Abstract
The lecture 5 gave an illustration of the theory of active gels by discussing the stability of a thin film of nematic active liquid on a solid substrate. The anchoring condition on both surfaces, the solid and the free surface, is that the orientation of the liquid components is parallel to the surface. The state in which the liquid orientation is parallel throughout the film and the film does not flow is a stationary state that satisfies the equations of active gel theory. However, if the film thickness is greater than a critical thickness, this stationary state is unstable. The stable state is one in which the orientation varies across the film thickness and the film flows with a velocity field parallel to the surfaces. The critical film thickness lc is inversely proportional to the square root of the active stress. This transition is analogous to the Fréedericksz transition of a passive nematic liquid film in an external electric or magnetic field, but in this problem there is no external field, and it is the active (internal) stress that plays the role of the external field.
Although we predicted this transition some ten years ago with J. Prost and Raphael Voituriez, it has only recently been observed by Pascal Silberzan's team at the Curie Institute. This team studied bands of elongated cells with a nematic order and observed, for fairly large bands, the appearance of spontaneous cell shear flow. This flow is well described by the theory of active gels.
A calculation quite similar to that for nematic film instability shows that the no-flow quiescent state of a macroscopic-sized active nematic liquid is not stable, and spontaneous flow occurs. All perturbations with wavelengths greater than the critical length lc are unstable.
