Contribution of an external magnetic field to the dynamics of phase separation in a binary magnetic mixture

About the authors:

Alexander Ya. Gilmanov, Cand. Sci. (Phys.-Math.), Associate Professor, Department of Modeling of Physical Processes and Systems, School of Natural Sciences, University of Tyumen, Tyumen, Russia; a.y.gilmanov@utmn.ru, https://orcid.org/0000-0002-7115-1629

Natalia E. Saraeva, Postgraduate Student, Department of Applied and Technical Physics, School of Natural Sciences, University of Tyumen, Tyumen, Russia; natalia.saraeva@yandex.ru, https://orcid.org/0009-0003-8717-3851

Alexander P. Shevelev, Cand. Sci. (Phys.-Math.), Associate Professor, Professor, Department of Modeling of Physical Processes and Systems, School of Natural Sciences, University of Tyumen, Tyumen, Russia; a.p.shevelev@utmn.ru; ORCID: 0000-0003-0017-4871

Abstract:

Phase separation in polymer mixtures with magnetic nanoparticles is a promising direction in the development of functional membrane materials, especially in the context of controlled pore morphology and selectivity. Modern research shows that the magnetic field can significantly affect the kinetics and structure of phase inversion, but quantitative models that take these effects into account have so far been poorly developed. In this paper, we propose a modified Kahn–Hilliard phase-field model for a two-component magnetic mixture that includes the contribution of an external magnetic field to the free energy of the system. The aim of the study is to analyze the effect of field strength and the effective interaction parameter on the dynamics of phase separation. The novelty of the work lies in the numerical confirmation of the energy mechanism of magnetically induced acceleration of phase separation and morphological ordering, which expands the possibilities of controlled synthesis of porous composites. The model is implemented numerically in the FEniCS environment with subsequent visualization in ParaView. The dynamics of the total free energy G(t) of a two-component mixture is analyzed in a phase-field model taking into account an external magnetic field. Calculations have shown that the magnetic field significantly alters the relaxation process of the system: with certain combinations of the field strength H and the magnetic sensitivity parameter λ, the system reaches an energy minimum faster. For example, at moderate λ, the free energy rapidly decreases to a steady value, whereas for a very strong field
(H = 10000 A/m), the relaxation process stretches over almost the entire simulation interval. The value of G(t) decreases monotonously, and the final energy values become significantly lower as H increases, which indicates an enhanced phase mixing process. At the same time, at sufficiently high λ, the function G(t) increases non-linearly to a stationary value. In the diagrams of phase evolution, the process of increasing free energy is accompanied by a rapid phase separation of the two-component mixture. Thus, the dynamics of free energy confirms the energetic nature of accelerated phase separation: the presence of a magnetic field leads to the transition of the system to a lower energy state and a faster establishment of an equilibrium distribution of components in these modes.

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