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

Per A. Löthman, Tijmen A.G. Hageman, Miko C. Elwenspoek, Gijs J.M. Krijnen, Massimo Mastrangeli, Andreas Manz, Leon Abelmann

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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 languageEnglish
Article number1900963
Pages (from-to)1-11
Number of pages11
JournalAdvanced Materials Interfaces
Issue number5
Publication statusPublished - 6 Mar 2020

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


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


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