  The interface formation model is applied to describe the initial stages of
the coalescence of two liquid drops in the presence of a viscous ambient fluid
whose dynamics is fully accounted for. Our focus is on understanding (a) how
this model's predictions differ from those of the conventionally used one, (b)
what influence the ambient fluid has on the evolution of the shape of the
coalescing drops and (c) the coupling of the intrinsic dynamics of coalescence
and that of the ambient fluid. The key feature of the interface formation model
in its application to the coalescence phenomenon is that it removes the
singularity inherent in the conventional model at the onset of coalescence and
describes the part of the free surface `trapped' between the coalescing volumes
as they are pressed against each other as a rapidly disappearing `internal
interface'. Considering the simplest possible formulation of this model, we
find experimentally-verifiable differences with the predictions of the
conventional model showing, in particular, the effect of drop size on the
coalescence process. According to the new model, for small drops a non-monotone
time-dependence of the bridge expansion speed is a feature that could be looked
for in further experimental studies. Finally, the results of both models are
compared to recently available experimental data on the evolution of the liquid
bridge connecting the coalescing drops, and the interface formation model is
seen to give a better agreement with the data.
