Electrospinning is a technique used to fabricate fibrillar materials for different applications. Understanding this process allows companies to reduce efforts and to have better control of the variables present in this phenomenon. A mathematical model is described in this article for Newtonian, Giesekus, FENE-P, and Oldroyd-B approaches. This was done by using radial basis functions through a localized collocation method that has not been used before to solve this kind of problems. The solutions of the viscoelastic and electric behavior were compared with a Python solver and with a previously obtained solution by other researchers. The rheological models, showed that they can be applied according to the size of fluid polymer chains. Thus, the Giesekus model rheologically describes more accurately fluids with small polymer chains, the FENE-P model describes larger polymer chains with low extensibility, and Oldroyd-B model describes same particles as FENE-P but with infinite extensibility. An interesting case of coil-stretching was obtained using the FENE-P model where the fluid becomes Newtonian while the relaxation time increases. In conclusion, The results show that by decreasing the tensile force in the jet, thinner fibers can be obtained and this can be controlled experimentally by using polymers with low molecular weight.

静电纺丝是一种用于制造用于不同应用的原纤维材料的技术。了解这个过程可以让公司减少努力并更好地控制这种现象中存在的变量。本文描述了牛顿法、Giesekus、FENE-P 和 Oldroyd-B 方法的数学模型。这是通过使用径向基函数通过局部搭配方法来完成的，这种方法以前从未用于解决此类问题。粘弹性和电行为的解决方案与 Python 求解器和其他研究人员先前获得的解决方案进行了比较。流变模型表明它们可以根据流体聚合物链的大小应用。因此，Giesekus 模型更准确地描述了具有小聚合物链的流体，FENE-P 模型描述了具有低延伸性的较大聚合物链，而 Oldroyd-B 模型描述了与 FENE-P 相同但具有无限延伸性的粒子。使用 FENE-P 模型获得了一个有趣的线圈拉伸案例，其中流体变为牛顿流体，同时弛豫时间增加。总之，结果表明，通过降低射流中的张力，可以获得更细的纤维，这可以通过使用低分子量聚合物进行实验控制。