Modeling and simulation of curved fibers in dry spinning scenarios

Abstract

Dry spinning is characterized by the simultaneous production of multiple thin polymeric fibers in airflows and the evaporation of the solvent contained in these fibers. This involves fiber-air interactions as well as radial diffusion effects over the fiber cross-sections. Recent models for fibers in such production processes assume the fiber curves to be strictly uni-axial. But there are industrial setups showing airflow induced lateral movements of the fibers which creates the need for curved fiber models. In this paper we present a special Cosserat rod model that describes curved fibers in such dry spinning processes. Adapting the efficient simulation framework from the uni-axial fiber setting makes the simulation of industrial setups for multiple curved fibers with two-way coupled airflows possible, for which we present results for the first time in literature. Keywords: Dry spinning, Fiber dynamics, Parametric boundary value problem, Homotopy method, Heat and mass transfer, Integral equations