Droplet

A droplet is a bounded amount of liquid surrounded by another phase, such as a gas or an immiscible liquid. Its interface carries surface energy. For a free droplet at fixed volume with uniform positive surface tension, reducing surface area lowers this contribution to the free energy; when other effects are negligible, the equilibrium shape is a sphere. This is the physical setting behind the isoperimetric inequality.

For a spherical droplet of radius $R$ and constant surface tension $\gamma$, write $F_s=4\pi \gamma R^2$ and $V=4\pi R^3/3$. Quasistatic expansion against the pressure difference givesThis is the spherical Young–Laplace equation: the pressure inside exceeds the outside pressure. An illustrative $\gamma =0.072\mathrm{N}{\mathrm{m}}^{-1}$ gives $\Delta p=144\mathrm{Pa}$ at $R=1\mathrm{mm}$, and twice that pressure difference at half the radius.

Real surface tension depends on material and temperature; the IAPWS release, for example, tabulates measured water values and supplies an interpolation formula.^[ref] Gravity, contact with a solid and motion can deform a droplet, so the spherical calculation states a regime rather than defining every possible droplet shape.