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Journal of Magnetism and Magnetic Materials
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Research articles
Ferrofluidic Taylor Couette flow in between finite length porous cylinders
with radial through-flow
Sebastian Altmeyer
Castelldefels School of Telecom and Aerospace Engineering, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
ABSTRACT
We study ferrofluidic Taylor Couette flow under the influence of radial inflow and outflow in combination with an external applied magnetic field in a finite-length
cavity via direct numerical simulations. As is the case for no magnetic field, the base state (cylindrical Couette flow and modified circular-Couette flow in presence of
a transverse magnetic field component, respectively) with an external magnetic field is stabilized for any radial inflow and strong radial outflow, while the system
becomes slightly destabilized for weak radial outflow. The particular parameter range for destabilization depends on the field strength of the applied magnetic field.
Slightly increasing the field strength shrinks the range, while it grows for larger field strengths. In general, a larger field strength tends to minimize and compensate
the effect of any radial flow, resulting in bifurcation thresholds (critical Reynolds number vs. radial flow) which have less curvature, i.e. they are more flat. We
elucidate the origin of this effect to be in the symmetry breaking nature of the transverse magnetic field itself. Azimuthal velocity isocontours are shifted different
strong due to radial flow, either in the part of the annulus that is aligned with the direction of the applied magnetic field or perpendicular to it. In particular, the
modulation amplitude in the isocontours perpendicular to the field increase. As a result the flow is locally stabilized with different strength, so that the overall
stabilization is weaker relative to the situation without any applied field. This diminishing curvature effect with variation of the radial flow becomes more pro-
nounced with stronger applied magnetic fields.
1. Introduction
The flow between two concentric cylinders driven by differential
rotation, Taylor-Couette flow, has played a paradigmatic role for the
development of hydrodynamic stability theory [1] and testing appli-
cations of low dynamical system theory [2]. The geometric simplicity
allows for well-controlled experiments that allow verification of nu-
merical simulations, which together shed light on hydrodynamic sta-
bility and the transition to turbulence.
In absence of any magnetic field, the stable azimuthal circular
Couette flow (CCF) of a Newtonian fluid between a rotating inner cy-
linder and a stationary outer cylinder becomes centrifugally unstable
upon exceeding a critical rotation speed. The result is the appearance of
axisymmetric toroidal closed Taylor vortices, typically called Taylor
vortex flow (TVF) [1]. However, the critical values for the appearance
of these vortex structures depend on various parameters that can be
altered in several ways. For instance, if both cylinders are permeable
and a radial through-flow is imposed through them, the system stability
changes. Based on linear stability analysis for axisymmetric dis-
turbances, the flow is stabilized by a radial inward flow or strong radial
outward flow, while a weak radial outward flow destabilizes the system
slightly [3–9].
Another situation in which the stability can be altered is by con-
sidering non-ordinary fluids such as ferrofluids [10], which are fluids
consisting of a dispersion of magnetized nanoparticles in a variety of
liquid carriers that are stabilized against particle agglomeration
through the addition of a surfactant monolayer on the particles. In the
absence of any magnetic field, the nanoparticles are randomly oriented
so that the fluid has zero net magnetization. In this case, the nano-
particles alter the viscosity and the density of the fluid very little. Thus,
in the absence of any external field a ferrofluid behaves as an ordinary
(classical) Newtonian fluid. However, when a magnetic field of suffi-
cient strength is applied, the hydrodynamical properties of the fluid,
such as the viscosity, can change dramatically [11–14], resulting in
very different dynamics.
The magnetoviscous effect in ferrofluids is highly dependent on the
orientation of the magnetic field with respect to the fluid flow [15].
Under a symmetry-breaking transverse magnetic field, all flow states in
the Taylor-Couette system (TCS) become intrinsically three-dimen-
sional [16–18], increasing the already large number of flow states
known to exist in the system [1,2,19–22]. Any external applied mag-
netic field results in a general stabilization of the basic state as well as
shifting bifurcation thresholds for any flow structure. If the external
applied magnetic field is either axial, radial or azimuthal orientated, its
orientation does not play any role qualitatively. Only quantitative dif-
ferences in the distance of the up-shift of primary bifurcation thresholds
can be detected [13,14,16–18,23,24]. However, it is crucial to note that
the presence of a transversal magnetic field alters the classical
https://doi.org/10.1016/j.jmmm.2019.166363
Received 20 August 2019; Received in revised form 25 December 2019; Accepted 27 December 2019
E-mail address: sebastian_altmeyer@t-online.de.
Journal of Magnetism and Magnetic Materials 500 (2020) 166363
Available online 30 December 2019
0304-8853/ © 2019 Elsevier B.V. All rights reserved.
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