A thermodynamic description of turbulence as a source of stochastic kinetic energy for 3D self-assembly

We investigate to what extent one can use a thermodynamic description of turbulent flow as a source of stochastic kinetic energy for three-dimensional self-assembly of magnetically interacting macroscopic particles. We confirm that the speed of the objects in the flow field generated in our system obeys the Maxwell--Boltzmann distribution, and their random walk can be defined by a diffusion coefficient following from the Einstein relation. However, we discovered that the analogy with Brownian dynamics breaks down when considering the directional components of the velocity. For the vectorial components, neither the equipartition theorem, nor the Einstein relation is obeyed. Moreover, the kinetic energy estimated from the random walk of individual objects is one order of magnitude higher than the value estimated from Boltzmann statistics on the interaction between two spheres with embedded magnets. These results show that introducing stochastic kinetic energy into a self-assembly process by means of turbulent flow can to a great extent be described by standard thermodynamic theory, but anisotropies and the specific nature of the interactions need to be taken into account.