In electrospinning, an applied electric field accelerates and drastically elongates a charged fluid jet to produce nanoscale fibers. Traditionally, the fluids used in the process have been polymer solutions but recently the method has been extended to polymer melts. The new solvent-free approach is environmentally benign, eliminates the solvent recovery and treatment costs, and can be applied to a wider selection of polymers, including polyethylene (PE), polypropylene (PP), and polyethylene teraphthalate (PET). However, the resulting fibers are typically thicker than those produced from solutions due to the absence of additional reduction in mass by solvent evaporation. Hence, melt electrospinning requires more careful process control and optimization, and such a task can be efficiently accomplished by rigorous numerical modeling.

In the present study, we formulate the governing equations for non-isothermal free surface flows of electrically charged viscoelastic fluids in the stable jet region. The model is based on thin filament approximation applied to fully coupled momentum, continuity, and energy equations, Gauss' law, and the non-isothermal Giesekus constitutive model. In addition to standard boundary conditions, we have developed a new asymptotic jet thinning relationship for polymer melts, which typically exhibit high viscosity and viscoelasticity, particularly under non-isothermal conditions. The resulting system of equations is solved numerically and the simulated initial jet profiles are compared to digitized experimental images of the stable melt jet near the spinneret. In addition, the predicted effect of melt temperature, viscoelasticity, and electric field strength on the final jet diameter is compared to the final fiber thickness from non-isothermal experiments where the whipping motion has been suppressed by rapid cooling. The simulation results are in good agreement with the flow visualization experiments on electrospinning of polylactic acid (PLA) under various spinning conditions.