一种三维形态弹性模型用于聚电解质水凝胶丝的自振荡
A three-dimensional morphoelastic model for self-oscillations in polyelectrolyte hydrogel filaments
AI总结：
本文提出一种三维模型，研究聚电解质水凝胶丝在电场下的自振荡行为，通过形态弹性框架分析其稳定性及动态响应。
摘要：
我们介绍了一种三维模型，用于研究在流体环境中受电场作用的聚电解质水凝胶丝。该模型基于不可伸长且不可剪切的杆的形态弹性框架，将丝的活动编码为由电场引起的自发曲率，而流体动力学相互作用则通过斯托克斯流的局部近似来捕捉。我们利用该框架研究了具有椭圆形横截面并固定在底部的丝的典型情况。在恒定且均匀的电场作用下，丝在临界电场强度以上发生颤振不稳定性，如线性稳定性分析所示。根据模型参数，不稳定性表现出二维或三维自维持振荡。我们进一步通过后临界区域的数值模拟研究了这种行为，显示颤振可能通过二次分岔发展为大振幅平面振荡或更复杂的三维运动。尽管该研究是将聚电解质水凝胶丝的最新模型扩展到三维的一个初步尝试，但由此产生的动态丰富性凸显了所提出驱动机制在设计仿生鞭毛和软体机器人系统中的潜力。
英文摘要：
We introduce a three-dimensional model for polyelectrolyte hydrogel filaments operating in a fluid environment under an electric field. The formulation builds on a morphoelastic framework for inextensible and unshearable rods, such that the filament's activity is encoded in electric-field-induced spontaneous curvatures, while hydrodynamic interactions are captured via a local approximation of Stokes flows. We employ this framework to investigate the prototypical case of a filament with elliptic cross-section clamped at its base. Under a constant and uniform electric field aligned with its axis, the filament undergoes flutter instability beyond a critical field strength, as revealed by a linear stability analysis. Depending on the model parameters, the instability is characterized by either two- or three-dimensional self-sustained oscillations. We further examine this behaviour through numerical simulations in the post-critical regime, showing that flutter may develop into large amplitude planar oscillations or more complex three-dimensional motions, through a secondary bifurcation. Although the study represents a first step towards extending state-of-the-art models for polyelectrolyte hydrogel filaments to three dimensions, the richness of the resulting dynamics achievable under time-independent forcing underscores the potential of the proposed actuation mechanism for the design of biomimetic cilia and soft robotic systems.
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