  Recent experiments have shown that colloidal suspensions can spontaneously
self-assemble into dense clusters of various internal structures, sizes and
dynamical properties when doped with active Janus particles.
Characteristically, these clusters move ballistically during their formation,
but dynamically revert their velocity and temporarily move opposite to the
self-propulsion direction of the Janus particles they contain. Here we explore
a simple effective model of colloidal mixtures which allows reproducing most
aspects seen in experiments, including the morphology and the velocity-reversal
of the clusters. We attribute the latter to the nonreciprocal phoretic
attractions of the passive particles to the active colloids' caps, taking place
even at close contact and pushing the active particles backwards. When the
phoretic interactions are repulsive, in turn, they cause dynamical aggregation
of passive colloids in the chemical density minima produced by the active
particles, as recently seen in experiments; in other parameter regimes they
induce travelling fronts of active particles pursued by passive ones coexisting
with an active gas.
