Resonances arising from hydrodynamic memory in Brownian motion

TLDR: In this paper, the authors measured the spectrum of thermal noise by confining the Brownian fluctuations of a microsphere in a strong optical trap, and showed that hydrodynamic correlations result in a resonant peak in the power spectral density of the sphere's positional fluctuations, in strong contrast to overdamped systems.

Abstract: In Brownian motion, a particle's movement is driven by rapid collisions with the surrounding solvent molecules; this thermal force is assumed to be random and characterized by a Gaussian white noise spectrum. Friction between the particle and the viscous solvent damps its motion. However, the displaced fluid acts back on the particle, giving rise to a hydrodynamic 'memory' and thermal forces with a coloured noise spectrum. Direct experimental observation of a coloured spectrum has proved difficult. Sylvia Jeney and colleagues now report clear evidence for it in measurements of the Brownian fluctuations of a microsphere in a strong optical trap. They anticipate that such details in thermal noise could be exploited for the development of new types of sensors and particle-based assays in lab-on-a-chip applications. Observation of the Brownian motion of a small probe interacting with its environment provides one of the main strategies for characterizing soft matter1,2,3,4. Essentially, two counteracting forces govern the motion of the Brownian particle. First, the particle is driven by 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 Gaussian white noise spectrum. The friction is assumed to be given by the Stokes drag, suggesting that motion is overdamped at long times in particle tracking experiments, when inertia becomes negligible. 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 particle and gives rise to long-range correlations5,6. This hydrodynamic ‘memory’ translates to thermal forces, which have a coloured, that is, non-white, noise spectrum. One hundred years after Perrin’s pioneering experiments on Brownian motion7,8,9, direct experimental observation of this colour is still elusive10. Here we measure the spectrum of thermal noise by confining the Brownian fluctuations of a microsphere in a strong optical trap. We show that hydrodynamic correlations result in a resonant peak in the power spectral density of the sphere’s positional fluctuations, in strong contrast to overdamped systems. Furthermore, we demonstrate different strategies to achieve peak amplification. By analogy with microcantilever-based sensors11,12, our results reveal that the particle–fluid–trap system can be considered a nanomechanical resonator in which the intrinsic hydrodynamic backflow enhances resonance. Therefore, instead of being treated as a disturbance, details in thermal noise could be exploited for the development of new types of sensor and particle-based assay in lab-on-a-chip applications13,14.