Parametric instability of liquid sheets subjected to a transverse AC electric field

Parametric resonance occurs at the gas-liquid interface when a liquid sheet moving in a transverse AC electrical field. In order to obtain the dispersion relation of liquid sheet under AC electric field and to provide the theoretical basis for the analysis of the breaking behavior of liquid sheet, in this paper, the temporal parametric instability under DC and AC electric field were both analyzed in the leaky dielectric model. The leaky dielectric model is used to characterize the electrical properties of liquid. Since the mean flow is time-dependent function, the Floquet theory is used to solve the stability problem. In this paper, the electric field is defined as a mixed electric field coupled by part of an ac electric field and part of a DC electric field. The dimensionless dispersion relation between wave number and temporal growth rate can be derived as a matrix. According to this relationship, the influence of various liquid properties on the parametric instability were discussed. The effects of the ratio of gas-to-liquid density (ρ), the Weber number (We), the Reynolds number (Re), the electrical Euler number (Eu), the relative relaxation time (τ) and the characteristic of the proportion of AC electric field (Pr) and the frequency of the electric field (Ω) was concluded in this paper. As a conclusion, the electrical Euler number (Eu) influence the instability of both capillary unstable and parametric unstable region, the proportion of electric field (Pr) effects as a constant electric field force, the frequency of the AC electric field (Ω) mainly influence the parametric instability region. In the experiment, in order to obtain parameter oscillation phenomenon more easily, increasing electrical Euler number (Eu) and reducing the frequency of AC electric field (Ω) are founded as effective methods. © 2021, Chinese Journal of Theoretical and Applied Mechanics Press. All right reserved.