Dynamics of ferrofluidic flow in the Taylor-Couette system with a small aspect ratio

TL;DR

This paper explores the complex nonlinear behavior of ferrofluidic Taylor-Couette flow with small aspect ratio, revealing new flow states and bifurcations influenced by magnetic fields, expanding understanding of ferrofluid dynamics.

Contribution

It introduces novel unsteady flow states and bifurcation phenomena in ferrofluidic Taylor-Couette flow under magnetic influence, extending previous fluid flow models.

Findings

Discovery of new unsteady flow states including azimuthally oscillating and rotating flows.

Identification of bifurcations leading to transitions between steady and unsteady states.

Observation of richer, controllable dynamics due to magnetic field effects.

Abstract

We investigate fundamental nonlinear dynamics of ferrofluidic Taylor-Couette flow - flow confined between two concentric independently rotating cylinders - consider small aspect ratio by solving the ferrohydrodynamical equations, carrying out systematic bifurcation analysis. Without magnetic field, we find steady flow patterns, previously observed with a simple fluid, such as those containing normal one- or two vortex cells, as well as anomalous one-cell and twin-cell flow states. However, when a symmetry-breaking transverse magnetic field is present, all flow states exhibit stimulated, finite two-fold mode. Various bifurcations between steady and unsteady states can occur, corresponding to the transitions between the two-cell and one-cell states. While unsteady, axially oscillating flow states can arise, we also detect the emergence of new unsteady flow states. In particular, we uncover two new states: one contains only the azimuthally oscillating solution in the configuration of the twin-cell flow state, and another a rotating flow state. Topologically, these flow states are a limit cycle and a quasiperiodic solution on a two-torus, respectively. Emergence of new flow states in addition to observed ones with classical fluid, indicates that richer but potentially more controllable dynamics in ferrofluidic flows, as such flow states depend on the external magnetic field.