Instabilities and Waves in Thin Films of Living Fluids

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

Figure 1

Top view of film with contractile polar filaments (solid arrows) with a preference for pointing downhill. Active stresses cause fluid flow (dashed arrows) towards the open end of a splay perturbation, leading to film-thickness gradients. Modes propagating forward experience a thickness gradient that further torques (dash-dotted arrow) the filaments in the direction in which they were already perturbed.

Figure 2

An object with head and tail of sizes $\ell$ and ${\ell }^{\prime }$ respectively, and length $\ell$, produces a spontaneous curvature $1/R\simeq (\ell -{\ell }^{\prime })/{\ell }^2$.