声振和静电场耦合作用下漏电介质平面液膜的线性不稳定性

Linear Instability of a Leaky Dielectric Planar Liquid Film Under the Coupling Effect of Acoustic Vibration and Electrostatic Field

在超声电喷推力器中,声振与电场力共同作用使得液膜界面失稳破裂,进而发射液滴并产生推力.为了揭示超声电喷推力器中液膜初始失稳的物理机制,针对超声与电场力耦合作用下液膜的线性不稳定性进行了理论研究.基于Floquet理论,对声振和静电场耦合作用下漏电介质平面液膜进行了线性不稳定性分析,求解了扰动增长率、频率与波数之间的色散关系,通过绘制色散曲线,获得电学、振荡及物性参数对线性失稳的影响规律.结果表明,根据极板间距与液膜厚度之比的不同,液体电导率和介电常数对不稳定性的影响规律会发生改变.当参数不稳定区域增长率较大时,电场力的增强会促进失稳,而当参数不稳定区域增长率较小时,电场力的增强会抑制失稳.

In ultrasonic aided electrospray thrusters,liquid films are destabilized and broken up under the effect of acoustic vibration and electrostatic field,then droplets emitted and thrust produced.In order to reveal the physical mechanism of initial instability of liquid films in ultrasonic aided electrospray thrusters,the linear instability of liquid films under the coupling effect of ultrasonic and electric field force is studied theoretically.Based on the Floquet theory,the linear instability of the planar liquid film under the coupling effect of acoustic vibration and electrostatic field is analyzed,and the dispersion relationship among the rate of disturbance growth,frequency and wavenumber is solved.According to the dispersion curves,the influence of electrical,oscillation and physical parameters on the linear instability is obtained.The results show that the effect of the liquid conductivity and dielectric constant on the instability can change with the ratio of the plate spacing to the liquid film thickness.When the growth rate of the parameter unstable region is large,the increase of the electric field force will promote the instability,and when the growth rate of the parameter unstable region is small,the increase of the electric field force will restrain the instability.