Setup of Viscous Cosserat Rod Model Describing Electrospinning

Abstract

Electrospinning is commonly used to produce very fine polymeric fibers. In this technique, a conducting liquid is pumped from an electrified needle into a surrounding dielectric media and the meniscus formed exhibits a conical shape, known as Taylor cone, due to the balance of electrical and surface tension forces. If the needle electrical potential is sufficiently high, the very strong electric field generated at the cone apex cannot be balanced by surface tension and a very thin jet is issued which eventually develops lateral instabilities that are responsible of additional stretching. In this work, we use a theoretical model that describes the kinematic of the midline of the jet, its radius and convective velocity from an Eulerian framework. Balances of mass, linear and angular momentum applied to a slice of the jet, as well as viscous law for stretching, bending and torsion describe the dynamics (nonlinear PDE in time and arclength of the midline). Capillary and electric forces are included in the momentum balance. If periodic orbits are explored, the time dependence of the PDE disappears when the motion is considered with respect to a frame rotating with the jet. One obtains a boundary value problem of ODEs with the frequency as a free parameter. This model is also suitable for describing other kinds of instabilities, such as the axisymmetric one which takes place in drop formation (dripping regime, electrospray).