Attractive interactions between particles do not always cause them to clump together into static aggregates. A new study led by researchers at the Tokyo University of Science in Japan reveals that when particles of different sizes interact through electrohydrodynamic flows, the forces they exert on each other become unequal, producing non-reciprocal interactions that keep the system in perpetual motion.
The finding, published in Physical Review Letters, challenges the intuitive expectation that attraction leads to aggregation. Instead, the team observed that mixing two different particle sizes in a colloidal suspension completely alters the collective behavior. «Instead of forming increasingly large crystal-like aggregates, as is the case for particles with the same size, the system remained highly dynamic,» explained Yutaka Sumino, who led the research with Kiwamu Yoshii in the department of applied physics.
The experiment involved suspending polystyrene colloidal particles with radii of 1 and 1.5 micrometers in water and confining them between transparent indium tin oxide-coated electrodes. By applying an alternating electric field, the researchers generated electrohydrodynamic flows around the particles. The strength of these flows increased strongly with particle size, making the attractive interactions asymmetric: larger particles attracted smaller ones more strongly than the reverse. This imbalance means a larger particle pushes a smaller one, but the smaller particle does not push back with equal force.
While this appears to violate Newton's third law, Sumino explained that momentum conservation is not broken. Momentum is transferred to the surrounding fluid through the induced flows and ultimately dissipated through friction with the substrate. The system thus maintains physical consistency while exhibiting behavior that mimics a breakdown of action-reaction symmetry.
The team tracked more than 10,000 particles for over an hour, a significant improvement over previous studies that could only observe dynamics for a few minutes. They found that particles of different sizes spontaneously pair together, forming asymmetric structures with a distinct front and tail. These pairs behave as self-propelled units, moving through the suspension even though individual particles cannot propel themselves. As more pairs form, they assemble into larger clusters, but these clusters do not grow indefinitely. Instead, they repeatedly fragment, rearrange, and reform.
«The larger particle tends to be at the front of these moving pairs,» the researchers noted. This head-heavy size asymmetry, combined with excluded-volume interactions, promotes the fragmentation of larger clusters and prevents continuous coarsening. The result is a highly dynamic state that continuously reorganizes rather than settling into a static configuration.
Numerical simulations confirmed that non-reciprocal pair motion is the microscopic origin of this behavior. The researchers suggest that non-reciprocal interactions could serve as a general design principle for creating active materials with structures that continuously reorganize. «An interesting aspect is that self-propulsion does not need to be built into each individual particle: it can emerge collectively from non-reciprocal interactions between particles that do not self-propel on their own,» Sumino said.
If such interactions can be controlled externally, they could provide a way to design microscopic systems that collectively gather, transport, fragment, or mix materials. Possible directions include programmable active materials and microrobotic systems, although Sumino cautions that these applications are still some way off.
The team now plans to investigate how general this non-reciprocal mechanism is and whether the same principle can be transferred to other experimental systems. In the current system, the strength of non-reciprocity depends on parameters such as particle size, composition, and the applied electric field. By systematically tuning these parameters, the researchers aim to explore what other types of collective states can be generated and whether transitions between them can be controlled. «A more detailed hydrodynamic analysis of the system is also needed to develop a quantitative understanding of the interactions and ultimately predict the collective motion of the colloids,» Sumino said.
