Effect of the orientation of the magnetic field on the flow of magnetorheological fluid. II. Cylindrical channel

Abstract

We consider the flow of a magnetorheological (MR) fluid in a cylindrical channel in the presence of a magnetic field inclined relatively to the channel axis (Oz). The stress tensor in the MR fluid is derived by assuming that chain structures are located in the planes parallel to the velocity and the magnetic field (plane Oxz). We show that the velocity field has two orthogonal axes of symmetry, Ox and Oy, in the plane perpendicular to Oz and that the plug zone can be approximated by an ellipsoid of major axis Ox. The plug zone is not defined in the usual way since inside the plug each line perpendicular to the Oy axis is moving at a different velocity. The experiments in a cylindrical capillary at high Mason numbers are compared for different angles between the flow and the field to theoretical predictions. We still recover Bingham behavior and all the pressure versus flow rate curves obtained at different field angles gather on a single straight line when represented against an average normalized yield stress. The slope of this master curve (−0.69) differs slightly from the prediction of the model (−0.85) but is closer than the prediction of the usual model (−4/3) for axial-symmetric flow. The channel hydraulic resistance is maximum for field perpendicular (θ=0) to the axis of the channel and decreases drastically when the angle θ of inclination of the field is larger than 45°; this behavior is reproduced well by our model.