  A basic feature of liquid drops is that they can merge upon contact to form a
larger drop. In spite of its importance to various applications, drop
coalescence on pre-wetted substrates has received little attention. Here, we
experimentally and theoretically reveal the dynamics of drop coalescence on a
thick layer of a low-viscosity liquid. It is shown that these so-called "liquid
lenses" merge by the self-similar vertical growth of a bridge connecting the
two lenses. Using a slender analysis, we derive similarity solutions
corresponding to the viscous and inertial limits. Excellent agreement is found
with the experiments without any adjustable parameters, capturing both the
spatial and temporal structure of the flow during coalescence. Finally, we
consider the crossover between the two regimes and show that all data of
different lens viscosities collapse on a single curve capturing the full range
of the coalescence dynamics.
