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When Brownian motion helps trapping particles

03 May. 2023
Brownian motion is associated with the idea of constant motion of particles on a liquid surface. However, a team involving researchers from the Hydrodynamics Laboratory (LadHyX*) has shown that in the presence of a cylindrical obstacle, an undisturbed zone is formed into which Brownian motion can send the particle. It is then temporarily trapped. This work is published in the journal Science Advances.
When Brownian motion helps trapping particles
The trajectory of a particle facing a cylindrical obstacle, seen from above. The initial trajectory is in blue, the moment of trapping in green and the following trajectory in yellow. Credit: Blaise Delmotte

This article is a translation of the text published in French on the CNRS website

Brownian motion describes the random trajectory that a particle takes because of the movement of other particles around it. This phenomenon explains, for example, why small elements that are supposed to remain motionless will start to move, even though no external force gives them the necessary energy. On the other hand, it is very rare that Brownian motion leads to the stopping of a particle already in motion. However, researchers from the Hydrodynamics Laboratory (LadHyX*), Northwestern University (USA), Argonne National Laboratory (USA) and the Basque Center for Applied Mathematics (Spain) have shown that Brownian motion can participate in the capture of particles that come into contact with a cylindrical obstacle. They are then temporarily trapped at the back of the cylinder.

The team used spherical particles of one to two microns in diameter, composed of polymers and of a magnet in its center. This feature allows the particle to rotate on itself thanks to the action of magnetic fields, without which trapping cannot take place. After a series of simulations and experiments, scientists were able to explain the phenomenon. By moving and turning on itself, the particle induces flows in the surrounding fluid, here slightly salty water. They cause the appearance of pockets where the medium stagnates, one of which is located behind the cylindrical obstacle. However, this trap is not on the natural trajectory of the particle. If it is small enough to be disturbed by the Brownian motion, then it has a chance that it will be pushed into this quiet zone where it will be temporarily captured. If not, it will simply bypass the obstacle and continue its course. The particle does not systematically enter this space, but the more the experiment is repeated, the more the probability that the particle will be trapped there becomes smoother. Similarly, the larger the obstacle relative to the particle, the longer and more efficient the trapping. Published in the journal Science Advances, this work could be exploited for trapping and sorting in microfluidic and drug delivery systems, both of which rely on navigating microparticles through complex, structured landscapes. 

*LadHyX: a joint research unit CNRS, École Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France