A Mathematical Approach to Nonlinear Travelling Waves on Polymeric Jets during Centrifugal Spinning

Centrifugal jet spinning is a novel method that is used to produce nanofibers. In this paper, theoretical and numerical study of the behavior of polymeric liquid jets during centrifugal spinning is investigated. The nonlinear instability of polymeric liquid jets is examined in the presence of centrifugal forces, gravity and surface tension. In addition, an asymptotic analysis and perturbation theory are applied for this polymeric jets during centrifugal spinning to simplify the governing equations into a set of one-dimensional equations. Then, the trajectory of non-Newtonian liquid jets during the centrifugal spinning has been determined. Furthermore, the two-step Lax-Wendroff method is used to determine the nonlinear travelling waves along the polymeric jets. Our results also show that when the rotation rate and gravitational force are high, shear thickening has more break-up lengths than shear thinning jets