Researchers have discovered previously unknown physical effects in systems made up of particles whose propulsion speed depends on their orientation.
The field of research focusing on self-propelled particles, known as active particles, is rapidly expanding. In most theoretical models, these particles are assumed to maintain a constant swimming speed. However, this assumption does not hold true for many experimentally produced particles, like those propelled by ultrasound for medical applications. Their propulsion speed varies with orientation.
A team of physicists, led by Prof. Raphael Wittkowski from the University of Münster and including Prof. Michael Cates from the University of Cambridge, conducted a collaborative study to explore how this orientation-dependent speed influences the behavior of particle systems, particularly in cluster formation.
They combined computer simulations with theoretical analysis to uncover new effects in systems of active particles with orientation-dependent speeds. Their findings were recently published in the journal Physical Review Letters.
Surprising Behaviors in Particle Systems
What is interesting from a physics point of view is that systems consisting of many active particles can spontaneously form clusters – even when the individual particles do not attract one another at all. When measuring the movement of the particles in the simulations, the researchers came up with a particularly surprising result.
“Normally, on a statistical average, the particles in such clusters simply stay where they are,” explains lead author Dr. Stephan Bröker from the Institute of Theoretical Physics at the University of Münster. “For that reason, we had expected that that would be the case here, too.” In fact, however, the physicists discovered something else: the particles constantly move out of the cluster on the one side and move back in on the other, thus producing a permanent flow of particles.
Novel Cluster Shapes and Practical Implications
There is also another difference from the “normal” case: the clusters that form in systems of active particles are normally circular. However, in the particles examined, the shape of the cluster depends on how strongly the orientation of the particles influences their propulsion speed – which can be stipulated by the experimentalist.
“Theoretically, at least, we can make the particles arrange themselves into any shape we want,” explains co-lead author Dr. Jens Bickmann.
“We can paint with them, so to speak.” In the simulations, the researchers observed ellipses, triangles, and squares. “This gives the results a practical importance,” says Dr. Michael te Vrugt from the Wittkowski team and likewise a co-author of the study. “For technical applications – for example, for the realization of programmable matter, it has to be possible to control the way the particles self-assemble – and with our approach that is indeed possible.”
The background: There are a large number of examples of active particles in biology – for instance, swimming bacteria or flying birds. Nowadays, it is also possible to realize artificially active particles (nano- and micro-robots): one aim, for example, is to implant them in the body for a targeted transportation of medication.
Reference: “Orientation-Dependent Propulsion of Active Brownian Spheres: From Self-Advection to Programmable Cluster Shapes” by Stephan Bröker, Jens Bickmann, Michael te Vrugt, Michael E. Cates and Raphael Wittkowski, 19 October 2023, Physical Review Letters.
The study was funded by the German Research Foundation and the Study Foundation of the German People.