  Fluid flows hosting electrical phenomena make the subject of a fascinating
and highly interdisciplinary scientific field. In recent years, the
extraordinary success of electrospinning and solution blowing technologies for
the generation of polymer nanofibers has motivated vibrant research aiming at
rationalizing the behavior of viscoelastic jets under applied electric fields
or other stretching fields including gas streams. Theoretical models unveiled
many original aspects in the underpinning physics of polymer solutions in jets,
and provided useful information to improve experimental platforms. This article
reviews advances in the theoretical description and numerical simulation of
polymer solution jets in electrospinning and solution blowing. Instability
phenomena of electrical and hydrodynamic origin are highlighted, which play a
crucial role in the relevant flow physics. Specifications leading to accurate
and computationally viable models are formulated. Electrohydrodynamic modeling,
theories for the jet bending instability, recent advances in Lagrangian
approaches to describe the jet flow, including strategies for dynamic
refinement of simulations, and effects of strong elongational flow on polymer
networks are reviewed. Finally, the current challenges and future perspectives
of the field are outlined and discussed, including the task of correlating the
physics of the jet flows with the properties of realized materials, as well as
the development of multiscale techniques for modelling viscoelastic jets.
