Print: | ISSN 0256-1115 |
Online: | ISSN 1975-7220 |
Korean Journal of Chemical Engineering,
Vol.22, No.4, 495-502, 2005 Finite-Amplitude Surface Waves on a Thin Film Flow Subject to a Unipolar-Charge Injection
The interaction of an electric field with a dielectric liquid film is investigated as it drains under gravity down an inclined plane electrode emitting uniform positive ions into the liquid region. By applying long-wave approximation to the governing equations, the evolution equation for the free surface is derived up to the first order of a thin film parameter ξ. To investigate the space charge effect on the development of a finite-amplitude surface wave, a neutral stability condition is obtained as a critical Reynolds number through a linear stability analysis, and the amplitude and velocity of a periodic disturbance are also calculated within a supercritically stable flow region. The presence of a unipolar space charge in the fluid makes a steady surface wave take on even higher amplitude and faster wave speed compared with the case of no space charge.
Keywords:
Finite-Amplitude Surface Waves; Unipolar-Charge Injection; Dielectric Liquid Film; Critical Reynolds Number
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