On the ridge of instability in ferrofluidic Couette flow via alternating magnetic field

Abstract

There is a huge number of natural and industrial flows, which are subjected to time-dependent boundary conditions. The flow of a magnetic fluid under the influence of temporal modulations is such an example. Here, we perform numerical simulations of ferrofluidic Couette flow subject to time-periodic modulation (with frequency $$\Omega _H$$ Ω H ) in a spatially homogeneous magnetic field and report how such a modulation can lead to a significant Reynolds number Re enhancement. Consider a modified Niklas approximation we explain the relation between modulation amplitude, driving frequency and stabilization effect. From this, we describe the system response around the primary instability to be sensitive/critical by an alternating field. We detected that such an alternating field provides an easy and in particular accurate controllable key parameter to trigger the system to change from subcritical to supercritical and vice versa. Our findings provide a framework to study other types of magnetic flows driven by time-dependent forcing.

Increasing Flow Complexity in Time-Dependent Modulated Ferrofluidic Couette Flow

“…Although the magnitude of stabilization is different, it does not change the bifurcation order (for here considered parameters). Similar numerical and experimental observations have been already found for increasing field strength in static magnetic fields [22][23][24] and recently for TVF in modulated magnetic fields [15] with the outer cylinder at rest. For sufficiently large modulation amplitudes the stability in the primary bifurcating solution is exchanged from SPI towards RIB.…”

“…This way, the effect of the magnetic field (here homogeneous but periodically alternating with ) and all the magnetic properties of the ferrofluid on the velocity field can be characterized by a single (here time-dependent) Niklas parameter [19] (1.6) with two time-independent control parameters (1.7) being the static contribution of the driving, the modulation amplitude, and the modulation frequency. In the present study we consider a pure modulated magnetic field (without any static contribution, ) in the high frequency limit , which means that the effects of inertia of the fluid can be neglected and the system basically sees an averaged magnetic field [15].…”

“…Considering a magnetic fluid, e.g., a ferrofluid [13][14][15] offers the great advantage to maintain a stationary setup while introducing any periodic forcing directly into the fluid within the bulk. To date numerous numerical and experimental studies for ferrofluidic Couette flows under static magnetic fields have been performed.…”

“…To date the studies of ferrofluids under alternating magnetic fields are relatively rare and if so special attention is given to viscosity effects [31] and heat behavior [32,33]. However, analogosly to static fields, the modulated fields with sufficiently high modulation frequency stabilize the CCF basic state [15,31] and can provide an accurate control parameter to balance the system to be either sub-or supercritical [15]. Different works, mainly focused on the use of temporal modulation in heating binary fluids and ferrofluids [34][35][36], illustrated that the parameter modulation in the hydrodynamic systems causes the parametric resonance.…”

Ferrofluidic wavy Taylor vortices under alternating magnetic field

“…The magnetic field H and the magnetization M are conveniently normalized by the quantity √ ρ/μ 0 ν/d, with free space permeability μ 0 . By using a modified Niklas approach [23,24,48,49], the effect of the magnetic field and the magnetic properties of the ferrofluid on the velocity field can be characterized by a single (time-dependent) function, the modulation frequency, respectively. See appendix A for further details.…”