Different buckling regimes in direct electrospinning: A comparative approach to rope buckling

Understanding the dynamics of direct electrospinning is the key to control fiber morphologies that are critical for the development of new electrospinning methods and novel materials. Here, we propose the theory for direct electrospinning based on theories for (liquid) "rope coiling" and experimentally test it. For the experiments, the buckling of microscale liquid ropes formed from polymer solutions is studied systematically using three different electrospinning setups and for different polymer concentrations. We show that different buckling regimes exist, whose dynamics are governed by an interplay of electrical, inertial, and viscous forces, and that three different buckling regimes emerge depending on the dominant forces. For low polymer concentrations, we observe an inertial regime similar to that observed for viscous liquid ropes at high velocities. By increasing the polymer concentration and consequently decreasing the rope velocity, we enter an inertial-electrical regime for which discontinuities occur in the buckling frequency as a function of applied voltage. These observations can be accounted for quantitatively by replacing the gravitational forces in viscous rope coiling theory with the electrical forces of our electrospinning experiment. Finally, for the highest polymer concentration, we observe a purely electrical regime for a solidified rope; this regime is well described by "elastic" rope coiling theory.