The dynamics of fattening and thinning 2D sessile droplets

We investigate the dynamics of a droplet on a planar substrate as the droplet volume changes dynamically due to liquid being pumped in or out through a pore. We adopt a diffuse-interface formulation which is appropriately modified to account for a localized inflow-outflow boundary condition (the pore) at the bottom of the droplet, hence allowing to dynamically control its volume, as the droplet moves on a flat substrate with a periodic chemical pattern. We find that the droplet undergoes a stick-slip 1 motion as the volume is increased (fattening droplet) which can be monitored by tracking the droplet contact points. If we then switch over to outflow conditions (thinning droplet) the droplet follows a different path (i.e. the distance of the droplet midpoint from the pore location evolves differently) giving rise to a hysteretic behavior. By means of geometrical arguments we are able to theoretically construct the full bifurcation diagram of the droplet equilibria (positions and droplet shapes) as the droplet volume is changed, finding excellent agreement with time-dependent computations of our diffuse-interface model.