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Pattern imaging of primary and secondary electrohydrodynamic instabilities

Published online by Cambridge University Press:  08 February 2006

FRANCISCO VEGA REYES  and
FRANCISCO J. GARCÍA
FRANCISCO VEGA REYES
Affiliation:
Department of Physics, Georgetown University, Washington, DC 20057, USAfvega@physics.georgetown.edu Departamento de Electrónica y Electromagnetismo, Facultad de Física, Avda. Reina Mercedes s/n. 41012 Sevilla, Spain
FRANCISCO J. GARCÍA
Affiliation:
Departamento de Física Aplicada I, EUITA, Universidad de Sevilla, Carretera de Utrera, km. 1, 41013 Sevilla, Spain Departamento de Electrónica y Electromagnetismo, Facultad de Física, Avda. Reina Mercedes s/n. 41012 Sevilla, Spain
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Abstract

A little known electrohydrodynamic instability, which we call a rose window, is observed in air/liquid interfaces in electric fields with unipolar space charge distributions. Depending on the liquid properties, the rose window may appear from an initial rest state (primary instability) or on top of another instability, the classical unipolar-injection-induced instability, destroying its pattern (secondary instability). After imaging of the rose window, we use an edge-detection filter to find the instability threshold and study the characteristic pattern as a function of the liquid properties. Results show that the specific properties of the electric field, due to charge injection, are the cause of the rose-window and that the primary and secondary rose windows are essentially different instabilities.

JFM classification

Nonlinear Dynamical Systems: Pattern formation Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 549 , 25 February 2006 , pp. 61 - 69
Copyright
© 2006 Cambridge University Press

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Reyes supplementary movie

Movie 1. Real time movie of the rose window in castor oil (primary instability), imaged from below the plane circular electrode (4.5 cm diameter). Applied voltage V=11.25 kV, liquid volume Vol=1.0 ml (liquid layer of depth ~0.63 mm), tip-to-plane distance h=4.0 cm. It can be noticed that the instability in this viscous liquid (ν=702 cSt) is static.

Download Reyes supplementary movie(Video)
Video 1.9 MB

Reyes supplementary movie

Movie 1. Real time movie of the rose window in castor oil (primary instability), imaged from below the plane circular electrode (4.5 cm diameter). Applied voltage V=11.25 kV, liquid volume Vol=1.0 ml (liquid layer of depth ~0.63 mm), tip-to-plane distance h=4.0 cm. It can be noticed that the instability in this viscous liquid (ν=702 cSt) is static.

Download Reyes supplementary movie(Video)
Video 3.5 MB
Supplementary material: PDF

FLMv549a770 supp pdf

Vega supplementary appendix

Download FLMv549a770 supp pdf(PDF)
PDF 24.8 KB

Reyes supplementary movie

Movie 2. Real time movie of the rose window in silicone oil 50 cSt (secondary instability). Imaged from below the plane circular electrode (4.5 cm diameter). Applied voltage V =12.0-12.25 kV, liquid volume Vol=2.0 ml (liquid layer of depth ~1.26 mm), tip-to-plane distance h =4.0 cm. Contrary to the primary instability in Movie 1, there is a clear convective movement in the instability cells of this secondary instability.

Download Reyes supplementary movie(Video)
Video 1.6 MB

Reyes supplementary movie

Movie 2. Real time movie of the rose window in silicone oil 50 cSt (secondary instability). Imaged from below the plane circular electrode (4.5 cm diameter). Applied voltage V =12.0-12.25 kV, liquid volume Vol=2.0 ml (liquid layer of depth ~1.26 mm), tip-to-plane distance h =4.0 cm. Contrary to the primary instability in Movie 1, there is a clear convective movement in the instability cells of this secondary instability.

Download Reyes supplementary movie(Video)
Video 3.3 MB

Reyes supplementary movie

Movie 3. Real time movie of the rose window in corn oil (primary instability). Imaged from below the circular plane electrode (4.5 cm diameter). Applied voltage V=6.5 kV, liquid volume Vol=2.0 ml (liquid layer of depth ~1.26 mm), tip-to-plane distance h=4.0 cm. The dynamics of the primary instability in this less viscous liquid (ν=56.4 cSt) is chaotic and clearly richer compared to the primary instability in a more viscous liquid (Movie 1). Movies 1 to 3 represent the three types of dynamics observed in the instabilities.

Download Reyes supplementary movie(Video)
Video 2.1 MB

Reyes supplementary movie

Movie 3. Real time movie of the rose window in corn oil (primary instability). Imaged from below the circular plane electrode (4.5 cm diameter). Applied voltage V=6.5 kV, liquid volume Vol=2.0 ml (liquid layer of depth ~1.26 mm), tip-to-plane distance h=4.0 cm. The dynamics of the primary instability in this less viscous liquid (ν=56.4 cSt) is chaotic and clearly richer compared to the primary instability in a more viscous liquid (Movie 1). Movies 1 to 3 represent the three types of dynamics observed in the instabilities.

Download Reyes supplementary movie(Video)
Video 4.4 MB