Hydrodynamic instabilities in chemotactic thin-film active suspensions*

In this work, we are interested in the hydrodynamic instabilities found in chemotactic thin-film suspensions of active swimmers. In the presence of an imposed attractant gradient, the preferential swimming exhibited by the swimmers gives rise to an anisotropic active stress within the suspension. Through a long-wave stability analysis, we show that the flow generated as a result gives rise to a new mode of instability associated with the film interface, in addition to modifying the instability mechanism predicted by Kasyap and Koch (2012). We further show that a coupling between the above two modes of instability destabilizes a suspension of pullers, which was previously shown to be unconditionally stable ( Kasyap and Koch (2012) & (2014) ). Additionally, we formulate a long-wave theory for the film evolution to ascertain the mechanism associated with the instabilities found in the system.