  Efficient nutrient mixing is crucial for the survival of bacterial colonies
and other living systems. This raises the question of whether the optimization
of mixing through the emergence of active turbulent motion in bacterial swarms
played a role in the evolution of bacterial shapes. Here, to address this
question, we solve the hydrodynamic equation for active nematics coupled with
an advection-diffusion equation for the nutrients. The latter models a
conserved activity field and mimics the conservation of nutrients in bacterial
swarms. At the interface between active and passive nematic phases, in addition
to diffusion, the activity is transported by interfacial flows and in turn
modifies them through active stresses. We find that the interfacial dispersion
of the conserved activity is subdiffusive due to the emergence of a barrier of
negative defects at the active-passive interface, which hinders the propagation
of the motile positive defects. Furthermore, we observe a non-monotonic
dependence of the generalized diffusion coefficient on the aligning parameter,
which is related to the shape of the particles. Our simulations suggest that
there is an optimal shape that maximizes the dispersion of conserved activity
at the active-passive nematic interface.
