利用弹性通过电流体动力学不稳定性产生自振荡
Harnessing elasticity to generate self-oscillation via an electrohydrodynamic instability
摘要：
在足够强度的稳定DC电场下，在具有较高电导率的介电溶剂中的弱导电介电球可以通过干草叉分叉经历自发自旋（昆克旋转）。我们设计了一个由介质球和弹性细丝组成的物体。通过数值求解弹性电流体动力学（EEH）问题，我们发现EEH不稳定性表现出不同的动态响应。通过改变灯丝的弯曲刚度，复合物体显示出三种行为：静止状态、波动游泳和稳定旋转，其中游泳是通过霍普夫分叉从自振荡不稳定性产生的。通过结合弹性流体动力学模型进行线性稳定性分析，我们从理论上预测了增长率和临界条件，这与数值计算结果吻合得很好。我们还提出了一个简化的模型系统组成的一个最小的弹性结构再现EEH不稳定性。复合材料结构的弹性-粘性响应能够将音叉分叉转变为Hopf分叉，从而导致自激振荡。我们的研究结果意味着一种新的方式利用弹性介质工程自振荡，更一般地说，操纵和多样化的分叉和相应的不稳定性。这些想法将有助于设计柔软的、环境适应性强的机器。
英文摘要：
Under a steady DC electric field of sufficient strength, a weakly conducting dielectric sphere in a dielectric solvent with higher conductivity can undergo spontaneous spinning (Quincke rotation) through a pitchfork bifurcation. We design an object composed of a dielectric sphere and an elastic filament. By solving an elasto-electro-hydrodynamic (EEH) problem numerically, we uncover an EEH instability exhibiting diverse dynamic responses. Varying the bending stiffness of the filament, the composite object displays three behaviours: a stationary state, undulatory swimming and steady spinning, where the swimming results from a self-oscillatory instability through a Hopf bifurcation. By conducting a linear stability analysis incorporating an elastohydrodynamic model, we theoretically predict the growth rates and critical conditions, which agree well with the numerical counterparts. We also propose a reduced model system consisting of a minimal elastic structure which reproduces the EEH instability. The elasto-viscous response of the composite structure is able to transform the pitchfork bifurcation into a Hopf bifurcation, leading to self-oscillation. Our results imply a new way of harnessing elastic media to engineer self-oscillations, and more generally, to manipulate and diversify the bifurcations and the corresponding instabilities. These ideas will be useful in designing soft, environmentally adaptive machines.
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