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We formulate the thin-film hydrodynamics of a suspension of polar self-drivenparticles and show that it is prone to several instabilities through theinterplay of activity, polarity and the existence of a free surface. Ourapproach extends, to self-propelling systems, the work of Ben Amar and Cummings[Phys Fluids 13 (2001) 1160] on thin-film nematics. Based on our estimates theinstabilities should be seen in bacterial suspensions and the lamellipodium,and are potentially relevant to the morphology of biofilms. We suggest severalexperimental tests of our theory.

Instabilities and waves in thin films of living fluids