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Magnetically Induced Rotating Rayleigh-Taylor Instability

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Published on: March 3, 2017

Magnetically induced interfacial instabilities in a ferrofluid annulus.

Pedro O S Livera¹, Pedro H A Anjos², José A Miranda¹

¹Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901 Brazil.

Physical Review. E

|January 15, 2022

Summary

This summary is machine-generated.

Magnetic fields drive pattern formation in ferrofluid annuli within Hele-Shaw cells. Nonlinear effects transform rounded patterns into sharp, polygonal shapes that reach a stable state, unlike linear patterns.

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Area of Science:

Fluid Dynamics
Magnetohydrodynamics
Interfacial Phenomena

Background:

Investigating pattern formation in confined fluid systems is crucial for understanding complex interfacial dynamics.
Ferrofluids offer unique possibilities for controlling fluid interfaces using magnetic fields.

Purpose of the Study:

To analyze the interfacial pattern formation of a viscous ferrofluid annulus surrounded by nonmagnetic fluids in a Hele-Shaw cell under a radial magnetic field.
To explore the interplay between magnetic forces, surface tension, and nonlinear effects on pattern evolution.

Main Methods:

Utilized mode-coupling analysis to study both linear and weakly nonlinear stages of the flow.
Employed linear stability analysis to identify coupling between annular boundaries.
Applied second-order weakly nonlinear analysis to characterize nonlinear morphological features.

Main Results:

Linear stability analysis revealed coupling between inner and outer annular boundaries, where outer perturbations can induce inner deformations.
Nonlinear analysis showed a transition from linear, rounded patterns to nonlinear, polygonal shapes with sharp fingers.
Nonlinear structures exhibited growth saturation, reaching a stationary state, unlike linear patterns.

Conclusions:

The study elucidates the complex pattern dynamics in ferrofluid annuli, driven by magnetic and surface tension forces.
Nonlinear effects are critical in shaping the final morphology and stability of interfacial patterns.
The findings highlight the influence of annulus thickness, force ratios, and magnetic susceptibility on pattern evolution.