An inverse-square force between evaporating sessile droplets

In this study, we present the discovery of an inverse-square force between evaporating sessile droplets. We find that one evaporating sessile droplet exerts a driving force on another, with the magnitude of the force decaying inversely proportional to the square of distance between their centres. The inverse-distance decay of the vapour concentration generated by the source droplet is a key ingredient leading to the inverse-square form of the force. A theoretical framework combining continuum hydrodynamics with an effective capillary line-force representation is developed to rationalize this force. The inverse-square form is robust over ranges of droplet size, composition and ambient humidity. Its broader applicability is further supported by our analysis of previously published kinematic data for pure-liquid sessile droplets and thermocapillary floating droplets.