Statics and dynamics of liquid barrels in wedge geometries

摘要

We present a theoretical study of the statics and dynamics of a partiallywetting liquid droplet, of equilibrium contact angle $\theta_{\rm e}$, confinedin a solid wedge geometry of opening angle $\beta$. We focus on a mostlynon-wetting regime, given by the condition $\theta_{\rm e} - \beta > 90^\circ$,where the droplet forms a liquid barrel -- a closed shape of positive meancurvature. Using a quasi-equilibrium assumption for the shape of the liquid-gasinterface, we compute the surface energy landscapes experienced by the liquidupon translations along the symmetry plane of the wedge. Close to equilibrium,our model is in good agreement with numerical calculations of the surfaceenergy minimisation subject to a constrained position of the centre of mass ofthe liquid. Beyond the statics, we put forward a Lagrangian description for the dropletdynamics. We focus on the the over-damped limit, where the driving capillaryforce is balanced by the frictional forces arising from the bulk hydrodynamics,the corner flow near the contact lines and the contact line friction. Ourresults provide a theoretical framework to describe the motion of partiallywetting liquids in confinement, and can be used to gain further understandingon the relative importance of dissipative processes that span from microscopicto macroscopic length scales.