  We present a solvable model inspired by dimensional analysis for the
time-dependent spreading of droplets that partially wet a substrate, where the
spreading eventually stops and the contact angle reaches a nonzero equilibrium
value. We separately consider small droplets driven by capillarity and large
droplets driven by gravity. To explore both regimes, we first measure the
equilibrium radius versus a comprehensive range of droplet volumes for four
household fluids, and we compare the results with predictions based on
minimizing the sum of gravitational and interfacial energies. The agreement is
good, and gives a reliable measurement of an equilibrium contact angle that is
consistent in both small and large droplet regimes. Next we use energy
considerations to develop equations of motion for the time dependence of the
spreading, in both regimes, where the driving forces are balanced against
viscous drag in the bulk of the droplet and by friction at the moving contact
line. Our approach leads to explicit prediction of the functional form of the
spreading dynamics. It successfully describes prior data for a small
capillary-driven droplet, and it fits well to new data we obtain for large
gravity-driven droplets with a wide range of volumes.
