We investigate the effects of uniform viscosity gradients on the spontaneous oscillations of an elastic, active filament in viscous fluids. Combining numerical simulations and linear stability analysis, we demonstrate that a viscosity gradient increasing from the filament's base to tip destabilises the system, facilitating its self-oscillation. This effect is elucidated through a reduced-order model, highlighting the delicate balance between destabilising active forces and stabilising viscous forces. Additionally, we reveal that while a perpendicular viscosity gradient to the filament's orientation minimally affects instability, it induces asymmetric ciliary beating, thus generating a net flow along the gradient. Our findings offer new insights into the complex behaviours of biological and artificial filaments in complex fluid environments, contributing to the broader understanding of filament dynamics in heterogeneous viscous media.

中文翻译：

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粘度梯度下活动丝的自发振荡

我们研究了均匀粘度梯度对粘性流体中弹性活性细丝自发振荡的影响。结合数值模拟和线性稳定性分析，我们证明从灯丝基部到尖端增加的粘度梯度会破坏系统的稳定性，从而促进其自振荡。通过降阶模型阐明了这种效应，强调了不稳定的主动力和稳定的粘性力之间的微妙平衡。此外，我们发现，虽然与细丝方向垂直的粘度梯度对不稳定性的影响最小，但它会引起不对称的纤毛跳动，从而产生沿梯度的净流。我们的研究结果为复杂流体环境中生物和人造丝的复杂行为提供了新的见解，有助于更广泛地了解异质粘性介质中的丝动力学。