Injeção de esferas magnéticas em uma cavidade circular parcialmente preenchida com um substrato

Abstract

Magnetic particle packing exploits dipolar interactions for spontaneous self-organization into chains or ordered structures, with applications in self-responsive systems and the understanding of complex biological structures. This study investigates packing patterns in a two-dimensional circular cavity, where linear chains of neodymium spheres are injected diametrically into a Hele-Shaw cell containing an inert granular substrate. The analysis reveals that the initial dipole configurations and the substrate area fraction (η) govern the emerging geometry. For initially parallel dipoles, the system forms loops whose areas follow a log-normal distribution, indicating hierarchical fragmentation of space, and whose quantity scales via a power law, while the number of contacts (Nc), between magnetic particles, remains invariant.Topological analysis via graphs revealed that increasing the substrate alters the network connectivity: the shortest-path distribution transitions from unimodal (η = 0.0 , cohesive network) to bimodal (η > 0.2 ), evidencing the formation of clusters isolated by low-coordination bottlenecks. Through the BFGS energy minimization method, it was identified that the system tends to organize into square symmetry networks with antiferromagnetic domains, presenting energies per particle (uN) close to the theoretical limit of linear chains (u∞ ≈ −2.404). Electrical transport properties were modeled by treating contacts as resistors and utilizing the Moore-Penrose inverse of the Laplacian matrix. It was observed that the equivalent resistance reaches peaks at diferente packing stages as η increases, reflecting the transition from parallel to serial conduction paths. In the critical regime of η = 0.83, substrate saturation prevents loop nucleation, resulting in monotonic resistive growth. The study demonstrates that current distribution concentrates on the network backbone, validating the integration between contact morphology and transport efficiency in heterogeneous media.The study expands the understanding of magnetic matter behavior in confined systems.