Influence of an inhomogeneous internal magnetic field on the flow dynamics of a ferrofluid between differentially rotating cylinders

Altmeyer, Sebastian; Do, Younghae; Lopez, Juan M.

doi:10.1103/physreve.85.066314

Cited by 21 publications

(71 citation statements)

References 23 publications

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“…(8)]. To the leading order, the internal magnetic field in the ferrofluid can be approximated by the externally imposed field [36], which is reasonable for obtaining the dynamical solutions of the magnetically driven fluid motion. Equation (6) can then be simplified as…”

Section: Methodsmentioning

confidence: 99%

Dynamics of ferrofluidic flow in the Taylor-Couette system with a small aspect ratio

Altmeyer

Lai

2017

Sci Rep

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We investigate fundamental nonlinear dynamics of ferrofluidic Taylor-Couette flow - flow confined be-tween two concentric independently rotating cylinders - consider small aspect ratio by solving the ferro-hydrodynamical equations, carrying out systematic bifurcation analysis. Without magnetic field, we find steady flow patterns, previously observed with a simple fluid, such as those containing normal one- or two vortex cells, as well as anomalous one-cell and twin-cell flow states. However, when a symmetry-breaking transverse magnetic field is present, all flow states exhibit stimulated, finite two-fold mode. Various bifurcations between steady and unsteady states can occur, corresponding to the transitions between the two-cell and one-cell states. While unsteady, axially oscillating flow states can arise, we also detect the emergence of new unsteady flow states. In particular, we uncover two new states: one contains only the azimuthally oscillating solution in the configuration of the twin-cell flow state, and an-other a rotating flow state. Topologically, these flow states are a limit cycle and a quasiperiodic solution on a two-torus, respectively. Emergence of new flow states in addition to observed ones with classical fluid, indicates that richer but potentially more controllable dynamics in ferrofluidic flows, as such flow states depend on the external magnetic field.

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Section: Methodsmentioning

confidence: 99%

Dynamics of ferrofluidic flow in the Taylor-Couette system with a small aspect ratio

Altmeyer

Lai

2017

Sci Rep

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“…In our study, we have used the Niklas approximation [18][19][20][21] at near equilibrium with small M − M eq and small relaxation times τ 1, where = ∇ × u/2 is the vorticity, is the absolute value, and τ is the magnetic relaxation time. To determine the relationship between the magnetization M, the magnetic field H, and the velocity u, we may consider an additional dependence of the magnetization on the symmetric part of the velocity gradient…”

Section: Governing Equations and Numerical Techniquementioning

confidence: 99%

Effect of elongational flow on ferrofuids under a magnetic field

Altmeyer

Lopez

2013

Phys. Rev. E

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To set up a mathematical model for the flow of complex magnetic fluids, noninteracting magnetic particles with a small volume or an even point size are typically assumed. Real ferrofluids, however, consist of a suspension of particles with a finite size in an almost ellipsoid shape as well as with particle-particle interactions that tend to form chains of various lengths. To come close to the realistic situation for ferrofluids, we investigate the effect of elongational flow incorporated by the symmetric part of the velocity gradient field tensor, which could be scaled by a so-called transport coefficient λ(2). Based on the hybrid finite-difference and Galerkin scheme, we study the flow of a ferrofluid in the gap between two concentric rotating cylinders subjected to either a transverse or an axial magnetic field with the transport coefficient. Under the influence of a transverse magnetic field with λ(2)=0, we show that basic state and centrifugal unstable flows are modified and are inherently three-dimensional helical flows that are either left-winding or right-winding in the sense of the azimuthal mode-2, which is in contrast to the generic cases. That is, classical modulated rotating waves rotate, but these flows do not. We find that under elongational flow (λ(2)≠0), the flow structure from basic state and centrifugal instability flows is modified and their azimuthal vorticity is linearly changed. In addition, we also show that the bifurcation threshold of the supercritical centrifugal unstable flows under a magnetic field depends linearly on the transport coefficient, but it does not affect the general stabilization effect of any magnetic field.

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“…Following, we will refer to this modified 2-fold symmetric CCF as 2-CCF. It is important to mention that this m ¼ 2 state is stationary [24], which is in contrast to the generic breaking of a SO 2 ðÞsymmetry which would result in a rotating wave.…”

Section: Basic State and Symmetriesmentioning

confidence: 99%

“…Although for magnetic fields that are orientated purely in the radial or azimuthal direction, the basic state changes but remains axisymmetric with deviations from CCF only having an azimuthal component [4,23]. As a result, in all of these cases, the basic state is invariant to a number of symmetries (azimuthal rotation, mirror symmetry, and axial translation) whose actions on a general velocity field are [24], a transverse magnetic field T breaks the continuous axisymmetry R Φ , resulting in a basic state with discrete symmetry R π , i.e., with azimuthal wavenumber m ¼ 2 [24]. Following, we will refer to this modified 2-fold symmetric CCF as 2-CCF.…”

Section: Basic State and Symmetriesmentioning

confidence: 99%

“…Now, using the latest modified magnetization (9), the magnetization part in (1) can be eliminated, similar to previous discussion in Section 2.2. We thus have the following ferrohydrodynamic equation of motion (including elongational flow effects) [12]: Assuming that the internal magnetic field is equal to the external imposed magnetic field (it is known as a leading-order approximation [24], see also following section 5) which is sufficiently good for a 'first' numerical investigation for the effect of elongational flow. Therefore, (10) can be simplified:…”

Section: Modified Internal Magnetic Fieldmentioning

confidence: 99%

See 1 more Smart Citation

Interaction of Magnetic Fields on Ferrofluidic Taylor-Couette Flow

Altmeyer¹

2020

Pattern Formation and Stability in Magnetic Colloids

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When studying ferrofluidic flows, as one example of magnetic flow dynamics, in terms of instability, bifurcation, and properties, one quickly finds out the additional challenges magnetic fluids introduce compared to the investigation of "classical", "ordinary" shear flows without any kind of particles. Approximation of ferrofluids as fluids including point-size particles or, more realistic fine size particles, the relaxation times of the magnetic particle, their interaction between each other, i.e., the agglomeration and chain forming effects, and the interaction/response between any external applied field and the internal magnetization are just few examples of challenges to overcome. Further dependence on the considered model system, the direction of the external applied magnetic field (homogeneous or inhomogeneous) is crucial, as it can break the system symmetry and thus generate new solutions. As a result, the classical Navier-Stokes equations become modified to the more complex ferrohydrodynamical equation of motion, incorporating magnetic field and magnetization of the fluid itself, which typically makes numerical simulations expensive and challenging. This chapter provides an overview of the tasks/difficulties from describing and simulating magnetic particles, their interaction, and thus finally resulting modification in rotating flow structures and in particular instabilities and bifurcation behavior.

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Influence of an inhomogeneous internal magnetic field on the flow dynamics of a ferrofluid between differentially rotating cylinders

Cited by 21 publications

References 23 publications

Dynamics of ferrofluidic flow in the Taylor-Couette system with a small aspect ratio

Dynamics of ferrofluidic flow in the Taylor-Couette system with a small aspect ratio

Effect of elongational flow on ferrofuids under a magnetic field

Interaction of Magnetic Fields on Ferrofluidic Taylor-Couette Flow

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