Parallel flow in Hele-Shaw cells with ferrofluids

Miranda, José A.; Widom, Michael

doi:10.1103/physreve.61.2114

Cited by 10 publications

(4 citation statements)

References 15 publications

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“…The linear theory of the Kelvin-Helmholtz instability for unconfined ferrofluids was developed by Rosensweig [13], which revealed how the strength of the applied magnetic field (on top of the velocity difference and viscosity contrast between the fluid) enters the threshold for instability. Miranda and Widom [14] extended this result to a parallel ferrofluid flow in a vertical Hele-Shaw cells under an external non-tilted magnetic field and deduced that the magnetic field does not affect the propagation speed of waves. Using a perturbative weakly nonlinear analysis, Lira and Miranda [15] further extended the latter analysis by adopting an in-plane tilted applied magnetic field, showing that the wave speed speed is sensitive to the angle.…”

Section: Introductionmentioning

confidence: 84%

Long-wave equation for a confined ferrofluid interface: Periodic interfacial waves as dissipative solitons

Yu,

Christov

2021

Preprint

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We study the dynamics of a ferrofluid thin film confined in a Hele-Shaw cell, and subjected to a tilted nonuniform magnetic field. It is shown that the interface between the ferrofluid and an inviscid outer fluid (air) supports traveling waves, governed by a novel modified Kuramoto-Sivashinsky-type equation derived under the long-wave approximation. The balance between energy production and dissipation in this long-wave equations allows for the existence of dissipative solitons. These permanent traveling wave's propagation velocity and profile shape are shown to be tunable via the external magnetic field. The traveling periodic interfacial waves discovered are identified as fixed points in an energy phase plane. It is shown that transitions between states (wave profiles) occur. These transitions are explained via the spectral stability of the traveling waves. Interestingly, multiperiodic waves, which are a non-integrable analog of the double cnoidal wave, also found to propagate under the model long-wave equation. These multiperiodic solutions are investigated numerically, and they are found to be long-lived transients, but ultimately abruptly transition to one of the stable periodic states identified above.

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Section: Introductionmentioning

confidence: 84%

Long-wave equation for a confined ferrofluid interface: Periodic interfacial waves as dissipative solitons

Yu,

Christov

2021

Preprint

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“…The linear theory of the Kelvin-Helmholtz instability for unconfined ferrofluids was developed by Rosensweig [14], which revealed how the strength of the applied magnetic field (on top of the velocity difference and viscosity contrast between the fluid) enters the threshold for instability. Miranda & Widom [15] extended this result to a parallel ferrofluid flow in a vertical Hele-Shaw cell under an external non-tilted magnetic field and deduced that the magnetic field does not affect the propagation speed of waves. Using a perturbative weakly nonlinear analysis, Lira & Miranda [16] further extended the latter analysis by adopting an in-plane tilted applied magnetic field, showing that the wave speed is sensitive to the angle.…”

Section: Introductionmentioning

confidence: 86%

Long-wave equation for a confined ferrofluid interface: periodic interfacial waves as dissipative solitons

Christov

2021

Proc. R. Soc. A.

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We study the dynamics of a ferrofluid thin film confined in a Hele-Shaw cell, and subjected to a tilted non-uniform magnetic field. It is shown that the interface between the ferrofluid and an inviscid outer fluid (air) supports travelling waves, governed by a novel modified Kuramoto–Sivashinsky-type equation derived under the long-wave approximation. The balance between energy production and dissipation in this long-wave equation allows for the existence of dissipative solitons. These permanent travelling waves’ propagation velocity and profile shape are shown to be tunable via the external magnetic field. A multiple-scale analysis is performed to obtain the correction to the linear prediction of the propagation velocity, and to reveal how the nonlinearity arrests the linear instability. The travelling periodic interfacial waves discovered are identified as fixed points in an energy phase plane. It is shown that transitions between states (wave profiles) occur. These transitions are explained via the spectral stability of the travelling waves. Interestingly, multi-periodic waves, which are a non-integrable analogue of the double cnoidal wave, are also found to propagate under the model long-wave equation. These multi-periodic solutions are investigated numerically, and they are found to be long-lived transients, but ultimately abruptly transition to one of the stable periodic states identified.

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“…This phenomenon is well documented, though largely through analytical studies. 9,30 Therefore, result of the increased magnetic field is faster aggregate dispersion, and lower half-life times. In addition, Figure 14 shows that the half life time is inversely dependent on the Reynolds number.…”

Section: B Aggregate Decay Scalingmentioning

confidence: 99%

“…2 Moreover, fluid instabilities have been the subject of significant scientific works, including the spike-shaped protrusions from a ferrofluid free surface known as the normal field instability, 3,4 the labyrinthine instability, 5 and the Rayleigh-Taylor instability. 6 The Kelvin-Helmholtz instability in ferrofluids has also been studied in several papers analytically, [7][8][9] but has been largely neglected experimentally.…”

Section: Introductionmentioning

confidence: 99%

Dispersion of ferrofluid aggregates in steady flows

Williams

Vlachos

2011

Physics of Fluids

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Using focused shadowgraphs, we investigate steady flows of a magnetically non-susceptible fluid interacting with ferrofluid aggregates comprised of superparamagnetic nanoparticles. The ferrofluid aggregate is retained at a specific site within the flow channel using two different applied magnetic fields. The bulk flow induces shear stresses on the aggregate, which give rise to the development of interfacial disturbances, leading to Kelvin-Helmholtz (K-H) instabilities and shedding of ferrofluid structures. Herein, the effects of bulk Reynolds number, ranging from 100 to 1000, and maximum applied magnetic fields of 1.2 × 105 and 2.4 × 105 A/m are investigated in the context of their impact on dispersion or removal of material from the core aggregate. The aggregate interaction with steady bulk flow reveals three regimes of aggregate dynamics over the span of Reynolds numbers studied: stable, transitional, and shedding. The first regime is characterized by slight aggregate stretching for low Reynolds numbers, with full aggregate retention. As the Reynolds number increases, the aggregate is in-transition between stable and shedding states. This second regime is characterized by significant initial stretching that gives way to small amplitude Kelvin-Helmholtz waves. Higher Reynolds numbers result in ferrofluid shedding, with Strouhal numbers initially between 0.2 and 0.3, wherein large vortical structures are shed from the main aggregate accompanied by precipitous decay of the accumulated ferrofluid aggregate. These behaviors are apparent for both magnetic field strengths, although the transitional Reynolds numbers are different between the cases, as are the characteristic shedding frequencies relative to the same Reynolds number. In the final step of this study, relevant parameters were extracted from the time series dispersion data to comprehensively quantify aggregate mechanics. The aggregate half-life is found to decrease as a function of the Reynolds number following a power law curve and can be scaled for different magnetic fields using the magnetic induction at the inner wall of the vessel. In addition, the decay rate of the ferrofluid is shown to be proportional to the wall shear rate. Finally, a dimensionless parameter, which scales the inertia-driven flow pressures, relative to the applied magnetic pressures, reveals a power law decay relationship with respect to the incident bulk flow.

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Parallel flow in Hele-Shaw cells with ferrofluids

Cited by 10 publications

References 15 publications

Long-wave equation for a confined ferrofluid interface: Periodic interfacial waves as dissipative solitons

Long-wave equation for a confined ferrofluid interface: Periodic interfacial waves as dissipative solitons

Long-wave equation for a confined ferrofluid interface: periodic interfacial waves as dissipative solitons

Dispersion of ferrofluid aggregates in steady flows

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