### 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.

Original language | English |
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Article number | 1900963 |

Number of pages | 11 |

Journal | Advanced materials interfaces |

Early online date | 18 Jul 2019 |

DOIs | |

Publication status | E-pub ahead of print/First online - 18 Jul 2019 |

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### Keywords

- magnetics
- self-assembly
- thermodynamic
- three-dimensional
- turbulence

### Cite this

*Advanced materials interfaces*, [1900963]. https://doi.org/10.1002/admi.201900963

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*Advanced materials interfaces*. https://doi.org/10.1002/admi.201900963

**A Thermodynamic Description of Turbulence as a Source of Stochastic Kinetic Energy for 3D Self-Assembly.** / Löthman, Per A.; Hageman, Tijmen A.G.; Elwenspoek, Michael C.; Krijnen, Gijs J.M.; Mastrangeli, Massimo; Manz, Andreas; Abelmann, Leon.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - A Thermodynamic Description of Turbulence as a Source of Stochastic Kinetic Energy for 3D Self-Assembly

AU - Löthman, Per A.

AU - Hageman, Tijmen A.G.

AU - Elwenspoek, Michael C.

AU - Krijnen, Gijs J.M.

AU - Mastrangeli, Massimo

AU - Manz, Andreas

AU - Abelmann, Leon

PY - 2019/7/18

Y1 - 2019/7/18

N2 - 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.

AB - 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.

KW - magnetics

KW - self-assembly

KW - thermodynamic

KW - three-dimensional

KW - turbulence

UR - http://www.scopus.com/inward/record.url?scp=85069933553&partnerID=8YFLogxK

U2 - 10.1002/admi.201900963

DO - 10.1002/admi.201900963

M3 - Article

JO - Advanced materials interfaces

JF - Advanced materials interfaces

SN - 2196-7350

M1 - 1900963

ER -