The study of singularities in free surface flows remains a subject of considerably
interest. Regarding droplet dynamics the pinch-off events and merging of droplets
have been extensively studied due its enormous interest in industrial applications. The
level set techniques allows to embed the partial differential equations posed on a free
boundary into one higher dimension equations posed on a fixed domain, in such a way that
the classical potential flow model can be re-formulated in a complete Eulerian frame work,
with the advantage that free boundary topological changes are automatically included.
The Laplace equation for the velocity potential is solved via its integral formulation and
a boundary element approximation, whereas the evolution of the level set function and
extended velocity potential function is approximated using first order finite differences
schemes. Merging and splitting events are therefore computationally possible. In the case
of two equal drops coalescing, initial instants are very difficult to compute and also to
see experimentally. After initial contact a liquid bridge connecting the two drops grows
on time and a capillary wave, generated at the point of contact, propagates towards the
drop end points. Numerical results regarding two droplet coalescence are presented and a
detail discussion of the main flow characteristics is addressed. Comparison with previous
computations and laboratory experiments will be also included.
