Effect of the orientation of the magnetic field on the flow of a magnetorheological fluid. I. Plane channel

Shear flow and Poiseuille flow of magnetorheological fluids in a plane channel under an inclined magnetic field are studied. The proposed theoretical model is based on stability analysis of chain-like clusters of dipolar magnetic particles. Hydrodynamic and magnetic torque acting on aggregates balances each other such that some misalignment between orientations of chains and the field takes place. Two magnetic field directions symmetric relative to the velocity gradient influence the aggregate behavior in different ways. In one case, the aggregates tend to turn along the flow whereas in the other case, they tend to turn transverse to the flow. The predicted peak value of the yield stress arises for θ0=−π/4 (where θ0 is the clockwise angle between the velocity gradient and the direction of the field) and is 1.8 times the value for θ0=0. If we consider Poiseuille flow between two parallel plates, the velocity gradient, being positive on one side and negative on the other, the stress is no longer symmetric r...