Interaction model for magnetic holes in a ferrofluid layer

TL;DR

This paper derives an analytical interaction model for magnetic holes in a ferrofluid layer under complex external magnetic fields, demonstrating equilibrium configurations, stability, and validating with experiments.

Contribution

It introduces a novel analytical model accounting for boundary conditions and external fields, advancing understanding of particle interactions in ferrofluids.

Findings

Existence of stable equilibrium configurations without contact.

Equilibrium separation depends on external field structure.

Model validated through experiments and simulations.

Abstract

Nonmagnetic spheres confined in a ferrofluid layer (magnetic holes) present dipolar interactions when an external magnetic field is exerted. The interaction potential of a microsphere pair is derived analytically, with a precise care for the boundary conditions along the glass plates confining the system. Considering external fields consisting of a constant normal component and a high frequency rotating in-plane component, this interaction potential is averaged over time to exhibit the average interparticular forces acting when the imposed frequency exceeds the inverse of the viscous relaxation time of the system. The existence of an equilibrium configuration without contact between the particles is demonstrated for a whole range of exciting fields, and the equilibrium separation distance depending on the structure of the external field is established. The stability of the system under out-of-plane buckling is also studied. The dynamics of such a particle pair is simulated and validated by experiments.