Electrohydrodynamic instability in an annular liquid layer with radial conductivity gradients
Wong, Teck Neng
Date of Issue2014
School of Mechanical and Aerospace Engineering
In this paper, the electrohydrodynamic stability in an annular liquid layer with a radial electrical conductivity gradient is investigated. A weak shear flow arises from a constant pressure gradient in the axial direction. In the radial direction, an electric field is applied. The three-dimensional linear instability analysis is implemented to study the influence of the inner radius, electrical conductivity gradient, shear flow, and ionic diffusion on the dynamics of the fluid layer. It is found that the critical unstable mode may either be oscillatory or stationary. The system becomes more unstable as the dimensionless inner radius a increases. When the inner radius a is small, the critical unstable mode is stationary, while it is given by three-dimensional oblique waves when a is large. When the conductivity gradient is small, the critical unstable mode is the three-dimensional oblique wave, while when the conductivity gradient is large, it would switch to the stationary mode rather than the oscillatory mode. The system becomes more unstable when the Reynolds number is slightly increased from zero. Additionally, it is found that the electrical Schmidt number has dual effects. The liquid layer becomes either more unstable or stable as the electric Schmidt number increases.
Physical review E
© 2014 American Physical Society. This paper was published in Physical Review E and is made available as an electronic reprint (preprint) with permission of American Physical Society. The paper can be found at the following official DOI: http://dx.doi.org/10.1103/PhysRevE.89.033010. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.