  Janus phoretic colloids (JPs) self-propel as a result of self-generated
chemical gradients and exhibit spontaneous nontrivial dynamics within phoretic
suspensions, on length scales much larger than the microscopic swimmer size.
Such collective dynamics arise from the competition of (i) the self-propulsion
velocity of the particles, (ii) the attractive/repulsive chemically-mediated
interactions between particles and (iii) the flow disturbance they introduce in
the surrounding medium. These three ingredients are directly determined by the
shape and physico-chemical properties of the colloids' surface. Owing to such
link, we adapt a recent and popular kinetic model for dilute suspensions of
chemically-active JPs where the particles' far-field hydrodynamic and chemical
signatures are intrinsically linked and explicitly determined by the design
properties. Using linear stability analysis, we show that self-propulsion can
induce a wave-selective mechanism for certain particles' configurations
consistent with experimental observations. Numerical simulations of the
complete kinetic model are further performed to analyze the relative importance
of chemical and hydrodynamic interactions in the nonlinear dynamics. Our
results show that regular patterns in the particle density are promoted by
chemical signaling but prevented by the strong fluid flows generated
collectively by the polarized particles, regardless of their chemotactic or
antichemotactic nature (i.e. for both puller and pusher swimmers).
