Study on Nonlinear Dynamics of Rotating Liquid Drop Vibration

对静电悬浮器悬浮液滴的非线性动力学进行了实验研究。采用碳酸丙烯酯的透明流体作为工作流体。结果表明：1.液滴直径在1 ~ 3 mm范围内，液滴尺寸对表面张力的影响不明显。表面张力随表面电荷的增加而降低。利用瑞利定理修正了表面电荷的影响。但这种修正并不完美，特别是在高电荷区。在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，非线性效应显著。当外力频率在液滴共振频率附近变化时，液滴的振动行为呈现非线性。3.液滴振动振幅越大，其共振频率越低。这一结果与Tsamopoulos和Brown的理论一致。4.悬浮液滴产生了沿着z轴的旋转（自旋）。由对称形式向非对称形式转变的临界值和共振频率的增量与Busse的理论相一致。5.采用含有非线性项的弹簧-质量块-阻尼器系统（Duffing方程）对非线性振动进行建模。在考虑非线性效应的情况下，振荡动力学与大振幅振荡的实验结果相似。结果表明，大振幅振荡包含了非线性振荡的影响。

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.