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

Abstract

The extent to which one can use a thermodynamic description of turbulent flow as a source of stochastic kinetic energy for 3D self‐assembly of magnetically interacting macroscopic particles is investigated. It is confirmed that the speed of the objects in the flow field generated in this system obeys the Maxwell–Boltzmann distribution, and their random walk can be defined by a diffusion coefficient following from the Einstein relation. However, it is 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.

Three-dimensional self-assembly using dipolar interaction

“…The experimental setup was introduced and characterized in (24,25). New to this setup was a cone-shaped inset, which created a flow gradient meant to center particles in the middle and prevent interaction with the top and bottom.…”

“…The adjustable turbulence in the flow created disturbing forces to enable the system to reach the global energy minimum. These disturbing forces provide stochastic kinetic energy to the objects, leading to a motion analogous to Brownian motion (25).…”

Bottom‐Up Assembly of Micro/Nanostructures

“…Moving to even larger scales, the contribution from Löthman et al pertains to an intriguing class of works that aim to investigate whether macroscopic systems can be used to reproduce the phenomenology of microscopic or molecular systems or, conversely, the extent to which the thermodynamic description of the latter can be used to capture self‐assembly in systems where gravity and inertia are to be reckoned with [ 24 ] – for the same reason that makes them observable without microscopes, i.e., size. [ 25 ] The authors present a study on a macroscopic fluidic system where spherical magnetic particles are suspended and interact thanks to a turbulent flow field. Having previously showed that their system can reproduce the Maxwell‐Boltzmann statistics of particle motion in dilute gases, [ 26 ] here Löthman et al analyse the functional analogy between temperature and turbulence as source of particle mobility respectively at molecular and macroscopic scale.…”

Self-assembly of millimeter-scale magnetic particles in suspension

“…mechanical vibration, heat, external field. 12,[16][17][18][19][20][21][22][23][24][25][26][27] Kinetic traps are intermediate states with local energy minima that hinder the evolution towards the most stable target configuration. 28,29 Reversible bonds may help to overcome kinetic traps and correct errors during assembly.…”