Self-propelled running droplets on solid substrates driven by chemical reactions

We study chemically driven running droplets on a partially wetting solid substrate by means of coupled evolution equations for the thickness profile of the droplets and the density profile of an adsorbate layer. Two models are introduced corresponding to two qualitatively different types of experiments described in the literature. In both cases an adsorption or desorption reaction underneath the droplets induces a wettability gradient on the substrate and provides the driving force for droplet motion. The difference lies in the behavior of the substrate behind the droplet. In case I the substrate is irreversibly changed whereas in case II it recovers allowing for a periodic droplet movement (as long as the overall system stays far away from equilibrium). Both models allow for a non-saturated and a saturated regime of droplet movement depending on the ratio of the viscous and reactive time scales. In contrast to model I, model II allows for sitting drops at high reaction rate and zero diffusion along the substrate. The transition from running to sitting drops in model II occurs via a super- or subcritical drift-pitchfork bifurcation and may be strongly hysteretic implying a coexistence region of running and sitting drops.