Three dimensional force balance of asymmetric droplets*

An equilibrium contact angle of a droplet is determined by a horizontal force balance among vapor, liquid, and solid, which is known as Young's law. Conventional wetting law is valid only for axis-symmetric droplets, whereas real droplets are often asymmetric. Here we show that three-dimensional geometry must be considered for a force balance for asymmetric droplets. By visualizing asymmetric droplets placed on a free-standing membrane in air with X-ray microscopy, we are able to identify that force balances in one side and in other side control pinning behaviors during evaporation of droplets. We find that X-ray microscopy is powerful for realizing the three-dimensional force balance, which would be essential in interpretation and manipulation of wetting, spreading, and drying dynamics for asymmetric droplets.