Active matter consists of large numbers of self-driven agents converting chemical energy, usually stored in the surrounding environment, into mechanical motion. In the last decade various realizations of active matter have been studied including living self-propelled particles as well as synthetically manufactured ones. The main motivation for our work is a potential usage of active ink (ink with active bi-metal nanoparticles) in 3D printers. It may result in smaller voxel size and increase the printing speed. Decreased viscosity allows for smaller outlet of nozzle which, in turn, results in better resolution of 3D printing.

In this presentation I focus on a kinetic description of active matter represented by self-propelled rods swimming in a viscous fluid and in presence of confinements. It is well-known that confinements may significantly affect trajectories of active rods in contrast to unbounded or periodic containers. Among such effects are accumulation at walls and upstream motion (also known as rheotaxis). The main result is the rigorous derivation of boundary conditions for the active rods' probability distribution function in the limit of zero inertia. These boundary conditions are important since the active rod possesses self-propulsion thus its velocity does not vanish at the no-slip wall, as for passive particles. Moreover, this limit allows us to reduce a dimension (and so computational complexity) of the kinetic description.

This is a joint work with Mykhailo Potomkin, Leonid Berlyand and Pierre-Emmanuel Jabin.