  Phase transitions and collective dynamics of active colloidal suspensions are
fascinating topics in soft matter physics, particularly for out-of-equilibrium
systems, which can lead to rich rheological behaviours in the presence of
steady shear flow. In this article, the role of self-propulsion in the
rheological response of a dense colloidal suspension is investigated by using
particle-resolved simulations. First, the interplay between activity and shear
in the solid to the liquid transition of the suspension is analysed. While both
self-propulsion and shear destroy order and melt the system by themselves above
their critical values, self-propulsion lowers the stress barrier that needs to
be overcome during the transition. Once the suspension reaches a
non-equilibrium steady state the rheological response is analysed. While
passive suspensions show a solid-like behaviour, turning on particle motility
fluidises the system and, at low self-propulsion, the suspension behaves as a
shear-thinning fluid. Increasing the self-propulsion of the colloids induces a
transition from a shear-thinning to a shear-thickening behaviour, which we
attribute to clustering in the suspensions induced by motility. This
interesting phenomenon of motility-induced shear thickening (MIST) can be used
to tailor the rheological response of colloidal suspensions.
