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Updated: Jul 6, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Ferrofluid patterns in a radial magnetic field: linear stability, nonlinear dynamics, and exact solutions
Rafael M Oliveira1, José A Miranda, Eduardo S G Leandro
1Departamento de Física, LFTC, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901 Brazil.
Summary
A radial magnetic field destabilizes ferrofluid interfaces in Hele-Shaw cells, promoting fingering and sharp, polygon-like patterns. These findings align with analytical solutions and offer insights into fluid dynamics under magnetic influence.
Area of Science:
- Fluid dynamics
- Magnetohydrodynamics
- Pattern formation
Background:
- Ferrofluid behavior in confined geometries is complex.
- Magnetic fields significantly influence ferrofluid dynamics.
- Hele-Shaw cells provide a controlled environment for studying fluid interfaces.
Purpose of the Study:
- Investigate ferrofluid droplet response to radial magnetic fields in a Hele-Shaw cell.
- Analyze the impact of magnetic fields on interface stability and pattern formation.
- Characterize the morphology of emerging patterns.
Main Methods:
- Linear stability analysis.
- Weakly nonlinear analysis.
- Determination of exact stationary solutions.
- Analytical and numerical simulations.
Main Results:
- Radial magnetic fields are destabilizing, promoting fingering.
- Magnetic fields favor sharp, peaked patterned structures.
- Exact solutions reveal polygon and starfish-like patterns.
- Pinch-off phenomena observed near fingertips at high fields.
Conclusions:
- Morphological features from exact solutions are consistent with linear and nonlinear predictions.
- Ferrofluid patterns under radial fields resemble rotating Hele-Shaw flows in a specific limit.
- Magnetic fields offer a tunable parameter for controlling ferrofluid pattern formation.
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