Velocity and Concentration Boundary Layers on Spinning Fibers

Abstract

In this paper a mathematical model for the viscose wet spinning process is presented: We consider a single fibre, which is produced by pressing a basic solution of viscose into a bath containing sulphuric acid. H 2 SO 4 diffuses into the viscose solution and reacts with the natrium hydroxide so that a solidifying fibre is formed which is pulled through the bath by drives. Due to the movement of the fibre and of diffusive transport of sulphuric acid into the fibre velocity and concentration boundary layers develop. Starting from the laminar boundary layer equations we investigate the flow and concentration fields in the bath induced by the fibre utilizing the Local Non-Similarity method. Mass transfer in the fibre is modelled by transport equations for sulphuric acid and natrium hydroxide taking into account the neutralization reaction. The model of the fibre is coupled to the bath phase model by appropriate boundary conditions for the mass flow density and the chemical potential of sulphuric acid. The non-constant diameter of the fibre is taken into account by a perturbation approach.