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 µJ versus 6.5 µJ, respectively). arXiv:1709.04978v1 [cond-mat.soft]

A Thermodynamic Description of Turbulence as a Source of Stochastic Kinetic Energy for 3D Self‐Assembly

“…We observed the movement of a single sphere and the interaction between two spheres in the reactor, and determined the stochastic kinetic energy as a function of the flow asymmetry, applying the methods introduced in ref. . We also investigated the directional dependency in the velocity distribution.…”

“…The analysis of particle trajectories and two‐particle interactions was introduced in ref. Here, we also analyze the diffusion coefficient and velocity distribution for the projection of the particle movement on the vertical axis ( z ), i.e., along the main direction of the flow, and in the horizontal plane perpendicular to the flow ( x , y ). The diffusion of a particle in a confined space was described in ref.…”

“…The diffusion of a particle in a confined space was described in ref. for 1D movement along a line segment. If the motions of the particle along the three projections are uncorrelated, we can apply the same expression for the average squared displacement where n ( x , σ x ) is the normal distribution and N ( x , σ x ) is the cumulative normal distribution.…”

“…In ref. , we used the Maxwell–Boltzmann distribution to describe the distribution of the speed in terms of the most probable speed (or mode) v p . The distribution of the individual components of the velocity is Gaussian with the standard deviation φ and zero mean velocity component where again x can be substituted with y or z .…”

“…In this system, we thoroughly analyzed the motion of the individual objects . We have concluded that the random motion of the objects can indeed to a large extent be described by standard thermodynamic theory.…”