  The Young-Dupr\'e equation is a cornerstone of the equilibrium theory of
capillary and wetting phenomena. In the biological world, interfacial phenomena
are ubiquitous, from the spreading of bacterial colonies to tissue growth and
flocking of birds, but the description of such active systems escapes the realm
of equilibrium physics. Here we show how a microscopic, mechanical definition
of surface tension allows us to build an Active Young-Dupr\'e equation able to
account for the partial wetting observed in simulations of active particles
interacting via pairwise forces. Remarkably, the equation shows that the
corresponding steady interfaces do not result from a simple balance between the
surface tensions at play but instead emerge from a complex feedback mechanism.
The interfaces are indeed stabilized by a drag force due to the emergence of
steady currents, which are themselves a by-product of the symmetry breaking
induced by the interfaces. These currents also lead to new physics by selecting
the sizes and shapes of adsorbed droplets, breaking the equilibrium scale-free
nature of the problem. Finally, we demonstrate a spectacular consequence of the
negative value of the liquid-gas surface tensions in systems undergoing
motility-induced phase separation: partially-immersed objects are expelled from
the liquid phase, in stark contrast with what is observed in passive systems.
All in all, our results lay the foundations for a theory of wetting in active
systems.
