Evidence of stretching/moving sheet-triggered nonlinear similarity flows: atomization and electrospinning with/without air resistance

Purpose The purpose of this study is two-fold. First, it aims to differentiate the response of a stretching jet encountering a quadratic air resistance from the classical jet shape formed in a frictionless medium. Second, it investigates how the resulting jet forms with and without air resistance, seeking evidence that supports the similarity flows frequently studied for stretching/moving thin bodies under the boundary layer approximation. Design/methodology/approach This study extends the established electrohydrodynamic stretching jet theory, used to model electrospinning or jet printing in the absence of air resistance, to encompass the impact of the retarding force on the jet stretching in both the cone and final regimes before it impinges on a substrate. Findings A close examination of the nonlinear governing equations reveals that the jet rapidly thins near the nozzle because of the combined action of viscous and electrical forces. In this region, the exponentially decaying jet receives further support from the air resistance, resulting in a closer alignment with the observed experimental jet. This exponential decay, accelerated by the inversely quadratic speed of the liquid particles, serves as clear evidence for the existence of a similarity flow over an exponentially stretching sheet. Furthermore, in the final regime, the jet stretching exhibits an algebraic decay in the absence of air friction, while with air resistance, it decays exponentially to reach a limiting speed. In the former case, a square root dependence of the stretching jet speed leads to the emergence of a similarity flow over a thin stretching jet, while in the latter case, a Sakiadis’ similarity flow appears over a continuously moving flat surface. Practical implications The analysis goes beyond jet hydrodynamics, delving into the interplay of electrostatic forces (including Coulomb’s law) and quadratic air drag, drawing upon experimental data on glycerol liquid presented in earlier publications. Originality/value Finally, the asymptotic behavior of the stretching jet under the combined influence of electrostatic pull and its electric currents because of bulk conduction and surface convection is validated through a comprehensive numerical simulation of the nonlinear system.