A cylindrical jet of incompressible liquid (viscous or inviscid)
that supports surface tension, is unstable to linear perturbations
and eventually breaks up into droplets. This talk is concerned
with the nonlinear aspects of this phenomenon and in particular
with the breakup event. The time scale of the phenomenon is very
short and has posed a challenge to theoreticians and experimentalists
alike. I will describe some of the asymptotic theory behind these
efforts and make comparisons with experiments. In the second half
of the talk, additional physical effects will be added and nonlinear
theories combining asymptotics and computations will be presented.
The added effects will include surfactants at a liquid/air interface,
the presence of a surrounding viscous liquid and the imposition
of axial electric fields. The latter is a promising mechanism in
microfluidic applications, some of which will be mentioned.
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