial-value problem directly. At a given wave speed there exists a certain value of Reynolds number beyond which a time-dependent buckling of the free surface appears. Like the other wave motions such as periodic and pulse-like solitary waves, the hydraulic-jump waves are also found to become more unstable as the electrostatic field is getting stronger.

Keywords:Hydraulic Jump;Electrostatic Field;Global Bifurcation Theory;Heteroclinic Trajectory

[References]

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Gjevik B, Phys. Fluids, 13, 1918 (1970)
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Chang HC, Annu. Rev. Fluid Mech., 26, 103 (1994)
Joo SW, Davis SH, Bankoff SG, J. Fluid Mech., 230, 117 (1991)
Kim H, Bankoff SG, Miksis MJ, Phys. Lett. A, 4, 2117 (1992)
Pumir A, Manneville P, Pomeau Y, J. Fluid Mech., 135, 27 (1983)
Prokopiou T, Cheng M, Chang HC, J. Fluid Mech., 222, 665 (1991)
Kim H, Bankoff SG, Miksis MJ, J. Heat Transf. -Trans. ASME, 116, 986 (1994)
Kim H, Korean J. Chem. Eng., 20(5), 803 (2003)
Schaffer E, Thurn-Albrecht T, Russell TP, Steiner U, Nature, 403, 874 (2000)
Schaffer E, Thurn-Albrecht T, Russell TP, Steiner U, Europhys. Lett., 53, 518 (2001)
Lin ZQ, Kerle T, Russell TP, Schaffer E, Steiner U, Macromolecules, 35(10), 3971 (2002)
Kim H, Korean J. Chem. Eng., 14(1), 41 (1997)
Wiggins S, Introduction to applied nonlinear dynamical systems and chaos, Springer-Verlag, New York (1990)

[Related Articles]

[1] Benjamin TB, J. Fluid Mech., 2, 554 (1957)

[2] Yih CS, Phys. Fluids, 5, 321 (1963)

[3] Benney DJ, J. Math. Phys., 45, 150 (1966)

[4] Gjevik B, Phys. Fluids, 13, 1918 (1970)

[5] Lin SP, J. Fluid Mech., 63, 417 (1974)

[6] Chang HC, Annu. Rev. Fluid Mech., 26, 103 (1994)

[7] Joo SW, Davis SH, Bankoff SG, J. Fluid Mech., 230, 117 (1991)

[8] Kim H, Bankoff SG, Miksis MJ, Phys. Lett. A, 4, 2117 (1992)

[9] Pumir A, Manneville P, Pomeau Y, J. Fluid Mech., 135, 27 (1983)

[10] Prokopiou T, Cheng M, Chang HC, J. Fluid Mech., 222, 665 (1991)

[11] Kim H, Bankoff SG, Miksis MJ, J. Heat Transf. -Trans. ASME, 116, 986 (1994)

[12] Kim H, Korean J. Chem. Eng., 20(5), 803 (2003)

[13] Schaffer E, Thurn-Albrecht T, Russell TP, Steiner U, Nature, 403, 874 (2000)

[14] Schaffer E, Thurn-Albrecht T, Russell TP, Steiner U, Europhys. Lett., 53, 518 (2001)

[15] Lin ZQ, Kerle T, Russell TP, Schaffer E, Steiner U, Macromolecules, 35(10), 3971 (2002)

[16] Kim H, Korean J. Chem. Eng., 14(1), 41 (1997)

[17] Wiggins S, Introduction to applied nonlinear dynamical systems and chaos, Springer-Verlag, New York (1990)