  This letter presents a theory on the coalescence of two spherical liquid
droplets that are initially stationary. The evolution of the radius of a liquid
neck formed upon coalescence was formulated as an initial value problem and
then solved to yield an exact solution without free parameters, with its two
asymptotic approximations reproducing the well-known scaling relations in the
viscous and inertial regimes. The viscous-to-inertial crossover observed by
Paulsen et al. [Phys. Rev. Lett. 106, 114501 (2011)] is also recovered by the
theory, rendering the collapse of data of different viscosities onto a single
curve.
