Symmetry-breaking and motion of active drops through polarization-surface coupling

Drops of active liquids are often considered as a simple realization of living cells adhering to a solid substrate. Here we present a model for shallow three-dimensional (3D) active free-surface drops with a mean polar order parallel to the substrate and a polarization-surface (PS) coupling. This allows us to identify a mechanism of motility in which active stresses drive drop motion through spatial variations of polarization strength. It induces motility even for liquid ridges (2D drops), in contrast to reported mechanisms based on splay and bend configurations. Resulting states include symmetric and asymmetric resting drops, motile drops and unstable drops that undergo splitting. The newly identified motility mode originates from a competition between the elastic bulk energy and the orientational control exerted by the drop surface and breaks parity-symmetry already for passive drops. This back-forth asymmetry enables active stresses to effectively pump liquid and drop motion ensues.