How to steer active colloids to climb up a vertical wall?

Flocking of birds and schooling of fishes are phenomena analogue to the separation of water and oil or of water and vapour. Birds like to be together rather than evenly fill the sky. So do water molecules that mostly gather in a glass and sparsely populate the volume of the room around. In the last decade, this analogy has been explored by physicists. It holds incredibly well given that molecules passively respond to the surrounding temperature, whereas birds and fishes self-propel, thus actively inject energy in the physical system. Bird flocks and fish schools are thus intrinsically out-of-equilibrium systems. More generally, other physical systems, made of living or abiotic particles, have been shown to phase separate between dense and dilute regions when the particles are gifted with self-propulsion. But how far does the analogy run with water-vapour passive equilibrium situation ?

Theories and simulations have identified the interface between the dense and the dilute phase as a place where the analogy might break down and give rise to new interesting phenomena. For instance, a negative surface tension has been predicted in some models of active systems. Instead of minimizing the interface area as a positive surface tension does, a negative surface tension should lead to an increasingly corrugated interface. But other models predict a positive surface tension and more subtle discrepancies with an equilibrium interface.

 

In this context, we set to reproduce the active matter version of the capillary rise experiment, where water in contact with a hydrophilic wall forms a meniscus against gravity. We studied a sediment of 2 µm spherical gold particles in contact with a vertical wall. One hemisphere of each particle is coated in platinum. The platinum is able to split a chemical fuel and this reaction propels the particle. In absence of fuel, the particles are passive and do not wet the wall. When we add fuel, the particles become active and climb up the wall. Surprisingly, this climbing occurs at relatively weak self-propulsion, too weak to induce phase separation, too weak to create an interface with a surface tension.

 

Indeed, we do not observe a meniscus, but an adsorbed layer, one particle thick. And in this layer, the particles point upward, actively climbing against gravity, a phenomenon that has no analogue in a passive system. With the help of numerical simulations, we were able to understand the necessary physical ingredients to observe this phenomenon. We understood that the particles need to align parallel to the wall, as elongated bacteria do. However, against an horizontal wall, particles can go indifferently right or left. What makes them go preferentially up in the case of a vertical wall?

To understand this, we had to remember previous studies of active particles in a sediment, but far from any wall. Models had predicted, and the experiments of some of us had confirmed, that high in a sediment the particles were pointing slightly upward. Indeed, to climb this far up, a particle had to be pointed upward just before the observation. If it was pointing downward, its propulsion would concur with gravity to make it fall down. Since the self-propulsion is persistent, particles that were pointing upward just before the observation are mostly still pointing upward. That is how gravity selects particles that point up. But far from any wall this propulsion slightly upward exactly compensate the gravity and the system is in steady state. By contrast at a wall, this small preference to point upward is enhanced by the alignment. Particles thus point exactly up. Their self-propulsion is now stronger than gravity and the particles climb up the wall in a steady state flux that has no equivalent in passive systems.

Effectively, a vertical wall is able to create a steady current in an active system. By herding active particles it makes them climb up against gravity. From microscopic active units, this simple situation produces a macroscopic work. Our results pave the way to microfluidic circuits able to pump themselves.

Bibliography

Adérito Fins Carreira, Adam Wysocki, Christophe Ybert, Mathieu Leocmach, Heiko Rieger and Cécile Cottin-Bizonne. How to steer active colloids up a vertical wall. Nat Commun 15, 1710 (2024). ArXiV 2307.02810