Hexagons become the secondary pattern if symmetry is broken

Reimann, Bert; Richter, R.; Knieling, Holger; Friedrichs, R.; Rehberg, Ingo

doi:10.1103/physreve.71.055202

Cited by 16 publications

(19 citation statements)

References 14 publications

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“…Experiments and computations of Gollwitzer et al (2009) performed in a small container confirm this. However, experimental photographs presented, for example, in Reimann et al (2005), Groh et al (2007) indicate that the magnetically forced periodic free-surface deformation patterns observed in the central part of a wide container appear to extend almost to its physical boundaries, thus downplaying the importance of the edge effects. The plausible explanation of this drastic difference between free-surface and magnetoconvection experiments is that in the former case the focussing of a magnetic field under the curved fluid surface leads to a comparable or even stronger distortion of the applied field than that caused by the refraction of the magnetic field at the edges.…”

Section: Introductionmentioning

confidence: 91%

Magneto-gravitational convection in a vertical layer of ferrofluid in a uniform oblique magnetic field

Rahman

Suslov

2016

J. Fluid Mech.

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The stability of base gravitational convection in a layer of ferrofluid confined between two vertical wide and tall non-magnetic plates, heated from one side, cooled from the other and placed in a uniform oblique external magnetic field is studied. Two distinct mechanisms, thermo-gravitational and thermo-magnetic, are found to be responsible for the appearance of various stationary and wave-like instability modes. The characteristics of all instability modes are investigated as functions of the orientation angles of the applied magnetic field and its magnitude for various values of magnetic parameters when both the thermo-magnetic and gravitational buoyancy mechanisms are active. The original three-dimensional problem is cast in an equivalent two-dimensional form using generalised Squire's transformations, which significantly reduces a computational cost. Subsequently, full three-dimensional instability patterns are recovered using the inverse Squire's transformation, and the optimal field and pattern orientations are determined.

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Section: Introductionmentioning

confidence: 91%

Magneto-gravitational convection in a vertical layer of ferrofluid in a uniform oblique magnetic field

Rahman

Suslov

2016

J. Fluid Mech.

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“…In contrast to the case of the static, tilted field instability [22], we could not fit the spatial modulation of the signal of the sensor array with periodic functions. This difficulty might stem from the higher complexity of the evolving pattern which can not fully be captured by a one-dimensional array, and the limited spatial resolution of the array.…”

Section: Discussionmentioning

confidence: 99%

“…In order to measure the temporal evolution of the growing amplitudes we utilize a linear array of Hall sensors [22], which is sketched together with the experimental arrangements in Sec. II.…”

Section: Introductionmentioning

confidence: 99%

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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“…[20], as detailed in Ref. [21]. The effective permeability r is the geometric mean r = (1 + χ ta )(1 + χ ch ), where χ ta = (∂M/∂H) denotes the tangential susceptibility, and χ ch = (M/H) the chord susceptibility [1].…”

Section: Modeling the Resonancementioning

confidence: 99%

Magnetic traveling-stripe forcing: Enhanced transport in the advent of the Rosensweig instability

Friedrich¹,

Rehberg²,

Richter³

2010

Phys. Rev. E

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A new kind of contactless pumping mechanism is realized in a layer of ferrofluid via a spatiotemporally modulated magnetic field. The resulting pressure gradient leads to a liquid ramp, which is measured by means of X-rays. The transport mechanism works best if a resonance of the surface waves with the driving is achieved. The behavior can be understood semi-quantitatively by considering the magnetically influenced dispersion relation of the fluid.

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Hexagons become the secondary pattern if symmetry is broken

Cited by 16 publications

References 14 publications

Magneto-gravitational convection in a vertical layer of ferrofluid in a uniform oblique magnetic field

Magneto-gravitational convection in a vertical layer of ferrofluid in a uniform oblique magnetic field

Growth of surface undulations at the Rosensweig instability

Magnetic traveling-stripe forcing: Enhanced transport in the advent of the Rosensweig instability

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