  Particle-tracking microrheology of dilute active (self-propelled) colloidal
suspensions is studied by considering the external force required to maintain
the steady motion of an immersed constant-velocity colloidal probe. If the
probe speed is zero, the suspension microstructure is isotropic but exhibits a
boundary accumulation of active bath particles at contact due to their
self-propulsion. As the probe moves through the suspension, the microstructure
is distorted from the nonequilibrium isotropic state, which allows us to define
a microviscosity for the suspension using the Stokes drag law. For a slow
probe, we show that active suspensions exhibit a swim-thinning behavior in
which their microviscosity is gradually lowered from that of passive
suspensions as the swim speed increases. When the probe speed is fast, the
suspension activity is obscured by the rapid advection of the probe and the
measured microviscosity is indistinguishable from that of passive suspensions.
Generally for finite activity, the suspension exhibits a velocity-thinning
behavior -- though with a zero-velocity plateau lower than passive suspensions
-- as a function of the probe speed. These behaviors originate from the
interplay between the suspension activity and the hard-sphere excluded-volume
interaction between the probe and a bath particle.
