Negative differential viscosity in magnetic suspensions

Recent experiments have shown that the dependence of the macroscopic viscous stress on the mean velocity gradient during the Couette flow of concentrated magnetic suspensions in an external magnetic field is N-shaped. As the field strength is decreased, the amplitude of the N-shaped curve decreases and in the absence of the field, the stress monotonically increases with the shear velocity. A model is proposed to explain the shape of the rheological curve. The model assumes that the magnetic field initiates the formation of dense aggregates in a suspension, which connect the opposite walls of a measurement cell. In the Couette flow, the friction of aggregates on the cell walls causes their deviation from the applied magnetic field through an angle determined by the velocity of the relative motion of the walls. For large enough velocities, the aggregates are detached from the wall and are destroyed by viscous forces. It is shown that the friction of aggregates on cell walls results in the initial increasing and decreasing part of the N-shaped rheogram, while the flow after the detachment of aggregates corresponds to its right increasing part.