Thin-film modeling of resting and moving active droplets

Trinschek, Sarah; Stegemerten, Fenna; John, K.; Thiele; Uwe;

Abstract

We propose a generic model for thin films and shallow drops of a polar active liquid that have a free surfaceand are in contact with a solid substrate. The model couples evolution equations for the film height and the localpolarization in the form of a gradient dynamics supplemented with active stresses and fluxes. A wetting energyfor a partially wetting liquid is incorporated allowing for motion of the liquid-solid-gas contact line. This givesa consistent basis for the description of drops of dense bacterial suspensions or compact aggregates of livingcells on solid substrates. As example, we analyze the dynamics of two-dimensional active drops (i.e., ridges)and demonstrate how active forces compete with passive surface forces to shape droplets and drive their motion.In our simple two-dimensional scenario we find that defect structures within the polarization profile drasticallyinfluence the shape and motility of active droplets. Thus, we can observe a transition from resting to motiledroplets via the elimination of defects in the polarization profile. Furthermore, droplet motility is modulated bystrong active stresses. Contractile stresses even lead to topological changes, i.e., drop splitting, which is naturallyencoded in the evolution equations.