Growth of surface undulations at the Rosensweig instability

TL;DR

This study examines the growth dynamics of surface patterns in magnetic liquids under magnetic fields, comparing experimental measurements with theoretical and numerical models to understand instability development.

Contribution

It combines experimental measurements with linear stability analysis and finite-element simulations to accurately model the growth of surface undulations in magnetic liquids.

Findings

Measured growth rates match linear stability predictions after accounting for nonlinear magnetization.

Finite-element simulations reproduce the temporal evolution of pattern amplitude.

Viscosity influences the growth dynamics of the surface patterns.

Abstract

We investigate the growth of a pattern of liquid crests emerging in a layer of magnetic liquid when subjected to a magnetic field oriented normally to the fluid surface. After a steplike increase of the magnetic field, the temporal evolution of the pattern amplitude is measured by means of a Hall-sensor array. The extracted growth rate is compared with predictions from linear stability analysis by taking into account the proper nonlinear magnetization curve M(H). The remaining discrepancy can be resolved by numerical calculations via the finite-element method. By starting with a finite surface perturbation, it can reproduce the temporal evolution of the pattern amplitude and the growth rate. The investigations are performed for two magnetic liquids, one with low and one with high viscosity.