Hydrodynamic behavior of an electrified thin film flowing down an inclined plane at high Reynolds numbers

Sunyoung Park; Hyo Kim

Korean Journal of Chemical Engineering, Vol.27, No.2, 390-398, February, 2010

DOI10.1007/s11814-010-0083-0 Export Citation

Hydrodynamic behavior of an electrified thin film flowing down an inclined plane at high Reynolds numbers

Sunyoung Park, and Hyo Kim^†

Department of Chemical Engineering, University of Seoul, 90 Jeonnong-dong,Dongdaemun-gu, Seoul 130-743, Korea

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To answer the questions on the dynamics of thin liquid flow down an inclined plane at high Reynolds numbers subjected to a uniform normal electrostatic field, we have derived evolution equations describing the free-surface behavior by using the von Karman-Pohlhausen approximation. The integration of the evolution equations is numerically performed to address two-dimensional finite-amplitude surface-wave propagation modes. The growth of a periodic disturbance is first examined to compare with the results linear-stability theory, and then to investigate the nonlinear surface-wave behavior the evolution equations are solved numerically by a Fourier-spectral method. For small evolution time the computed nonlinear modes of instability are well consistent with the results from the linear theory. The effect of an electrostatic field makes the flow system significantly unstable.

Keywords:Hydrodynamic Behavior;High Reynolds Number;Electrostatic Field;von Karman-Pohlhausen Approximation;Fourier-spectral Method

[References]

Benjamin TB, J. Fluid Mech., 2, 554 (1957)
Yih CS, Phys. Fluids, 5, 321 (1963)
Kim H, Bankoff SG, Miksis MJ, Phys. Fluids A, 4, 2117 (1992)
Kim H, Korean J. Chem. Eng., 14(1), 41 (1997)
Kim H, Korean J. Chem. Eng., 20(5), 803 (2003)
Kim KS, Kim H, Korean J. Chem. Eng., 25, 25 (2007)
Griffing EM, Bankoff SG, Miksis MJ, Schluter RA, ASME I: J. Fluids Engng, 128, 276 (2006)
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)
Blyth MG, J. Fluid Mech., 595, 221 (2008)
Rahman MM, Faghri A, Hankey WL, Swanson TD, Proc. Natl. Heat Transfer. Conf., 110, 161 (1989)
Prokopiou T, Cheng M, Chang HC, J. Fluid Mech., 222, 665 (1991)
Yiantsios SG, Higgins BR, Phys. Fluids, 31, 11 (1988)

[Related Articles]

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

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

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

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

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

[6] Kim KS, Kim H, Korean J. Chem. Eng., 25, 25 (2007)

[7] Griffing EM, Bankoff SG, Miksis MJ, Schluter RA, ASME I: J. Fluids Engng, 128, 276 (2006)

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

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

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

[11] Blyth MG, J. Fluid Mech., 595, 221 (2008)

[12] Rahman MM, Faghri A, Hankey WL, Swanson TD, Proc. Natl. Heat Transfer. Conf., 110, 161 (1989)

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

[14] Yiantsios SG, Higgins BR, Phys. Fluids, 31, 11 (1988)