Sessile Liquid Droplets Can Achieve Equilibrium with Surrounding Atmosphere in the Presence of Gravity

The equilibrium between a sessile liquid droplet and its environment under gravity hold both theoretical significance and practical implications. However, debates regarding the existence of such equilibrium have persisted for decades. Here, the effects of gravity on liquid-gas systems are first analyzed, and the results show that the gravitational influence need not be included in the Kelvin equation. Then, by considering the changes in both the atmospheric pressure and the liquid surface curvature, a generalized Kelvin equation is derived. Using this generalized Kelvin equation rather than the simplified classical form, we show that sessile liquid droplets resting on a flat, horizontal solid surface can indeed achieve full equilibrium with their atmosphere even in the presence of gravity.