Coarsening dynamics of ferromagnetic granular networks

In the recent years, networks such as connections in-between routers of the internet, nested citations, transport networks in leaves, or even the Tokyo rail system have begun to attract a lot of attention. Neither completely regular nor completely random, they owe their salience to balancing a lack of transient nature with the capability to evolve in time. Nature provides us with another, more intriguing class of networks. These so-called transient networks, forming under specific conditions, evolve in time becoming increasingly compact until they lose their network characteristics. After being observed at a microscopic level for a solution of a polymer in solvent by Tanaka in 2000, the effect was termed viscoelastic phase separation (VPS). This discovery continues to fascinate because it shows the existence of a qualitatively new scenario of material transformations. Could this be a universal process, on par with gas/liquid or paramagnetic-ferromagnetic transformations? Our project studies a dispersion of ferromagnetic particles in a magnetically neutral granular medium, left to evolve from a fully homogeneous state under the influence of intrinsic magnetic forces. This can be regarded as mixture, in which magnetic particles will form a transient network before crystallisation. We perform experiments and computer simulations. The experimental investigation focuses on a flat vessel with steel and glass spheres, which is mechanically vibrated and monitored by camera. In simulations, the sudden freezing of a high-temperature gas of magnetic and nonmagnetic beads is modelled. These approaches are complementary, as their strengths alleviate the technical challenges of their counterpart. In experiment, the complex magnetic nature of the steel beads fully manifests itself. However, it is difficult to avoid finite size effects and time consuming to change the properties of the mixture components. Whereas in computer simulations, one can easily investigate different types of spheres, but simplifications in the interparticle interactions are unavoidable. Our project will serve as a node connecting four different research fields which are rarely brought together: two material-oriented ones -- magnetic nanoparticles and granular matter; and two phenomena-oriented ones -- network formation and phase separation. Combining the effort and experience of the experimental and the modelling group, we will use and develop powerful techniques and advanced approaches to not only deepen our understanding of network formation and phase separation in ferro-granular material and analyse the magnetic response of these systems, but also to elucidate the parallels with nano-scale magnetic soft materials. Beyond the nano-scale, our project can shed the light on early stage planet formation: due to the abundance of iron and nickel in stardust, M-type asteroids and many planets, the coarsening dynamics of susceptible and magnetised particles might play a decisive role.

This project investigated the coarsening dynamics of ferrogranulates-mixtures of magnetised steel and glass beads-driven by anisotropic magnetic interactions. Inspired by earlier observations of chain and network formation in vibrated ferrogranular systems, and drawing on the concept of viscoelastic phase separation (VPS) from molecular mixtures, we examined whether VPS principles could describe such behaviour at the macroscale. We employed a combination of experiments and computer simulations to uncover the fundamental mechanisms behind structure formation. The experimental setup involved vibrated flat vessels monitored via high-speed imaging, while simulations used a newly developed coarse-grained model of magnetically susceptible particles. This dual approach enabled us to balance physical realism with access to long time scales and a broad parameter space. The research successfully bridged the fields of granular matter, magnetic fluids, phase transitions, and complex networks. It revealed universal physical mechanisms governing magnetically induced aggregation, with potential relevance to diverse systems, including magnetorheological suspensions and the early stages of planetary formation. The project was led by PD Dr. Reinhard Richter (University of Bayreuth), who supervised the experimental work, and Prof. PD Dr. Sofia Kantorovich (University of Vienna), who guided the modelling and simulation efforts.