Rose-Window Instability of Oil Surfaces Exposed In Corona Discharge

We studied the Rose Window instability phenomenon on a layer of low conducting liquid (e.g. oil) that is exposed under corona discharge. Most of the current researches focus on deducting qualitative descriptions of this phenomenon in fluid mechanical aspect, but lacks experiments and the study of micro mechanism of the forming of cellular structure. In this thesis, a series of verification experiments were designed then and the results showed wavelength of instability have positive relation with oil layer thickness and negative relation with the voltage applied through the oil layer. We also developed simulation methods of shape under large amplitude condition, in contrast with existing infinitesimal amplitude results. By assuming the border between oil and air as an equipotential surface with surface tensional force, and with two approximation methods of the electric field perpendicular to the oil layer under axisymmetrical and translational symmetrical conditions, we are able to write down the pressure balance equations on the border in the form of differential equation and take it as the constraint of the shape function. By using this pressure balance constraint on the oil surface, we simulated the stable shape of oil surface. The constraint equations have no analytical solution but can be solved numerically by Mathematica. From those simulated results we achieved the theoretical curve of wavelength with respect of oil layer thickness and voltage drop across the oil layer. These theoretical results are in good agreement with quantitative experiment data, which show previous approximation method of electric field is credible. The systematic error in our experiment is discussed, which is useful for further experimental accuracy optimization. This thesis not only concluded and concentrated previous research findings in Rose Window instability but also provided a new method to study this phenomenon of numerical solving pressure balance constraint differential equations. These studies may contribute to our understanding of this phenomenon and provide reference to later researches.