  We introduce a novel mesoscopic computational model based on a
multiphase-multicomponent lattice Boltzmann method for the simulation of
self-phoretic particles in the presence of liquid-liquid interfaces. Our model
features fully resolved solvent hydrodynamics and, thanks to its versatility,
it can handle important aspects of the multiphysics of the problem, including
particle wettability and differential solubility of the product in the two
liquid phases. The method is extensively validated in simple numerical
experiments, whose outcome is theoretically predictable, and then applied to
the study of the behaviour of active particles next to and trapped at
interfaces. We show that their motion can be variously steered by tuning
relevant control parameters, such as the phoretic mobilities, the contact angle
and the product solubility.
