A local collocation method with radial basis functions for an electrospinning problem

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.