Ferrofluids under oscillatory magnetic fields

TL;DR

This paper systematically explores the surface states of ferrofluids under oscillatory magnetic fields, revealing stable patterns and phase boundaries, and introduces a surface-wave theory explaining these phenomena.

Contribution

It provides the first comprehensive phase diagram of ferrofluid surface states driven by purely AC magnetic fields and develops a theory capturing key experimental observations.

Findings

Identified stable square lattice and peak-valley regimes under AC driving.

Phase boundaries follow a near-square root frequency scaling.

Wave vector of patterns increases linearly with frequency.

Abstract

Ferrofluids exhibit two canonical interfacial instabilities, a static Rosensweig (normal-field) instability that produces a lattice of peaks and a dynamical Faraday instability that produces parametrically excited standing waves. Here we present a systematic phase diagram of ferrofluid surface states driven by a purely AC vertical magnetic field with zero mean. Scanning a broad range of frequencies and field amplitudes, we resolve two robust branches: a Faraday-wave regime that includes a stable square lattice and a Rosensweig-like peak--valley regime indistinguishable in morphology from Rosensweig peaks. The Faraday-onset boundary is well described by a power law close to $\sqrt{f}$, while the Rosensweig-like peak onset becomes essentially frequency independent at low viscosity. The wave vector of the square lattice grows linearly with frequency over our accessible band. We present a surface-wave theory that captures the full phenomenology, including the emergence of Rosensweig peaks under zero-mean AC driving, the near-$\sqrt{f}$ scaling of the phase boundaries, the linear growth of the selected wave vector with frequency, and the preference for square over hexagonal lattices.