The normal field instability under side-wall effects: comparison of experiments and computations

TL;DR

This study investigates the behavior of a ferrofluid spike in a cylindrical container under a magnetic field, combining experiments and finite element simulations to understand bifurcation and wall effects.

Contribution

It provides a detailed comparison of experimental and numerical results, revealing an imperfect bifurcation caused by side-wall effects, which contrasts with standard bifurcation types.

Findings

Numerical and experimental results agree on the spike behavior.

Finite size effects induce an imperfect bifurcation.

Hysteresis is explained by wall wetting phenomena.

Abstract

We consider a single spike of ferrofluid, arising in a small cylindrical container, when a vertically oriented magnetic field is applied. The height of the spike as well as the surface topography is measured experimentally by two different technologies and calculated numerically using the finite element method. As a consequence of the finite size of the container, the numerics uncovers an imperfect bifurcation to a single spike solution, which is forward. This is in contrast to the standard transcritical bifurcation to hexagons, common for rotational symmetric systems with broken up-down symmetry. The numerical findings are corroborated in the experiments. The small hysteresis observed is explained in terms of a hysteretic wetting of the side wall.