The growth of localized states on the surface of magnetic fluids

Knieling, Holger; Rehberg, Ingo; Richter, R.

doi:10.1016/j.phpro.2010.11.045

Cited by 3 publications

(2 citation statements)

References 8 publications

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“…The ramp is introduced in order to minimize the differences between the amplitudes obtained in a finite and an infinite geometry. For details of the magnetic ramp see Knieling et al (2010). Filling the container to a height of 5 mm with ferrofluid enhances the magnetic induction in comparison with the empty coils for the same current I.…”

Section: Methodsmentioning

confidence: 99%

Homoclinic snaking near the surface instability of a polarisable fluid

et al. 2015

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We report on localised patches of cellular hexagons observed on the surface of a magnetic fluid in a vertical magnetic field. These patches are spontaneously generated by jumping into the neighbourhood of the unstable branch of the domain-covering hexagons of the Rosensweig instability upon which the patches equilibrate and stabilise. They are found to coexist in intervals of the applied magnetic field strength parameter around this branch. We formulate a general energy functional for the system and a corresponding Hamiltonian that provide a pattern selection principle allowing us to compute Maxwell points (where the energy of a single hexagon cell lies in the same Hamiltonian level set as the flat state) for general magnetic permeabilities. Using numerical continuation techniques, we investigate the existence of localised hexagons in the Young-Laplace equation coupled to the Maxwell equations. We find that cellular hexagons possess a Maxwell point, providing an energetic explanation for the multitude of measured hexagon patches. Furthermore, it is found that planar hexagon fronts and hexagon patches undergo homoclinic snaking, corroborating the experimentally detected intervals. Besides making a contribution to the specific area of ferrofluids, our work paves the ground for a deeper understanding of homoclinic snaking of two-dimensional localised patches of cellular patterns in many physical systems.

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Section: Methodsmentioning

confidence: 99%

Homoclinic snaking near the surface instability of a polarisable fluid

et al. 2015

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“…4(b). 1,77,78 For the Rosensweig instability, as the ferrouid layer becomes thinner, the lateral boundaries no longer determine its shape and a droplet is formed on the planar surface. Patterns generated by applied elds normal to the surface change in these conditions, as shown in Fig.…”

Section: Ferrofluid Instabilities and Controlmentioning

confidence: 99%

Recent progress in ferrofluids research: novel applications of magnetically controllable and tunable fluids

2014

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Ferrofluids are suspensions of magnetic nanoparticles that have the attractive feature of being controlled by applied magnetic fields. Ferrofluids have been studied for decades in an ever growing number of applications that take advantage of their response to applied magnetic fields. Here, we provide a summary of recent advances in established and emerging applications of ferrofluids, including applications in optics, sensors, actuators, seals, lubrication, and static/dynamic magnetically driven assembly of structures.

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