[论文解读] Resonances arising from hydrodynamic memory in Brownian motion - The colour of thermal noise

Thomas Franosch, Matthias Grimm+5 more|arXiv (Cornell University)|Jun 30, 2011

Mechanical and Optical Resonators参考文献 33被引用 7

一句话总结

本文展示了粘性流体中的流体动力记忆效应在布朗运动中诱导出彩色热噪声，导致光学捕获微球的功率谱密度出现共振峰。通过结合强光学捕获与高分辨率干涉测量，作者实验观测到由频率依赖的流体动力摩擦引起的非白噪声，揭示了经典白噪声朗之万理论未预测的纳米机械谐振行为。

ABSTRACT

Observation of the Brownian motion of a small probe interacting with its environment is one of the main strategies to characterize soft matter. Essentially two counteracting forces govern the motion of the Brownian particle. First, the particle is driven by the rapid collisions with the surrounding solvent molecules, referred to as thermal noise. Second, the friction between the particle and the viscous solvent damps its motion. Conventionally, the thermal force is assumed to be random and characterized by a white noise spectrum. Friction is assumed to be given by the Stokes drag, implying that motion is overdamped. However, as the particle receives momentum from the fluctuating fluid molecules, it also displaces the fluid in its immediate vicinity. The entrained fluid acts back on the sphere and gives rise to long-range correlation. This hydrodynamic memory translates to thermal forces, which display a coloured noise spectrum. Even 100 years after Perrin's pioneering experiments on Brownian motion, direct experimental observation of this colour has remained elusive. Here, we measure the spectrum of thermal noise by confining the Brownian fluctuations of a microsphere by a strong optical trap. We show that due to hydrodynamic correlations the power spectral density of the spheres positional fluctuations exhibits a resonant peak in strong contrast to overdamped systems. Furthermore, we demonstrate that peak amplification can be achieved through parametric excitation. In analogy to Microcantilever-based sensors our results demonstrate that the particle-fluid-trap system can be considered as a nanomechanical resonator, where the intrinsic hydrodynamic backflow enhances resonance. Therefore, instead of being a disturbance, details in thermal noise can be exploited for the development of new types of sensors and particle-based assays for lab-on-a-chip applications.

研究动机与目标

• 通过实验检测长期以来预测的由于流体动力记忆效应导致的布朗运动中热噪声的彩色特性。
• 通过测量流体-粒子系统中频率依赖的摩擦力，挑战朗之万方程中白噪声的常规假设。
• 证明流体相关性可增强粒子-阱系统中的共振，从而实现新型传感范式。
• 利用位置涨落的高精度测量，验证频率依赖摩擦力的理论模型（例如，含记忆效应的斯托克斯定律）。
• 探索粒子-流体-阱系统作为可调谐纳米机械谐振器在芯片上实验室应用中的潜力。

提出的方法

• 在粘性流体中对微球进行光学捕获，以限制其布朗运动并抑制惯性效应。
• 利用高分辨率干涉测量技术检测微球位置涨落，以测量位置自相关函数（PAF）。
• 对PAF进行傅里叶变换，获得功率谱密度（PSD），其直接反映热力谱特性。
• 采用包含频率依赖摩擦核 γ̂(ω) 的广义朗之万方程对系统进行建模，该核由流体动力理论推导得出。
• 利用涨落-耗散定理将PSD与复摩擦核的实部关联：PSD(ω) = 2kBT Re[γ̂(ω)] |Ĝ(ω)|²。
• 将实验测得的PSD数据与基于含记忆效应的斯托克斯摩擦理论（涉及涡旋扩散时间 τf = R²/ν）及多粒子碰撞动力学模拟的理论预测进行比较。

实验结果

研究问题

• RQ1 粘性流体中的流体动力记忆是否会导致布朗运动中出现非白、频率依赖的热噪声谱？
• RQ2 由此产生的彩色噪声是否会在被捕获粒子的功率谱密度中表现为共振峰？
• RQ3 在低频下，频率依赖的摩擦核 γ̂(ω) 与经典斯托克斯值的偏离程度如何？
• RQ4 如机械谐振器中所示，能否通过参数激励增强粒子-流体-阱系统中的共振？
• RQ5 所观测到的共振是否可归因于流体回流效应，而非外部驱动或仪器误差？

主要发现

• 被捕获微球位置涨落的功率谱密度（PSD）表现出明显的共振峰，与阻尼过大的布朗运动所预期的洛伦兹形曲线相矛盾。
• 该共振峰源于频率依赖的流体动力摩擦核 γ̂(ω)，其包含由于涡旋扩散引起的非解析项 √(−iωτf)。
• 通过干涉测量技术测量PSD并将其与基于含记忆效应斯托克斯定律的理论模型比较，实验验证了该共振现象。
• 共振频率与阱刚度K及流体的运动粘度ν成比例，与理论预测 τK = γ/K 和 τf = R²/ν 一致。
• 对阱进行参数激励可放大共振峰，证明该系统表现出可调谐纳米机械谐振器行为。
• 结果验证了在存在流体动力记忆时涨落-耗散定理的适用性，并表明热噪声并非白噪声，而是携带了流体动力学的信息。