Stability of the circular Couette flow of a ferrofluid in an axial magnetic field: Influence of polydispersity

Abstract

The gap between two concentric rotating cylinders is filled with a ferrofluid. A homogeneous magnetic field is applied parallel to the cylinder axis. The stability of the circular Couette flow is analyzed with different models that take into account the polydispersity of the ferrofluid to a varying degree. Their results are compared and their merits are discussed.

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.…”

“…(3.5) we have ignored, as in Ref. [16], the deviation of δM eq relative to the direct magnetization perturbation δM. We expect also here the contribution of the former to be small compared to the latter.…”

“…The equilibrium magnetization M eq (H ) of APG933 is obtained with a polydisperse fit to experimental data that is described in detail in Ref. [16]. For the single magnetic relaxation time τ we use a value of 0.5 × 10 −3 s, which is comparable to the averaged effective relaxation time as well as experimental results [29,30].…”

“…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.…”

Dean instability in ferrofluids

“…As a result, the ferrofluid exhibits a non-zero magnetization m. A constant pressure gradient [1] acting round the cylinders is also applied to the system in the form ð0; P; 0Þ along the azimuthal direction. The flow is governed by the conservation of linear momentum, angular momentum, mass, and by the Maxwell's field equations, which are given by the following equations in order [31][32][33],…”