Study on Nonlinear Dynamics of Rotating Liquid Drop Vibration

对静电悬浮液滴的非线性动力学进行了实验研究。采用透明的碳酸亚丙酯流体作为工质。结果表明：1.液滴直径在1~3 mm范围内对测定的表面张力没有明显影响。而表面张力则随表面电荷的增加而降低。利用瑞利定理对表面电荷的影响进行了修正。但这种修正并不完美，尤其是在高电荷区。修正方程中应考虑表面电荷的不均匀性。2.随着振荡幅度的增大，非线性效应明显。当诱发振荡运动的外力频率围绕液滴的共振频率变化时，观察到了非线性行为。3.振荡幅度越大，共振频率越低。这一结果与Tsamopoulos和Brown的理论很好地吻合。4.悬浮液滴上诱导了沿z轴的旋转(自旋)。从对称形式到非对称形式的转变临界值和共振频率的增量与Busse5的理论一致。5.采用一个包含非线性的弹簧-质量-翻车机系统来模拟非线性振动，称为Duffing方程。在考虑非线性影响的情况下，振动动力学与实验结果基本一致。结果表明，大振幅振动包含了非线性振动的影响。

Experimental study on nonlinear dynamics of liquid droplet levitated by a electrostatic levitator was performed. A transparent fluid of propylene carbonate was employed as a working fluid. The result was summarized as follows:1.Effect of droplet size on measured surface tension did not appear ranging from 1 to 3 mm in diameter. However the surface tension decreased with increasing the surface charge. Influence of surface charge was corrected by using Rayleigh theorem. But this correction could not perfect especially in the highly charge region. It seems that nonuniformity of surface charge should be taken into account in corrective equitation.2.Nonlinear effect remarkably appeared with increasing the amplitude of oscillation. And nonlinear behavior was observed when the frequency of external force to induce oscillatory motion was changed around the resonant frequency of droplet.3.When an oscillation amplitude became lager, the resonant frequency was getting lower. This result agree well with a theory derived by Tsamopoulos and Brown.4.The rotation (spin) along z axis was induced on the levitating droplet. The critical value of transition from symmetric to asymmetric form and the increment of resonant frequency consisted with theory by Busse.5.Nonlinear oscillation was modeled by using a spring-mass-dumper system including nonlinearity which called Duffing equation. In case of taking into account of nonlinear effect, oscillation dynamics was similar to experimental result in large-amplitude oscillation. The result indicates that the large-amplitude oscillation includes the effect of nonlinear oscillation.