  The experimental observation of D. Duft, T. Achtzehn, R. Muller, B. A. Huber,
and T. Leisner, Nature 421, 128 (2003) on the sequential progression of the
instability of a charged liquid drop points at the formation of a jet followed
by the emission of progeny droplets as a crucial pathway of the Rayleigh
fission process. In spite of considerable theoretical progress, a quantitative
understanding of this breakup pathway through mathematical models has largely
remained inconclusive. This limitation has mainly been due to the fact that the
generally applied electrostatic boundary condition of the equipotential surface
may not be valid near conical ends that experience a singularly fast dynamics
near the point of fission. Considering this, we address the problem by invoking
the surface charge dynamics within the framework of an axisymmetric boundary
element method (BEM), in the viscous limit. The abandonment of the
equipotential assumption gives rise to weak tangential electric stresses which
turn out to be key the contributors to the emergence of a jet followed by
formation of a progeny droplet. The simulations further predict that the size
of the progeny droplet follows an inverse power-law scaling relationship with
the conductivity of the liquid drop and the smaller sized progenies carry a
charge close to its Rayleigh limit.
