Nonaxisymmetric modes of the Couette--Taylor instability in ferrofluids with radial flow

Abstract

The stability of a ferrofluid flow against nonaxisymmetric disturbances in an annular region between two co-axially rotating porous cylinders, with a radial flow, in the presence of an axial magnetic field, has been investigated numerically. The critical value of the angular velocity ratio Ω ∗ of the cylinders at the onset of first nonaxisymmetric mode of instability has been found to depend upon the magnetic field parameter ψ, the radial Reynolds number Re and the radius ratio ξ of the cylinders. 1. Introduction. The stability characteristics of a viscous flow between two co-axially rotating cylinders are of interest in several technical areas. The first successful treatment of this flow was attempted by Taylor [1]. His experiments on this flow demonstrated the onset of instability in the form of a regular pattern of horizontal toroidal vortices, extending periodically along the vertical axis of the cylinders. There after, this stability problem has been studied by many authors with generally excellent agreement between theory and experiment (See Chandrasekhar [2], Koschmeider [3], Chossat & Ioos [4]). Various patterns are observed under different physical conditions governing the flow between rotating cylinders. A magnetic field applied axially to the Couette flow of ferrofluids delays the Couette–Taylor instability. This has been studied by Niklas et al. [5], Chang et al. [6], and Singh & Bajaj [7]. The stability of the Taylor–Couette flow can also be enhanced by imposing an additional flow on it. The stability of the viscous flow in between two co-axially rotating porous cylinders with superposition of a radial flow has been studied by Mishra et al. [8], Min et al. [9], Johnson et al. [10], Wereley et al. [11], Lee et al. [12] etc. This flow has led to applications in making dynamic rotating filter devices, consisting of two concentric cylinders, in which the inner permeable cylinder is free to rotate, while the outer non-porous cylinder is held fixed. The suspension to be filtered is contained in the annular space between the cylinders, and the inner porous cylinder is rotated about the vertical axis. The Taylor-vortices, which appear as a result of instability, greatly reduce the plugging of the filter pores with particles. This property of such filters has a technological advantage if compared to other standard filtration techniques. Today, the rotating filters are being used for separating plasma from blood and in other biological filtrations. Singh & Bajaj [13] have discussed the stability of the axisymmetric Couette ferrofluid flow in porous cylinders with superposition of a radial flow and an axial magnetic field. They have found that the basic flow is stabilized by the applied magnetic field for the considered range of the radial Reynolds number Re. The stability characteristics of the flow with Re and the normalized profiles for the perturbation variables depend strongly upon the parameter ξ. The angular velocity ratio Ω ∗ has a destabilizing effect on the flow for all considered values of (Re ,ψ ).