We study the effect of magnetic field on the rheology of magnetic
micro-swimmers suspensions. We use a model of a dilute suspension under simple
shear and subjected to a constant magnetic field. Particle shear stress is
obtained for both pusher and puller types of micro-swimmers. In the limit of
low shear rate, the rheology exhibits a constant shear stress, called actuated
stress, which only depends on the swimming activity of the particles. This
stress is induced by the magnetic field and can be positive (brake state) or
negative (motor state). In the limit of low magnetic fields, a scaling relation
of the motor-brake effect is derived as a function of the dimensionless
parameters of the model. In this case, the shear stress is an affine function
of the shear rate. The possibilities offered by such an active system to
control the rheological response of a uid are finally discussed.Comment: 10 pages, 6 figures, accepted in PRFluid
