An important aspect of Brownian motion predicted decades ago has been observed for the first time by researchers in Europe. The team has measured how micrometre-sized spheres interact with a surrounding fluid and have shown that the spheres “remember” their previous motion. Their experimental technique, the researchers claim, could be used as a biophysical sensor.

Famously explained by Albert Einstein in 1905, Brownian motion describes the erratic motion of a tiny particle in a fluid. It is caused by the many small “kicks” that the particle receives as a result of the thermal motion of the fluid. Initially, Einstein and other physicists believed these kicks to be independent of the motion of the particle and to be characterized by white noise.

Remembering motion

In the mid-20th century, however, physicists began to realize that when the densities of the particle and fluid are similar, the kicks are not completely random. Instead, “persistent correlations” are predicted between the motions of the fluid and the particle. These arise because particles moving through a fluid will cause the surrounding fluid to move, which in turn will affect the motion of the particle and so on. For example, a person swimming at a constant speed will pull some of the surrounding water with them. But if they stop suddenly, they will feel a push forward from the moving water. Researchers refer to this as “hydrodynamic memory”, but its observation has remained elusive for the tiny single particles that undergo Brownian motion.

Now, Sylvia Jeney at EPFL in Switzerland and colleagues in Switzerland and Germany claim to have seen clear evidence for this effect in the Brownian motions of particles. Their measurements are based on the idea that this hydrodynamic “memory” gives rise to the power spectrum of the particle being described by “coloured noise”, rather than white noise.

In the context of Brownian motion, white noise means that the particle fluctuates with the same magnitude (or power) regardless of the frequency of the fluctuation. Jeney’s experiments, however, show that higher frequencies actually have higher magnitudes of fluctuation – which means that the noise is no longer white but is coloured.

Specialized trap

Jeney’s group made the measurement by trapping a single micrometre-sized melamine sphere in optical tweezers created by a tightly focused laser beam. Although similar to a commercial set-up already used by biophysicists, the researchers spent several years optimizing their apparatus. In particular, they improved the time resolution of the system by a factor of 1000 and boosted its spatial resolution so it can measure distances of less than a nanometre.

The experiments involved single particles trapped by the tweezers and immersed in liquid. The parameters of the experiment were chosen so that time it takes for the fluid to diffuse over the diameter of the particle is about one-sixth of the time it takes for the sphere to reach its equilibrium position in the tweezers. This diffusion time is the timescale on which the hydrodynamic memory is expected to occur and therefore the set-up allowed the researchers to study the correlated behaviour.

“Currently, there are two maybe three labs in the world that have similar high-precision set-ups,” explains Jeney. She says that the team wants to establish the optical-trapping technique as an advanced biophysical tool.