Influence of homogeneous magnetic fields on the flow of a ferrofluid in the Taylor-Couette system

Abstract

We investigate numerically the influence of a homogeneous magnetic field on a ferrofluid in the gap between two concentric, independently rotating cylinders. The full Navier-Stokes equations are solved with a combination of a finite difference method and a Galerkin method. Structure, dynamics, symmetry properties, bifurcation, and stability behavior of different vortex structures are investigated for axial and transversal magnetic fields, as well as combinations of them. We show that a transversal magnetic field modulates the Taylor vortex flow and the spiral vortex flow. Thus, a transversal magnetic field induces wavy structures: wavy Taylor vortex flow (wTVF) and wavy spiral vortex flow. In contrast to the classic wTVF, which is a secondarily bifurcating structure, these magnetically generated wavy Taylor vortices are pinned by the magnetic field, i.e., they are stationary and they appear via a primary forward bifurcation out of the basic state of circular Couette flow.

Elongational flow effects on the vortex growth out of Couette flow in ferrofluids

“…Thus the CCF basic state is stabilized against the two types of vortex perturbations in the magnetic field. This behavior has been seen already [15,16,31] for λ 2 = 0. Here we want to remind the reader that for λ 2 = 0 model ML reduces to model D.…”

“…Some of the reasons are that magnetic fields influence their macroscopic flow behavior and vice versa [1][2][3][4][5] and their rheology and transport properties can be changed by a magnetic field [6][7][8][9]. Also, the question of how the flow of a ferrofluid in the Taylor-Couette system is influenced by magnetic fields has been the subject of several theoretical and experimental analyses [10][11][12][13][14][15][16][17], most of them being focused on the relaxation phenomena of the magnetic particles.…”

Thermomagnetic convection in a layer of ferrofluid placed in a uniform oblique external magnetic field

“…An alternative setup that has been extensively studied numerically consists of two coaxial co-rotating or differentially rotating cylinders (e.g. Zebib 1996;Tagg & Weidman 2007;Altmeyer et al 2010). However as mentioned in Suslov et al (2010) experimental implementation of such a geometry is somewhat more complicated and the magnetic field applied in this case is necessarily non-uniform, which complicates the understanding of basic thermomagnetic mechanisms that are of interest here.…”

Turbulent flow of a fluid with anisotropic viscosity

“…Our approach is thus fundamentally different from other experiments studying anisotropic turbulence where anisotropy is produced for example by rotation (Lamriben, Cortet & Moisy 2011), mean velocity gradients (Shen & Warhaft 2000) or by modulation of many mixers inside a flow chamber (Chang, Bewley & Bodenschatz 2012). Uniform magnetic field forcing has so far been used primarily in studies on the global evolution of laminar and transitional flows (Altmeyer et al 2010;Reindl & Odenbach 2011). Another investigative route being followed is the study of the energy transfer in flows with long chained polymers.…”