Macroscopic equivalence for microscopic motion in a turbulence driven three-dimensional self-assembly reactor

Abstract

We built and characterised a macroscopic self-assembly reactor that agitates magnetic, centimeter-sized particles with a turbulent water flow. By scaling up the self-assembly processes to the centimeter-scale, the characteristic time constant scale also drastically increases. This makes the system a physical simulator of microscopic self-assembly, where the interaction of inserted particles are easily observable. Trajectory analysis of single particles reveals their velocity to be a Maxwell-Boltzmann distribution and it shows that their average squared displacement over time can be modelled by a confined random walk model, demonstrating a high level of similarity to Brownian motion. The interaction of two particles has been modelled and verified experimentally by observing the distance between two particles over time. The disturbing energy (analogue to temperature) that was obtained experimentally increases with sphere size, and differs by an order of magnitude between single-sphere and two-sphere systems (approximately 80 $\mathrm{\mu J}$ versus 6.5 $\mathrm{\mu J}$, respectively).