Linear and nonlinear approach to the Rosensweig instability

Lange, Adrian; Richter, R.; Tobiska, Lutz

doi:10.1002/gamm.200790006

Cited by 8 publications

(7 citation statements)

References 23 publications

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“…For a sudden increase of the magnetic induction B the wave number q m of the fastest-growing mode was measured in the linear range, i.e. for small amplitudes [17,18,19,20]. In agreement with theory its value increases monotonically with the supercritical magnetic induction.…”

Section: Introductionsupporting

confidence: 78%

Growth of surface undulations at the Rosensweig instability

et al. 2007

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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.

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Section: Introductionsupporting

confidence: 78%

Growth of surface undulations at the Rosensweig instability

et al. 2007

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“…The first term of equation (2.9) is the usual magnetic potential considered in several papers on the Rosensweig instability, e.g. Friedrichs & Engel (2001); Lange et al (2007). It cannot be directly integrated because H depends on the interface of the fluid distribution through its boundary conditions.…”

Section: Surface Potentialsmentioning

confidence: 99%

“…In order to do relevant quantitative predictions, one has to carry a nonlinear analysis, as done in e.g. Gailitis (1977); Friedrichs & Engel (2001); Lange et al (2007). This is left for future work.…”

Section: Rosensweig Instability In a Non-uniform Magnetic Fieldmentioning

confidence: 99%

“…In the presence of a vertical magnetic field, the competition between gravity, surface tension and magnetic energy generates various phenomena, from lattices of spikes in three dimensional layers of fluid, created by the normal-field instability (e.g. Rosensweig (1985); Gailitis (1977); Friedrichs & Engel (2001); Lange et al (2007) and the review by Richter & Lange (2009)) and characterized by the capillary wavelength λ c (see figure 1), to specific patterns in thin ferrofluid layers (e.g. Bacri & Elias 2011), as the labyrinthine patterns discovered by Cebers & Maiorov (1980).…”

Section: Introductionmentioning

confidence: 99%

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Shape and fission instabilities of ferrofluids in non-uniform magnetic fields

Vieu

Walter

2018

J. Fluid Mech.

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We study static distributions of ferrofluid submitted to non-uniform magnetic fields. We show how the normal-field instability is modified in the presence of a weak magnetic field gradient. Then we consider a ferrofluid droplet and show how the gradient affects its shape. A rich phase transitions phenomenology is found. We also investigate the creation of droplets by successive splits when a magnet is vertically approached from below and derive theoretical expressions which are solved numerically to obtain the number of droplets and their aspect ratio as function of the field configuration. A quantitative comparison is performed with previous experimental results, as well as with our own experiments, and yields good agreement with the theoretical modeling.

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“…layer under magnetic force, surface tension force, gravity and hydrodynamics [33,34,35,36]. In [37], the Rosensweig instability is investigated numerically for the diffusion of magnetic particles.…”

Section: Introductionmentioning

confidence: 99%

Ferrofluids and magnetically guided superparamagnetic particles in flows: a review of simulations and modeling

Afkhami

Renardy

2017

J Eng Math

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Ferrofluids are typically suspensions of magnetite nanoparticles, and behave as a homogeneous continuum. The production of nanoparticles with a narrow size distribution and the achievement of colloidal stability are important technological issues. The ability of the ferrofluid to respond to an external magnetic field in a controllable manner has made it emerge as a smart material in a variety of applications, such as seals, lubricants, electronics cooling, shock absorbers and adaptive optics. Magnetic nanoparticle suspensions have also gained attraction recently in a range of biomedical applications, such as cell separation, hyperthermia, MRI, drug targeting and cancer diagnosis. In this review, we provide an introduction to mathematical modeling of three problems: motion of superparamagnetic nanoparticles in magnetic drug targeting, the motion of a ferrofluid drop consisting of chemically bound nanoparticles without a carrier fluid, and the breakage of a thin film of a ferrofluid.

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Linear and nonlinear approach to the Rosensweig instability

Cited by 8 publications

References 23 publications

Growth of surface undulations at the Rosensweig instability

Growth of surface undulations at the Rosensweig instability

Shape and fission instabilities of ferrofluids in non-uniform magnetic fields

Ferrofluids and magnetically guided superparamagnetic particles in flows: a review of simulations and modeling

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