Lattice model for active flows in microchannels

We introduce a one-dimensional lattice model to study active particles in narrow channel connecting finite reservoirs. The model describes interacting run-and-tumble swimmers exerting pushing forces on neighboring particles, allowing the formation of long active clusters inside the channel. Our model is able to reproduce the emerging oscillatory dynamics observed in full molecular dynamics simulations of self-propelled bacteria [Paoluzzi et al., Phys. Rev. Lett. 115, 188303 2015)] and allows us to extend in a simple way the analysis to a wide range of system parameters (box length, number of swimmers), taking into account different physical conditions (presence or absence of tumbling, different forms of the entrance probability into the channel). We find that the oscillatory behavior is suppressed for short channels length L < L* and for high tumbling rates lambda > lambda*, with threshold values L* and lambda* which in general depend on physical parameters. Moreover, we find that oscillations persist by using different entrance probabilities, which, however, affect the oscillation properties and the filling dynamics of reservoirs.