Electrospinning is the most widely used production method for polymer fibers formed from an electrified fluid jet. This method is very versatile, relatively inexpensive and simple. When the sufficiently high electric potential (about 20kV) is applied to the polymer solution, the electrostatic forces overcome the surface tension of the polymer and a thin liquid jet is ejected from the nozzle. However, after short straight distance of the motion of the fiber it rapidly grows into an electric charge driven bending instability and results in a 3D spiraling trajectory leading to a very random deposition on the grounded collector. This significantly reduces the positive qualities of the fiber and its use in biomechanical engineering like a production of tissue scaffolds mimicking the structure of the extracellular matrix or a delivery of expandable chemo- and radio-therapeutic stents. In this work we present the initial results from investigating the feasibility of using dynamic focusing of the electrified jet in a linear quadrupole trap. This is a new alternative to the more generally used mechanical approach with rotating mandrel, could in principle lead to the ability to control the deposition location without the use of any moving components. The proposed approach was originally developed for trapping and transporting individual charged ions. In contrast to ions, an electrified continuous fiber represents an infinite degree of freedom system, with potentially much richer dynamics and unknown stability regions in the parameter space.

In order to understand the dynamics of the fiber, we present a discretized 2D reduced-order mathematical model which is investigated numerically. The resulting ODEs represent multi-dimensional form of a non-linear Mathieu’s and Meissner’s differential equations for harmonic, and step excitation functions, respectively. The model parameters were obtained from static experiments with electrodes compressing the fibers in a single plane. Finite-element model of the electrodes resulted in detailed potential maps, which were used to develop estimates of the required strength of the electrostatic field needed to steer the fibers.

The estimated parameters were used to obtain stable solutions of the reduced-order approximate of a spring-mass-charged dumbbell model of the fiber.

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