Mathematical modeling of a whipping instability of an electrically charged liquid jet

Recent experiments have demonstrated that a fundamental mechanism of the electrospinning process is the rapid whipping of an electrically charged liquid jet. This article focuses on the mathematical modeling of such a whipping, also called a bending, instability of the electrically charged liquid jet, which is created from a polymer solution by electrospinning. The ideal rectilinear segment of the electrically charged jet, the so-called “viscoelastic dumbbell”, is a key attribute of the mathematical model presented herein. We have formulated governing equations which can be used to describe the physical properties and dynamics of this segment in a three-dimensional Cartesian coordinate system. We developed a multi-threaded computer application that allows us to simulate the electrospinning process. This application is the algorithmization of a numerical discretization. Using three-dimensional computer graphics we are able to visualize the results of the computer simulations of paths of the jet as well as the depositions of electrospun nanofiber. These theoretical results are in agreement with previously published laboratory experiments.