%0 Journal Article
%T A Confirmed Model to Polymer Core-Shell Structured Nanofibers Deposited via Coaxial Electrospinning
%A K. Boubaker
%J ISRN Polymer Science
%D 2012
%R 10.5402/2012/603108
%X A model to core-shell structured polymer nanofibers deposited via coaxial electrospinning is presented. Investigations are based on a modified Jacobi-Gauss collocation spectral method, proposed along with the Boubaker Polynomials Expansion Scheme (BPES), for providing solution to a nonlinear Lane-Emden-type equation. The spatial approximation has been based on shifted Jacobi polynomials with was n the polynomial degree. The Boubaker Polynomials Expansion Scheme (BPES) main features, concerning the embedded boundary conditions, have been outlined. The modified Jacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the technique, and a comparison is made with existing results. It has been revealed that both methods are easy to implement and yield very accurate results. 1. Introduction Polymer nanofibers have gained much attention due to their great potential applications, such as filtration, catalysis, scaffolds for tissue engineering, protective clothing, sensors, electrodes electronics applications, reinforcement, and biomedical use [1¨C6]. Particularly, polymeric nanofibers with core-shell structure have been attractive in the past decades [4, 5]. Coaxial electrospinning, which has emerged as a method of choice due to the simplicity of the technology and its cost effectiveness, provides an effective and versatile way to fabricate such nanofibers [6¨C8]. This technique uses a high electric field to extract a liquid jet of polymer solution from the bot core and shell reservoirs. The yielded jet experiences stretching and bending effects due to charge repulsion and, in the process, can reach very small radii. Coaxial electrospinning cannot only be used to spin the unspinnable polymers (polyaramid, nylon, and polyaniline) into ultrafine fibers, but also ensures keeping functionalizing agents like antibacterial and biomolecules agents inside nanofibers [9¨C11]. In this paper, a mathematical model to coaxial electrospinning dynamics, in a particular setup, is presented. The model is based on solutions to the related Lane-Emden equation on semi-infinite domains as follows: Lane-Emden-type equations model many phenomena in mathematical physics and nanoapplications. They were first published by Lane in 1870 [12], and further explored in detail by Emden [13]. In the last decades, Lane-Emden has been used to model several phenomena such as the theory of stellar structure, quantum mechanics, astrophysics, and the theory of thermionic currents in the neighbourhood of a hot body in thermal
%U http://www.hindawi.com/journals/isrn.polymer.science/2012/603108/